%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 03:48:23 EDT 2022 % Result : Theorem 21.08s 6.38s % Output : Proof 35.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0. % 0.08/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n029.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jun 17 15:42:58 EDT 2022 % 0.13/0.35 % CPUTime : % 0.66/0.63 ____ _ % 0.66/0.63 ___ / __ \_____(_)___ ________ __________ % 0.66/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.66/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.66/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.66/0.63 % 0.66/0.63 A Theorem Prover for First-Order Logic % 0.66/0.63 (ePrincess v.1.0) % 0.66/0.63 % 0.66/0.63 (c) Philipp Rümmer, 2009-2015 % 0.66/0.63 (c) Peter Backeman, 2014-2015 % 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.66/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.66/0.63 Bug reports to peter@backeman.se % 0.66/0.63 % 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.66/0.63 % 0.67/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.84/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.91/1.02 Prover 0: Preprocessing ... % 2.62/1.25 Prover 0: Warning: ignoring some quantifiers % 2.62/1.28 Prover 0: Constructing countermodel ... % 18.25/5.76 Prover 0: gave up % 18.25/5.76 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 18.25/5.80 Prover 1: Preprocessing ... % 19.11/5.92 Prover 1: Constructing countermodel ... % 19.11/5.96 Prover 1: gave up % 19.11/5.96 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 19.61/6.00 Prover 2: Preprocessing ... % 20.10/6.15 Prover 2: Warning: ignoring some quantifiers % 20.10/6.16 Prover 2: Constructing countermodel ... % 21.08/6.38 Prover 2: proved (420ms) % 21.08/6.38 % 21.08/6.38 No countermodel exists, formula is valid % 21.08/6.38 % SZS status Theorem for theBenchmark % 21.08/6.38 % 21.08/6.38 Generating proof ... Warning: ignoring some quantifiers % 33.75/9.76 found it (size 564) % 33.75/9.76 % 33.75/9.76 % SZS output start Proof for theBenchmark % 33.75/9.76 Assumed formulas after preprocessing and simplification: % 33.75/9.76 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v0, v3) = 0 & incident_point_and_line(v0, v2) = 0 & equal_points(v0, v4) = v5 & intersection_point(v2, v3) = v4 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ? [v11] : ((v11 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v6, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v7) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v8) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_lines(v9, v8) = v7) | ~ (orthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (incident_point_and_line(v9, v8) = v7) | ~ (incident_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_lines(v9, v8) = v7) | ~ (parallel_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_lines(v9, v8) = v7) | ~ (equal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_points(v9, v8) = v7) | ~ (equal_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (orthogonal_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (incident_point_and_line(v6, v7) = v8) | apart_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (parallel_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_lines(v6, v7) = v8) | distinct_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_points(v6, v7) = v8) | distinct_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | orthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v6, v7) = v8) | incident_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | parallel_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | equal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | equal_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (point(v8) = v7) | ~ (point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (line(v8) = v7) | ~ (line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & point(v8) = 0) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & point(v6) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (orthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (incident_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (parallel_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & orthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & incident_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & point(v8) = 0 & intersection_point(v6, v7) = v8) | ( ~ (v8 = 0) & line(v7) = v8) | ( ~ (v8 = 0) & line(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & parallel_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & line(v8) = 0 & line_connecting(v6, v7) = v8) | ( ~ (v8 = 0) & point(v7) = v8) | ( ~ (v8 = 0) & point(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_points(v6, v7) = v8)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : orthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : incident_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_points(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : orthogonal_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unorthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8 & ? [v6] : ? [v7] : point(v6) = v7 & ? [v6] : ? [v7] : line(v6) = v7) % 34.17/9.86 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 34.17/9.86 | (1) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_5_5, all_0_2_2) = 0 & incident_point_and_line(all_0_5_5, all_0_3_3) = 0 & equal_points(all_0_5_5, all_0_1_1) = all_0_0_0 & intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1 & convergent_lines(all_0_3_3, all_0_2_2) = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 % 34.17/9.90 | % 34.17/9.90 | Applying alpha-rule on (1) yields: % 34.17/9.90 | (2) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 % 34.17/9.90 | (3) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) % 34.17/9.90 | (4) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 34.17/9.90 | (5) ! [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))) % 34.17/9.90 | (6) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 34.17/9.90 | (7) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 34.17/9.90 | (8) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 34.17/9.90 | (9) ! [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))) % 34.17/9.90 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 34.17/9.90 | (11) ! [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))) % 34.17/9.90 | (12) incident_point_and_line(all_0_5_5, all_0_3_3) = 0 % 34.17/9.90 | (13) ! [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))) % 34.17/9.90 | (14) ! [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)) % 34.17/9.90 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) % 34.17/9.90 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 34.17/9.90 | (17) ! [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))) % 34.17/9.90 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 34.17/9.90 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 34.17/9.90 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 34.17/9.90 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) % 34.17/9.91 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 34.17/9.91 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 34.17/9.91 | (24) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 34.17/9.91 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 34.17/9.91 | (26) equal_points(all_0_5_5, all_0_1_1) = all_0_0_0 % 34.17/9.91 | (27) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 34.17/9.91 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 34.17/9.91 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 34.17/9.91 | (30) ! [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))) % 34.17/9.91 | (31) ! [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))) % 34.17/9.91 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 34.17/9.91 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 34.17/9.91 | (34) intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1 % 34.17/9.91 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) % 34.17/9.91 | (36) ! [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))) % 34.17/9.91 | (37) ! [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))) % 34.17/9.91 | (38) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 34.17/9.91 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 34.17/9.91 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 34.17/9.91 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) % 34.17/9.91 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 34.17/9.91 | (43) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 34.17/9.91 | (44) ! [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))) % 34.17/9.91 | (45) ! [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))) % 34.17/9.91 | (46) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 % 34.17/9.91 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 34.17/9.91 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 34.17/9.91 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 34.17/9.91 | (50) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 34.17/9.91 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 34.17/9.91 | (52) ! [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))) % 34.72/9.91 | (53) ! [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)) % 34.72/9.92 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 34.72/9.92 | (55) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 % 34.72/9.92 | (56) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 34.72/9.92 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 34.72/9.92 | (58) ! [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))) % 34.72/9.92 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) % 34.72/9.92 | (60) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) % 34.72/9.92 | (61) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 34.72/9.92 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 34.72/9.92 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 34.72/9.92 | (64) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 % 34.72/9.92 | (65) ! [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) % 34.72/9.92 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 34.72/9.92 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 34.72/9.92 | (68) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) % 34.72/9.92 | (69) ? [v0] : ? [v1] : point(v0) = v1 % 34.72/9.92 | (70) ! [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))) % 34.72/9.92 | (71) ~ (all_0_0_0 = 0) % 34.72/9.92 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 34.72/9.92 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 34.72/9.92 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 34.72/9.92 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) % 34.72/9.92 | (76) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 34.72/9.92 | (77) ! [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)) % 34.72/9.92 | (78) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 34.72/9.92 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) % 34.72/9.92 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) % 34.72/9.92 | (81) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 34.72/9.92 | (82) ! [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))) % 34.72/9.92 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 34.72/9.92 | (84) ! [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))) % 34.72/9.92 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 34.72/9.92 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 34.72/9.92 | (87) ! [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) % 34.72/9.92 | (88) ! [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) % 34.72/9.92 | (89) ! [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))) % 34.72/9.93 | (90) ! [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))) % 34.72/9.93 | (91) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 34.72/9.93 | (92) ! [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))) % 34.72/9.93 | (93) ! [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)) % 34.72/9.93 | (94) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) % 34.72/9.93 | (95) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 % 34.72/9.93 | (96) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 % 34.72/9.93 | (97) ! [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))) % 34.72/9.93 | (98) ! [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))) % 34.72/9.93 | (99) ? [v0] : ? [v1] : line(v0) = v1 % 34.72/9.93 | (100) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 % 34.72/9.93 | (101) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 34.72/9.93 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) % 34.72/9.93 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 34.72/9.93 | (104) ! [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)) % 34.72/9.93 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 34.72/9.93 | (106) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) % 34.72/9.93 | (107) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 34.72/9.93 | (108) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 34.72/9.93 | (109) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 34.72/9.93 | (110) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 34.72/9.93 | (111) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 34.72/9.93 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 34.72/9.93 | (113) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) % 34.72/9.93 | (114) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 34.72/9.93 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 34.72/9.93 | (116) ! [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))) % 34.72/9.93 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 34.72/9.93 | (118) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 34.72/9.93 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 34.72/9.93 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 34.72/9.93 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 34.72/9.93 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 34.72/9.93 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 34.72/9.93 | (124) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 34.72/9.93 | (125) ! [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))) % 34.72/9.93 | (126) ! [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))) % 34.72/9.93 | (127) incident_point_and_line(all_0_5_5, all_0_2_2) = 0 % 34.72/9.93 | (128) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) % 34.72/9.93 | (129) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 34.72/9.93 | (130) distinct_points(all_0_5_5, all_0_4_4) = 0 % 34.72/9.93 | (131) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 34.72/9.93 | (132) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 34.72/9.93 | (133) ! [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))) % 34.72/9.93 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 34.72/9.93 | (135) ! [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))) % 34.72/9.94 | (136) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) % 34.72/9.94 | (137) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) % 34.72/9.94 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 34.72/9.94 | (139) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) % 34.72/9.94 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 34.72/9.94 | (141) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 34.72/9.94 | (142) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 34.72/9.94 | (143) ! [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) % 34.72/9.94 | (144) ! [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))) % 34.72/9.94 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 34.72/9.94 | (146) ! [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))) % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (7) with all_0_2_2, all_0_5_5 and discharging atoms incident_point_and_line(all_0_5_5, all_0_2_2) = 0, yields: % 34.72/9.94 | (147) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0) % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (7) with all_0_3_3, all_0_5_5 and discharging atoms incident_point_and_line(all_0_5_5, all_0_3_3) = 0, yields: % 34.72/9.94 | (148) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = v0) % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_5_5 and discharging atoms equal_points(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 34.72/9.94 | (149) all_0_0_0 = 0 | distinct_points(all_0_5_5, all_0_1_1) = 0 % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (83) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 34.72/9.94 | (150) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (32) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 34.72/9.94 | (151) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (132) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 34.72/9.94 | (152) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_2_2) = v0 & apart_point_and_line(v0, all_0_2_2) = v1) % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (118) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 34.72/9.94 | (153) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_2_2) = v0 & apart_point_and_line(v0, all_0_3_3) = v1) % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (56) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.94 | (154) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1) % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (78) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.94 | (155) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_5_5, v0) = v1) % 34.72/9.94 | % 34.72/9.94 | Instantiating (155) with all_42_0_53, all_42_1_54 yields: % 34.72/9.94 | (156) ~ (all_42_0_53 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_42_1_54 & apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53 % 34.72/9.94 | % 34.72/9.94 | Applying alpha-rule on (156) yields: % 34.72/9.94 | (157) ~ (all_42_0_53 = 0) % 34.72/9.94 | (158) line_connecting(all_0_5_5, all_0_4_4) = all_42_1_54 % 34.72/9.94 | (159) apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53 % 34.72/9.94 | % 34.72/9.94 | Instantiating (154) with all_49_0_62, all_49_1_63 yields: % 34.72/9.94 | (160) ~ (all_49_0_62 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_49_1_63 & apart_point_and_line(all_0_4_4, all_49_1_63) = all_49_0_62 % 34.72/9.94 | % 34.72/9.94 | Applying alpha-rule on (160) yields: % 34.72/9.94 | (161) ~ (all_49_0_62 = 0) % 34.72/9.94 | (162) line_connecting(all_0_5_5, all_0_4_4) = all_49_1_63 % 34.72/9.94 | (163) apart_point_and_line(all_0_4_4, all_49_1_63) = all_49_0_62 % 34.72/9.94 | % 34.72/9.94 | Instantiating (153) with all_51_0_64, all_51_1_65 yields: % 34.72/9.94 | (164) ~ (all_51_0_64 = 0) & intersection_point(all_0_3_3, all_0_2_2) = all_51_1_65 & apart_point_and_line(all_51_1_65, all_0_3_3) = all_51_0_64 % 34.72/9.94 | % 34.72/9.94 | Applying alpha-rule on (164) yields: % 34.72/9.94 | (165) ~ (all_51_0_64 = 0) % 34.72/9.94 | (166) intersection_point(all_0_3_3, all_0_2_2) = all_51_1_65 % 34.72/9.94 | (167) apart_point_and_line(all_51_1_65, all_0_3_3) = all_51_0_64 % 34.72/9.94 | % 34.72/9.94 | Instantiating (148) with all_56_0_70 yields: % 34.72/9.94 | (168) ~ (all_56_0_70 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70 % 34.72/9.94 | % 34.72/9.94 | Applying alpha-rule on (168) yields: % 34.72/9.94 | (169) ~ (all_56_0_70 = 0) % 34.72/9.94 | (170) apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70 % 34.72/9.94 | % 34.72/9.94 | Instantiating (151) with all_58_0_71 yields: % 34.72/9.94 | (171) ( ~ (all_58_0_71 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_71) | ( ~ (all_58_0_71 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_58_0_71) % 34.72/9.94 | % 34.72/9.94 | Instantiating (150) with all_59_0_72 yields: % 34.72/9.94 | (172) ( ~ (all_59_0_72 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72) | ( ~ (all_59_0_72 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_59_0_72) % 34.72/9.94 | % 34.72/9.94 | Instantiating (147) with all_60_0_73 yields: % 34.72/9.94 | (173) ~ (all_60_0_73 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73 % 34.72/9.94 | % 34.72/9.94 | Applying alpha-rule on (173) yields: % 34.72/9.94 | (174) ~ (all_60_0_73 = 0) % 34.72/9.94 | (175) apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73 % 34.72/9.94 | % 34.72/9.94 | Instantiating (152) with all_63_0_75, all_63_1_76 yields: % 34.72/9.94 | (176) ~ (all_63_0_75 = 0) & intersection_point(all_0_3_3, all_0_2_2) = all_63_1_76 & apart_point_and_line(all_63_1_76, all_0_2_2) = all_63_0_75 % 34.72/9.94 | % 34.72/9.94 | Applying alpha-rule on (176) yields: % 34.72/9.94 | (177) ~ (all_63_0_75 = 0) % 34.72/9.94 | (178) intersection_point(all_0_3_3, all_0_2_2) = all_63_1_76 % 34.72/9.94 | (179) apart_point_and_line(all_63_1_76, all_0_2_2) = all_63_0_75 % 34.72/9.94 | % 34.72/9.94 +-Applying beta-rule and splitting (149), into two cases. % 34.72/9.94 |-Branch one: % 34.72/9.94 | (180) distinct_points(all_0_5_5, all_0_1_1) = 0 % 34.72/9.94 | % 34.72/9.94 +-Applying beta-rule and splitting (171), into two cases. % 34.72/9.94 |-Branch one: % 34.72/9.94 | (181) ~ (all_58_0_71 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_71 % 34.72/9.94 | % 34.72/9.94 | Applying alpha-rule on (181) yields: % 34.72/9.94 | (182) ~ (all_58_0_71 = 0) % 34.72/9.94 | (183) apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_71 % 34.72/9.94 | % 34.72/9.94 +-Applying beta-rule and splitting (172), into two cases. % 34.72/9.94 |-Branch one: % 34.72/9.94 | (184) ~ (all_59_0_72 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72 % 34.72/9.94 | % 34.72/9.94 | Applying alpha-rule on (184) yields: % 34.72/9.94 | (185) ~ (all_59_0_72 = 0) % 34.72/9.94 | (186) apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72 % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (122) with all_0_3_3, all_0_2_2, all_63_1_76, all_0_1_1 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_63_1_76, intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 34.72/9.94 | (187) all_63_1_76 = all_0_1_1 % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (122) with all_0_3_3, all_0_2_2, all_51_1_65, all_63_1_76 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_63_1_76, intersection_point(all_0_3_3, all_0_2_2) = all_51_1_65, yields: % 34.72/9.94 | (188) all_63_1_76 = all_51_1_65 % 34.72/9.94 | % 34.72/9.94 | Instantiating formula (117) with all_0_5_5, all_0_4_4, all_42_1_54, all_49_1_63 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_49_1_63, line_connecting(all_0_5_5, all_0_4_4) = all_42_1_54, yields: % 34.72/9.94 | (189) all_49_1_63 = all_42_1_54 % 34.72/9.94 | % 34.72/9.94 | Combining equations (187,188) yields a new equation: % 34.72/9.94 | (190) all_51_1_65 = all_0_1_1 % 34.72/9.94 | % 34.72/9.94 | Combining equations (190,188) yields a new equation: % 34.72/9.94 | (187) all_63_1_76 = all_0_1_1 % 34.72/9.94 | % 34.72/9.95 | From (187) and (179) follows: % 34.72/9.95 | (192) apart_point_and_line(all_0_1_1, all_0_2_2) = all_63_0_75 % 34.72/9.95 | % 34.72/9.95 | From (190) and (167) follows: % 34.72/9.95 | (193) apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64 % 34.72/9.95 | % 34.72/9.95 | From (189) and (163) follows: % 34.72/9.95 | (194) apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62 % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (119) with all_0_1_1, all_0_2_2, all_63_0_75, all_59_0_72 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_63_0_75, apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, yields: % 34.72/9.95 | (195) all_63_0_75 = all_59_0_72 % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (119) with all_0_1_1, all_0_3_3, all_51_0_64, all_58_0_71 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_71, apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, yields: % 34.72/9.95 | (196) all_58_0_71 = all_51_0_64 % 34.72/9.95 | % 34.72/9.95 | Equations (195) can reduce 177 to: % 34.72/9.95 | (185) ~ (all_59_0_72 = 0) % 34.72/9.95 | % 34.72/9.95 | Equations (196) can reduce 182 to: % 34.72/9.95 | (165) ~ (all_51_0_64 = 0) % 34.72/9.95 | % 34.72/9.95 | From (195) and (192) follows: % 34.72/9.95 | (186) apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72 % 34.72/9.95 | % 34.72/9.95 | From (196) and (183) follows: % 34.72/9.95 | (193) apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64 % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (58) with all_59_0_72, all_59_0_72, all_0_2_2, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, yields: % 34.72/9.95 | (201) all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_59_0_72, all_59_0_72, all_0_2_2, all_0_2_2, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, yields: % 34.72/9.95 | (202) all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (58) with all_51_0_64, all_59_0_72, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, yields: % 34.72/9.95 | (203) all_59_0_72 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (58) with all_59_0_72, all_51_0_64, all_0_2_2, all_0_3_3, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, yields: % 34.72/9.95 | (204) all_59_0_72 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_51_0_64, all_59_0_72, all_0_3_3, all_0_2_2, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, yields: % 34.72/9.95 | (205) all_59_0_72 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_59_0_72, all_51_0_64, all_0_2_2, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, yields: % 34.72/9.95 | (206) all_59_0_72 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (58) with all_51_0_64, all_51_0_64, all_0_3_3, all_0_3_3, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, yields: % 34.72/9.95 | (207) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_51_0_64, all_51_0_64, all_0_3_3, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, yields: % 34.72/9.95 | (208) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_59_0_72, all_49_0_62, all_0_2_2, all_42_1_54, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, yields: % 34.72/9.95 | (209) all_59_0_72 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (89) with all_49_0_62, all_59_0_72, all_0_2_2, all_42_1_54, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, yields: % 34.72/9.95 | (210) all_59_0_72 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (89) with all_59_0_72, all_49_0_62, all_42_1_54, all_0_2_2, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, yields: % 34.72/9.95 | (211) all_59_0_72 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_49_0_62, all_51_0_64, all_42_1_54, all_0_3_3, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, yields: % 34.72/9.95 | (212) all_51_0_64 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_51_0_64, all_49_0_62, all_0_3_3, all_42_1_54, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, yields: % 34.72/9.95 | (213) all_51_0_64 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (89) with all_49_0_62, all_51_0_64, all_0_3_3, all_42_1_54, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, yields: % 34.72/9.95 | (214) all_51_0_64 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (89) with all_51_0_64, all_49_0_62, all_42_1_54, all_0_3_3, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, yields: % 34.72/9.95 | (215) all_51_0_64 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_42_0_53, all_59_0_72, all_42_1_54, all_0_2_2, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, yields: % 34.72/9.95 | (216) all_59_0_72 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_59_0_72, all_42_0_53, all_0_2_2, all_42_1_54, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, yields: % 34.72/9.95 | (217) all_59_0_72 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (89) with all_42_0_53, all_59_0_72, all_0_2_2, all_42_1_54, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, yields: % 34.72/9.95 | (218) all_59_0_72 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (89) with all_59_0_72, all_42_0_53, all_42_1_54, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, yields: % 34.72/9.95 | (219) all_59_0_72 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.95 | % 34.72/9.95 | Instantiating formula (82) with all_42_0_53, all_51_0_64, all_42_1_54, all_0_3_3, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, yields: % 34.72/9.95 | (220) all_51_0_64 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_51_0_64, all_42_0_53, all_0_3_3, all_42_1_54, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, yields: % 34.72/9.96 | (221) all_51_0_64 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (89) with all_42_0_53, all_51_0_64, all_0_3_3, all_42_1_54, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, yields: % 34.72/9.96 | (222) all_51_0_64 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (89) with all_51_0_64, all_42_0_53, all_42_1_54, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, yields: % 34.72/9.96 | (223) all_51_0_64 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_60_0_73, all_59_0_72, all_0_2_2, all_0_2_2, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (224) all_60_0_73 = 0 | all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_59_0_72, all_60_0_73, all_0_2_2, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (225) all_60_0_73 = 0 | all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_60_0_73, all_51_0_64, all_0_2_2, all_0_3_3, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (226) all_60_0_73 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_51_0_64, all_60_0_73, all_0_3_3, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (227) all_60_0_73 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (89) with all_60_0_73, all_51_0_64, all_0_3_3, all_0_2_2, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (228) all_60_0_73 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (89) with all_51_0_64, all_60_0_73, all_0_2_2, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (229) all_60_0_73 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_60_0_73, all_49_0_62, all_0_2_2, all_42_1_54, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (230) all_60_0_73 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_49_0_62, all_60_0_73, all_42_1_54, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (231) all_60_0_73 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (89) with all_60_0_73, all_49_0_62, all_42_1_54, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (232) all_60_0_73 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (89) with all_49_0_62, all_60_0_73, all_0_2_2, all_42_1_54, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (233) all_60_0_73 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (9) with all_60_0_73, all_42_0_53, all_0_2_2, all_42_1_54, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.96 | (234) all_60_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (9) with all_42_0_53, all_60_0_73, all_42_1_54, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.96 | (235) all_60_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (58) with all_60_0_73, all_42_0_53, all_0_2_2, all_42_1_54, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (236) all_60_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_42_1_54, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (58) with all_42_0_53, all_60_0_73, all_42_1_54, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (237) all_60_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_60_0_73, all_42_0_53, all_0_2_2, all_42_1_54, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (238) all_60_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_42_0_53, all_60_0_73, all_42_1_54, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (239) all_60_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (9) with all_60_0_73, all_60_0_73, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.96 | (240) all_60_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (58) with all_60_0_73, all_60_0_73, all_0_2_2, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (241) all_60_0_73 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_60_0_73, all_60_0_73, all_0_2_2, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, yields: % 34.72/9.96 | (242) all_60_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_56_0_70, all_59_0_72, all_0_3_3, all_0_2_2, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.96 | (243) all_59_0_72 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_59_0_72, all_56_0_70, all_0_2_2, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.96 | (244) all_59_0_72 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (89) with all_56_0_70, all_59_0_72, all_0_2_2, all_0_3_3, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.96 | (245) all_59_0_72 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (89) with all_59_0_72, all_56_0_70, all_0_3_3, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.96 | (246) all_59_0_72 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.96 | % 34.72/9.96 | Instantiating formula (82) with all_56_0_70, all_51_0_64, all_0_3_3, all_0_3_3, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.96 | (247) all_56_0_70 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (82) with all_51_0_64, all_56_0_70, all_0_3_3, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (248) all_56_0_70 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (82) with all_56_0_70, all_49_0_62, all_0_3_3, all_42_1_54, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (249) all_56_0_70 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (82) with all_49_0_62, all_56_0_70, all_42_1_54, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (250) all_56_0_70 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (89) with all_56_0_70, all_49_0_62, all_42_1_54, all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (251) all_56_0_70 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (89) with all_49_0_62, all_56_0_70, all_0_3_3, all_42_1_54, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_42_1_54) = all_49_0_62, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (252) all_56_0_70 = 0 | all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_56_0_70, all_42_0_53, all_0_3_3, all_42_1_54, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.97 | (253) all_56_0_70 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_42_0_53, all_56_0_70, all_42_1_54, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.97 | (254) all_56_0_70 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (58) with all_56_0_70, all_42_0_53, all_0_3_3, all_42_1_54, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (255) all_56_0_70 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_42_1_54, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (58) with all_42_0_53, all_56_0_70, all_42_1_54, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (256) all_56_0_70 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (82) with all_56_0_70, all_42_0_53, all_0_3_3, all_42_1_54, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (257) all_56_0_70 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (82) with all_42_0_53, all_56_0_70, all_42_1_54, all_0_3_3, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (258) all_56_0_70 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_56_0_70, all_60_0_73, all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.97 | (259) all_60_0_73 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_60_0_73, all_56_0_70, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.97 | (260) all_60_0_73 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (58) with all_56_0_70, all_60_0_73, all_0_3_3, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (261) all_60_0_73 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (58) with all_60_0_73, all_56_0_70, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (262) all_60_0_73 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (82) with all_56_0_70, all_60_0_73, all_0_3_3, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (263) all_60_0_73 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (82) with all_60_0_73, all_56_0_70, all_0_2_2, all_0_3_3, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (264) all_60_0_73 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_56_0_70, all_56_0_70, all_0_3_3, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 34.72/9.97 | (265) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (58) with all_56_0_70, all_56_0_70, all_0_3_3, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (266) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (82) with all_56_0_70, all_56_0_70, all_0_3_3, all_0_3_3, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, yields: % 34.72/9.97 | (267) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (84) with all_59_0_72, all_59_0_72, all_0_2_2, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.97 | (268) all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (84) with all_59_0_72, all_51_0_64, all_0_2_2, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.97 | (269) all_59_0_72 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (84) with all_51_0_64, all_59_0_72, all_0_3_3, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_59_0_72, apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.97 | (270) all_59_0_72 = 0 | all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (84) with all_51_0_64, all_51_0_64, all_0_3_3, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.97 | (271) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_42_0_53, all_60_0_73, all_42_1_54, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.97 | (272) all_60_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_42_0_53, all_56_0_70, all_42_1_54, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.97 | (273) all_56_0_70 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_60_0_73, all_42_0_53, all_0_2_2, all_42_1_54, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.97 | (274) all_60_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/9.97 | % 34.72/9.97 | Instantiating formula (9) with all_56_0_70, all_42_0_53, all_0_3_3, all_42_1_54, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_42_1_54) = all_42_0_53, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.97 | (275) all_56_0_70 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0)) % 34.72/9.98 | % 34.72/9.98 | Instantiating formula (9) with all_56_0_70, all_60_0_73, all_0_3_3, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 34.72/9.98 | (276) all_60_0_73 = 0 | all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (266), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (280) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (265), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (284) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (268), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (285) all_59_0_72 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (285) can reduce 185 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (185) ~ (all_59_0_72 = 0) % 34.72/9.98 | (288) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (267), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (292) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (271), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (293) all_51_0_64 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (293) can reduce 165 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (165) ~ (all_51_0_64 = 0) % 34.72/9.98 | (296) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (255), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (300) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_42_1_54, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (256), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (304) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (261), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (305) all_60_0_73 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (305) can reduce 174 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (174) ~ (all_60_0_73 = 0) % 34.72/9.98 | (308) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (262), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (305) all_60_0_73 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (305) can reduce 174 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (174) ~ (all_60_0_73 = 0) % 34.72/9.98 | (312) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (244), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (285) all_59_0_72 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (285) can reduce 185 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (185) ~ (all_59_0_72 = 0) % 34.72/9.98 | (316) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (247), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (320) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (254), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (324) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (273), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (328) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (249), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (332) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (253), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (336) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (248), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (340) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (246), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (285) all_59_0_72 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (285) can reduce 185 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (185) ~ (all_59_0_72 = 0) % 34.72/9.98 | (344) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (243), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (285) all_59_0_72 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (285) can reduce 185 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (185) ~ (all_59_0_72 = 0) % 34.72/9.98 | (348) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (258), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (352) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (252), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (277) all_56_0_70 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (277) can reduce 169 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (169) ~ (all_56_0_70 = 0) % 34.72/9.98 | (356) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/9.98 | % 34.72/9.98 +-Applying beta-rule and splitting (260), into two cases. % 34.72/9.98 |-Branch one: % 34.72/9.98 | (305) all_60_0_73 = 0 % 34.72/9.98 | % 34.72/9.98 | Equations (305) can reduce 174 to: % 34.72/9.98 | (278) $false % 34.72/9.98 | % 34.72/9.98 |-The branch is then unsatisfiable % 34.72/9.98 |-Branch two: % 34.72/9.98 | (174) ~ (all_60_0_73 = 0) % 34.72/9.98 | (360) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.98 | % 34.72/9.99 +-Applying beta-rule and splitting (259), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (305) all_60_0_73 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (305) can reduce 174 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (174) ~ (all_60_0_73 = 0) % 34.72/9.99 | (364) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (257), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (277) all_56_0_70 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (277) can reduce 169 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (169) ~ (all_56_0_70 = 0) % 34.72/9.99 | (368) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (272), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (305) all_60_0_73 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (305) can reduce 174 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (174) ~ (all_60_0_73 = 0) % 34.72/9.99 | (372) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (245), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (285) all_59_0_72 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (285) can reduce 185 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (185) ~ (all_59_0_72 = 0) % 34.72/9.99 | (376) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (251), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (277) all_56_0_70 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (277) can reduce 169 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (169) ~ (all_56_0_70 = 0) % 34.72/9.99 | (380) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (250), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (277) all_56_0_70 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (277) can reduce 169 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (169) ~ (all_56_0_70 = 0) % 34.72/9.99 | (384) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (263), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (305) all_60_0_73 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (305) can reduce 174 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (174) ~ (all_60_0_73 = 0) % 34.72/9.99 | (388) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (269), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (285) all_59_0_72 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (285) can reduce 185 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (185) ~ (all_59_0_72 = 0) % 34.72/9.99 | (392) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (264), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (305) all_60_0_73 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (305) can reduce 174 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (174) ~ (all_60_0_73 = 0) % 34.72/9.99 | (396) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (270), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (285) all_59_0_72 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (285) can reduce 185 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (185) ~ (all_59_0_72 = 0) % 34.72/9.99 | (400) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (308), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (277) all_56_0_70 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (277) can reduce 169 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (169) ~ (all_56_0_70 = 0) % 34.72/9.99 | (404) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (312), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (277) all_56_0_70 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (277) can reduce 169 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (169) ~ (all_56_0_70 = 0) % 34.72/9.99 | (408) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (344), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (277) all_56_0_70 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (277) can reduce 169 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (169) ~ (all_56_0_70 = 0) % 34.72/9.99 | (412) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.99 | % 34.72/9.99 | Instantiating (412) with all_237_0_586 yields: % 34.72/9.99 | (413) (all_237_0_586 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_237_0_586 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (all_237_0_586 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_237_0_586) | ( ~ (all_237_0_586 = 0) & distinct_points(all_0_5_5, all_0_1_1) = all_237_0_586) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (348), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (277) all_56_0_70 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (277) can reduce 169 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (169) ~ (all_56_0_70 = 0) % 34.72/9.99 | (417) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (388), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (277) all_56_0_70 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (277) can reduce 169 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (169) ~ (all_56_0_70 = 0) % 34.72/9.99 | (421) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (392), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (293) all_51_0_64 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (293) can reduce 165 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (165) ~ (all_51_0_64 = 0) % 34.72/9.99 | (425) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (400), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (293) all_51_0_64 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (293) can reduce 165 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (165) ~ (all_51_0_64 = 0) % 34.72/9.99 | (429) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/9.99 | % 34.72/9.99 | Instantiating (429) with all_257_0_591 yields: % 34.72/9.99 | (430) (all_257_0_591 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (all_257_0_591 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (all_257_0_591 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_257_0_591) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (430), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (431) (all_257_0_591 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (all_257_0_591 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (431), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (432) all_257_0_591 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0 % 34.72/9.99 | % 34.72/9.99 | Applying alpha-rule on (432) yields: % 34.72/9.99 | (433) all_257_0_591 = 0 % 34.72/9.99 | (434) apart_point_and_line(all_0_5_5, all_0_2_2) = 0 % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (241), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (305) all_60_0_73 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (305) can reduce 174 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (174) ~ (all_60_0_73 = 0) % 34.72/9.99 | (438) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (240), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (305) all_60_0_73 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (305) can reduce 174 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (174) ~ (all_60_0_73 = 0) % 34.72/9.99 | (442) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (227), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (305) all_60_0_73 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (305) can reduce 174 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (174) ~ (all_60_0_73 = 0) % 34.72/9.99 | (446) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/9.99 | % 34.72/9.99 +-Applying beta-rule and splitting (228), into two cases. % 34.72/9.99 |-Branch one: % 34.72/9.99 | (305) all_60_0_73 = 0 % 34.72/9.99 | % 34.72/9.99 | Equations (305) can reduce 174 to: % 34.72/9.99 | (278) $false % 34.72/9.99 | % 34.72/9.99 |-The branch is then unsatisfiable % 34.72/9.99 |-Branch two: % 34.72/9.99 | (174) ~ (all_60_0_73 = 0) % 34.72/9.99 | (450) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (239), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (454) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (230), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (458) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (233), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (462) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (231), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (466) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (232), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (470) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (234), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (474) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (236), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (478) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_42_1_54, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (237), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (482) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (242), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (486) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (274), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (490) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (224), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (494) all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (225), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (498) all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (226), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (502) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (238), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (506) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (276), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (510) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (235), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (514) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 34.72/10.00 | % 34.72/10.00 | Instantiating formula (119) with all_0_5_5, all_0_2_2, 0, all_60_0_73 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (517) all_257_0_591 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 34.72/10.00 | % 34.72/10.00 | Applying alpha-rule on (517) yields: % 34.72/10.00 | (433) all_257_0_591 = 0 % 34.72/10.00 | (519) apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (241), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (438) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (240), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (442) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 34.72/10.00 | % 34.72/10.00 +-Applying beta-rule and splitting (227), into two cases. % 34.72/10.00 |-Branch one: % 34.72/10.00 | (305) all_60_0_73 = 0 % 34.72/10.00 | % 34.72/10.00 | Equations (305) can reduce 174 to: % 34.72/10.00 | (278) $false % 34.72/10.00 | % 34.72/10.00 |-The branch is then unsatisfiable % 34.72/10.00 |-Branch two: % 34.72/10.00 | (174) ~ (all_60_0_73 = 0) % 34.72/10.00 | (446) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (228), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (450) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (239), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (454) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (229), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (543) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (230), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (458) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (233), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (462) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (231), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (466) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (232), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (470) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (234), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (474) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (396), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (277) all_56_0_70 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (277) can reduce 169 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (169) ~ (all_56_0_70 = 0) % 34.72/10.01 | (567) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (242), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (486) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (236), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (478) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_42_1_54, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (237), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (482) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (238), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (506) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (235), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (514) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (275), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (277) all_56_0_70 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (277) can reduce 169 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (169) ~ (all_56_0_70 = 0) % 34.72/10.01 | (591) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (226), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (502) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (274), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (490) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (224), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (305) all_60_0_73 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (305) can reduce 174 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (174) ~ (all_60_0_73 = 0) % 34.72/10.01 | (494) all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 34.72/10.01 | % 34.72/10.01 +-Applying beta-rule and splitting (360), into two cases. % 34.72/10.01 |-Branch one: % 34.72/10.01 | (277) all_56_0_70 = 0 % 34.72/10.01 | % 34.72/10.01 | Equations (277) can reduce 169 to: % 34.72/10.01 | (278) $false % 34.72/10.01 | % 34.72/10.01 |-The branch is then unsatisfiable % 34.72/10.01 |-Branch two: % 34.72/10.01 | (169) ~ (all_56_0_70 = 0) % 34.72/10.01 | (607) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 35.17/10.01 | % 35.17/10.01 +-Applying beta-rule and splitting (364), into two cases. % 35.17/10.01 |-Branch one: % 35.17/10.01 | (277) all_56_0_70 = 0 % 35.17/10.01 | % 35.17/10.01 | Equations (277) can reduce 169 to: % 35.17/10.01 | (278) $false % 35.17/10.01 | % 35.17/10.01 |-The branch is then unsatisfiable % 35.17/10.01 |-Branch two: % 35.17/10.01 | (169) ~ (all_56_0_70 = 0) % 35.17/10.01 | (611) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 35.17/10.01 | % 35.17/10.01 +-Applying beta-rule and splitting (376), into two cases. % 35.17/10.01 |-Branch one: % 35.17/10.01 | (277) all_56_0_70 = 0 % 35.17/10.01 | % 35.17/10.01 | Equations (277) can reduce 169 to: % 35.17/10.01 | (278) $false % 35.17/10.01 | % 35.17/10.01 |-The branch is then unsatisfiable % 35.17/10.01 |-Branch two: % 35.17/10.01 | (169) ~ (all_56_0_70 = 0) % 35.17/10.01 | (615) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.01 | % 35.17/10.01 +-Applying beta-rule and splitting (276), into two cases. % 35.17/10.01 |-Branch one: % 35.17/10.01 | (305) all_60_0_73 = 0 % 35.17/10.01 | % 35.17/10.01 | Equations (305) can reduce 174 to: % 35.17/10.01 | (278) $false % 35.17/10.01 | % 35.17/10.01 |-The branch is then unsatisfiable % 35.17/10.01 |-Branch two: % 35.17/10.01 | (174) ~ (all_60_0_73 = 0) % 35.17/10.01 | (510) all_56_0_70 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 35.17/10.01 | % 35.17/10.01 +-Applying beta-rule and splitting (510), into two cases. % 35.17/10.01 |-Branch one: % 35.17/10.01 | (277) all_56_0_70 = 0 % 35.17/10.01 | % 35.17/10.01 | Equations (277) can reduce 169 to: % 35.17/10.01 | (278) $false % 35.17/10.01 | % 35.17/10.01 |-The branch is then unsatisfiable % 35.17/10.01 |-Branch two: % 35.17/10.01 | (169) ~ (all_56_0_70 = 0) % 35.17/10.01 | (623) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 35.17/10.01 | % 35.17/10.01 | Instantiating formula (119) with all_0_5_5, all_0_3_3, 0, all_56_0_70 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_56_0_70, apart_point_and_line(all_0_5_5, all_0_3_3) = 0, yields: % 35.17/10.01 | (277) all_56_0_70 = 0 % 35.17/10.01 | % 35.17/10.01 | Equations (277) can reduce 169 to: % 35.17/10.01 | (278) $false % 35.17/10.01 | % 35.17/10.01 |-The branch is then unsatisfiable % 35.17/10.01 |-Branch two: % 35.17/10.01 | (626) ~ (all_257_0_591 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_257_0_591 % 35.17/10.01 | % 35.17/10.01 | Applying alpha-rule on (626) yields: % 35.17/10.01 | (627) ~ (all_257_0_591 = 0) % 35.17/10.01 | (628) distinct_lines(all_0_2_2, all_0_3_3) = all_257_0_591 % 35.17/10.01 | % 35.17/10.01 +-Applying beta-rule and splitting (241), into two cases. % 35.17/10.01 |-Branch one: % 35.17/10.01 | (305) all_60_0_73 = 0 % 35.17/10.01 | % 35.17/10.01 | Equations (305) can reduce 174 to: % 35.17/10.01 | (278) $false % 35.17/10.01 | % 35.17/10.01 |-The branch is then unsatisfiable % 35.17/10.01 |-Branch two: % 35.17/10.01 | (174) ~ (all_60_0_73 = 0) % 35.17/10.01 | (438) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (240), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (442) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (202), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (285) all_59_0_72 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (285) can reduce 185 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (185) ~ (all_59_0_72 = 0) % 35.17/10.02 | (640) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (218), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (285) all_59_0_72 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (285) can reduce 185 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (185) ~ (all_59_0_72 = 0) % 35.17/10.02 | (644) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (220), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (293) all_51_0_64 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (293) can reduce 165 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (165) ~ (all_51_0_64 = 0) % 35.17/10.02 | (648) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (221), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (293) all_51_0_64 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (293) can reduce 165 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (165) ~ (all_51_0_64 = 0) % 35.17/10.02 | (652) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (217), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (285) all_59_0_72 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (285) can reduce 185 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (185) ~ (all_59_0_72 = 0) % 35.17/10.02 | (656) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (219), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (285) all_59_0_72 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (285) can reduce 185 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (185) ~ (all_59_0_72 = 0) % 35.17/10.02 | (660) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (223), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (293) all_51_0_64 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (293) can reduce 165 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (165) ~ (all_51_0_64 = 0) % 35.17/10.02 | (664) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (222), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (293) all_51_0_64 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (293) can reduce 165 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (165) ~ (all_51_0_64 = 0) % 35.17/10.02 | (668) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (228), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (450) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (230), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (458) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (239), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (454) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (233), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (462) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (231), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (466) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (232), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (470) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (234), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (474) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (207), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (293) all_51_0_64 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (293) can reduce 165 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (165) ~ (all_51_0_64 = 0) % 35.17/10.02 | (280) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (242), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (486) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (236), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (478) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_42_1_54, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (237), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (482) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_42_1_54) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (226), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (502) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (238), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (506) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (224), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (494) all_59_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (274), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (490) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0)) % 35.17/10.02 | % 35.17/10.02 +-Applying beta-rule and splitting (235), into two cases. % 35.17/10.02 |-Branch one: % 35.17/10.02 | (305) all_60_0_73 = 0 % 35.17/10.02 | % 35.17/10.02 | Equations (305) can reduce 174 to: % 35.17/10.02 | (278) $false % 35.17/10.02 | % 35.17/10.02 |-The branch is then unsatisfiable % 35.17/10.02 |-Branch two: % 35.17/10.02 | (174) ~ (all_60_0_73 = 0) % 35.17/10.02 | (514) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (320), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (736) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (201), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (438) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (213), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (744) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (214), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (748) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (215), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (752) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (450), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (756) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (502), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (760) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (494), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (764) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (413), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (765) (all_237_0_586 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_237_0_586 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (all_237_0_586 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_237_0_586) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (765), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (766) (all_237_0_586 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_237_0_586 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (766), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (767) all_237_0_586 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0 % 35.17/10.03 | % 35.17/10.03 | Applying alpha-rule on (767) yields: % 35.17/10.03 | (768) all_237_0_586 = 0 % 35.17/10.03 | (769) apart_point_and_line(all_0_1_1, all_0_3_3) = 0 % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (208), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (773) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (216), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (777) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (209), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (781) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (210), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (785) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_42_1_54, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (211), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (789) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (212), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (793) all_49_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_42_1_54) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_42_1_54) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (203), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (797) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (204), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (801) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (205), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (805) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (206), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (285) all_59_0_72 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (285) can reduce 185 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (185) ~ (all_59_0_72 = 0) % 35.17/10.03 | (809) all_51_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (797), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (404) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (801), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.03 | (408) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)) % 35.17/10.03 | % 35.17/10.03 +-Applying beta-rule and splitting (805), into two cases. % 35.17/10.03 |-Branch one: % 35.17/10.03 | (293) all_51_0_64 = 0 % 35.17/10.03 | % 35.17/10.03 | Equations (293) can reduce 165 to: % 35.17/10.03 | (278) $false % 35.17/10.03 | % 35.17/10.03 |-The branch is then unsatisfiable % 35.17/10.03 |-Branch two: % 35.17/10.03 | (165) ~ (all_51_0_64 = 0) % 35.17/10.04 | (821) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 35.17/10.04 | % 35.17/10.04 +-Applying beta-rule and splitting (809), into two cases. % 35.17/10.04 |-Branch one: % 35.17/10.04 | (293) all_51_0_64 = 0 % 35.17/10.04 | % 35.17/10.04 | Equations (293) can reduce 165 to: % 35.17/10.04 | (278) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 |-Branch two: % 35.17/10.04 | (165) ~ (all_51_0_64 = 0) % 35.17/10.04 | (825) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 35.17/10.04 | % 35.17/10.04 | Instantiating formula (119) with all_0_1_1, all_0_3_3, 0, all_51_0_64 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_51_0_64, apart_point_and_line(all_0_1_1, all_0_3_3) = 0, yields: % 35.17/10.04 | (293) all_51_0_64 = 0 % 35.17/10.04 | % 35.17/10.04 | Equations (293) can reduce 165 to: % 35.17/10.04 | (278) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 |-Branch two: % 35.17/10.04 | (828) all_237_0_586 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0 % 35.17/10.04 | % 35.17/10.04 | Applying alpha-rule on (828) yields: % 35.17/10.04 | (768) all_237_0_586 = 0 % 35.17/10.04 | (434) apart_point_and_line(all_0_5_5, all_0_2_2) = 0 % 35.17/10.04 | % 35.17/10.04 | Instantiating formula (119) with all_0_5_5, all_0_2_2, 0, all_60_0_73 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_60_0_73, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields: % 35.17/10.04 | (305) all_60_0_73 = 0 % 35.17/10.04 | % 35.17/10.04 | Equations (305) can reduce 174 to: % 35.17/10.04 | (278) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 |-Branch two: % 35.17/10.04 | (833) ~ (all_237_0_586 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_237_0_586 % 35.17/10.04 | % 35.17/10.04 | Applying alpha-rule on (833) yields: % 35.17/10.04 | (834) ~ (all_237_0_586 = 0) % 35.17/10.04 | (835) distinct_lines(all_0_2_2, all_0_3_3) = all_237_0_586 % 35.17/10.04 | % 35.17/10.04 | Instantiating formula (49) with all_0_2_2, all_0_3_3, all_237_0_586, all_257_0_591 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_257_0_591, distinct_lines(all_0_2_2, all_0_3_3) = all_237_0_586, yields: % 35.17/10.04 | (836) all_257_0_591 = all_237_0_586 % 35.17/10.04 | % 35.17/10.04 | Equations (836) can reduce 627 to: % 35.17/10.04 | (834) ~ (all_237_0_586 = 0) % 35.17/10.04 | % 35.17/10.04 | From (836) and (628) follows: % 35.17/10.04 | (835) distinct_lines(all_0_2_2, all_0_3_3) = all_237_0_586 % 35.17/10.04 | % 35.17/10.04 | Instantiating formula (22) with all_237_0_586, 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, distinct_lines(all_0_2_2, all_0_3_3) = all_237_0_586, yields: % 35.17/10.04 | (839) all_237_0_586 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0 % 35.17/10.04 | % 35.17/10.04 +-Applying beta-rule and splitting (839), into two cases. % 35.17/10.04 |-Branch one: % 35.17/10.04 | (840) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 35.17/10.04 | % 35.17/10.04 | Instantiating formula (50) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 35.17/10.04 | (841) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 |-Branch two: % 35.17/10.04 | (842) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0) % 35.17/10.04 | (768) all_237_0_586 = 0 % 35.17/10.04 | % 35.17/10.04 | Equations (768) can reduce 834 to: % 35.17/10.04 | (278) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 |-Branch two: % 35.17/10.04 | (845) ~ (all_237_0_586 = 0) & distinct_points(all_0_5_5, all_0_1_1) = all_237_0_586 % 35.17/10.04 | % 35.17/10.04 | Applying alpha-rule on (845) yields: % 35.17/10.04 | (834) ~ (all_237_0_586 = 0) % 35.17/10.04 | (847) distinct_points(all_0_5_5, all_0_1_1) = all_237_0_586 % 35.17/10.04 | % 35.17/10.04 | Instantiating formula (74) with all_0_5_5, all_0_1_1, all_237_0_586, 0 and discharging atoms distinct_points(all_0_5_5, all_0_1_1) = all_237_0_586, distinct_points(all_0_5_5, all_0_1_1) = 0, yields: % 35.17/10.04 | (768) all_237_0_586 = 0 % 35.17/10.04 | % 35.17/10.04 | Equations (768) can reduce 834 to: % 35.17/10.04 | (278) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 |-Branch two: % 35.17/10.04 | (850) ~ (all_59_0_72 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_59_0_72 % 35.17/10.04 | % 35.17/10.04 | Applying alpha-rule on (850) yields: % 35.17/10.04 | (185) ~ (all_59_0_72 = 0) % 35.17/10.04 | (852) convergent_lines(all_0_3_3, all_0_2_2) = all_59_0_72 % 35.17/10.04 | % 35.17/10.04 | Instantiating formula (51) with all_0_3_3, all_0_2_2, all_59_0_72, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_59_0_72, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 35.17/10.04 | (285) all_59_0_72 = 0 % 35.17/10.04 | % 35.17/10.04 | Equations (285) can reduce 185 to: % 35.17/10.04 | (278) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 |-Branch two: % 35.17/10.04 | (855) ~ (all_58_0_71 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_58_0_71 % 35.17/10.04 | % 35.17/10.04 | Applying alpha-rule on (855) yields: % 35.17/10.04 | (182) ~ (all_58_0_71 = 0) % 35.17/10.04 | (857) convergent_lines(all_0_3_3, all_0_2_2) = all_58_0_71 % 35.17/10.04 | % 35.17/10.04 | Instantiating formula (51) with all_0_3_3, all_0_2_2, all_58_0_71, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_58_0_71, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 35.17/10.04 | (858) all_58_0_71 = 0 % 35.17/10.04 | % 35.17/10.04 | Equations (858) can reduce 182 to: % 35.17/10.04 | (278) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 |-Branch two: % 35.17/10.04 | (860) ~ (distinct_points(all_0_5_5, all_0_1_1) = 0) % 35.17/10.04 | (861) all_0_0_0 = 0 % 35.17/10.04 | % 35.17/10.04 | Equations (861) can reduce 71 to: % 35.17/10.04 | (278) $false % 35.17/10.04 | % 35.17/10.04 |-The branch is then unsatisfiable % 35.17/10.04 % SZS output end Proof for theBenchmark % 35.17/10.04 % 35.17/10.04 9394ms %------------------------------------------------------------------------------