%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO221+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 03:48:54 EDT 2022 % Result : Theorem 5.69s 1.94s % Output : Proof 9.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO221+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Fri Jun 17 16:31:51 EDT 2022 % 0.13/0.35 % CPUTime : % 0.56/0.60 ____ _ % 0.56/0.60 ___ / __ \_____(_)___ ________ __________ % 0.56/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.60 % 0.56/0.60 A Theorem Prover for First-Order Logic % 0.56/0.60 (ePrincess v.1.0) % 0.56/0.60 % 0.56/0.60 (c) Philipp Rümmer, 2009-2015 % 0.56/0.60 (c) Peter Backeman, 2014-2015 % 0.56/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.60 Bug reports to peter@backeman.se % 0.56/0.60 % 0.56/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.60 % 0.62/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.74/0.95 Prover 0: Preprocessing ... % 2.18/1.11 Prover 0: Warning: ignoring some quantifiers % 2.18/1.13 Prover 0: Constructing countermodel ... % 3.24/1.41 Prover 0: gave up % 3.24/1.41 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.24/1.44 Prover 1: Preprocessing ... % 3.92/1.55 Prover 1: Constructing countermodel ... % 3.92/1.60 Prover 1: gave up % 3.92/1.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.27/1.63 Prover 2: Preprocessing ... % 5.04/1.79 Prover 2: Warning: ignoring some quantifiers % 5.15/1.80 Prover 2: Constructing countermodel ... % 5.69/1.94 Prover 2: proved (339ms) % 5.69/1.94 % 5.69/1.94 No countermodel exists, formula is valid % 5.69/1.94 % SZS status Theorem for theBenchmark % 5.69/1.94 % 5.69/1.94 Generating proof ... Warning: ignoring some quantifiers % 8.66/2.67 found it (size 182) % 8.66/2.67 % 8.66/2.67 % SZS output start Proof for theBenchmark % 8.66/2.67 Assumed formulas after preprocessing and simplification: % 8.66/2.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & orthogonal_through_point(v2, v1) = v5 & orthogonal_through_point(v2, v0) = v3 & apart_point_and_line(v1, v3) = v4 & distinct_lines(v3, v5) = 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 | ~ (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) = 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] : ( ~ (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] : (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_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(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(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) = 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(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 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [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] : ( ~ (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] : ( ~ (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) & 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] : ( ~ (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] : ( ~ (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] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [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) % 9.19/2.73 | 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: % 9.19/2.73 | (1) ~ (all_0_1_1 = 0) & orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0 & orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2 & apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1 & distinct_lines(all_0_2_2, all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 9.19/2.75 | % 9.19/2.75 | Applying alpha-rule on (1) yields: % 9.19/2.75 | (2) ! [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) % 9.19/2.75 | (3) orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0 % 9.19/2.75 | (4) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 9.19/2.75 | (5) ! [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))) % 9.19/2.75 | (6) ! [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)) % 9.19/2.75 | (7) ! [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))) % 9.19/2.75 | (8) ! [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))) % 9.19/2.75 | (9) distinct_lines(all_0_2_2, all_0_0_0) = 0 % 9.19/2.75 | (10) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 9.19/2.75 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 9.19/2.75 | (12) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 % 9.19/2.75 | (13) ! [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) % 9.19/2.75 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 9.19/2.75 | (15) ! [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))) % 9.19/2.75 | (16) ! [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))) % 9.19/2.75 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 9.19/2.75 | (18) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 9.19/2.75 | (19) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 9.19/2.75 | (20) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 9.19/2.75 | (21) ! [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))) % 9.19/2.75 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 9.19/2.75 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 9.19/2.75 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 9.19/2.76 | (25) ! [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))) % 9.19/2.76 | (26) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 9.19/2.76 | (27) ! [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))) % 9.19/2.76 | (28) ! [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))) % 9.19/2.76 | (29) ! [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))) % 9.19/2.76 | (30) ! [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))) % 9.19/2.76 | (31) ! [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))) % 9.19/2.76 | (32) ! [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))) % 9.19/2.76 | (33) ! [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))) % 9.19/2.76 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 9.19/2.76 | (35) ! [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))) % 9.19/2.76 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 9.19/2.76 | (37) ! [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))) % 9.19/2.76 | (38) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 9.19/2.76 | (39) ! [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))) % 9.19/2.76 | (40) ! [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))) % 9.19/2.76 | (41) ! [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))) % 9.19/2.76 | (42) ! [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)) % 9.19/2.76 | (43) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 9.19/2.76 | (44) apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1 % 9.19/2.76 | (45) ! [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))) % 9.19/2.76 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 9.19/2.76 | (47) ! [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)) % 9.19/2.76 | (48) ! [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))) % 9.19/2.76 | (49) ! [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))) % 9.19/2.76 | (50) ~ (all_0_1_1 = 0) % 9.19/2.76 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 9.19/2.76 | (52) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 9.19/2.76 | (53) ! [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))) % 9.19/2.76 | (54) ! [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))) % 9.19/2.76 | (55) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 9.19/2.76 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 9.19/2.76 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 9.19/2.76 | (58) ! [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))) % 9.19/2.76 | (59) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 9.19/2.76 | (60) ! [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))) % 9.19/2.76 | (61) ! [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) % 9.19/2.76 | (62) ! [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)) % 9.19/2.77 | (63) orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2 % 9.19/2.77 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 9.19/2.77 | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 9.19/2.77 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 9.19/2.77 | (67) ! [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))) % 9.19/2.77 | (68) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 % 9.19/2.77 | (69) ! [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))) % 9.19/2.77 | (70) ! [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)) % 9.19/2.77 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 9.19/2.77 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 9.19/2.77 | (73) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 9.19/2.77 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 9.19/2.77 | (75) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 9.19/2.77 | (76) ! [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))) % 9.19/2.77 | (77) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 9.19/2.77 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 9.19/2.77 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 9.19/2.77 | (80) ! [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))) % 9.19/2.77 | (81) ! [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)) % 9.19/2.77 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) % 9.19/2.77 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 9.19/2.77 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 9.19/2.77 | (85) ! [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))) % 9.19/2.77 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) % 9.19/2.77 | (87) ! [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) % 9.19/2.77 | % 9.19/2.77 | Instantiating formula (86) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0, yields: % 9.19/2.77 | (88) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_3_3) = v0) % 9.19/2.77 | % 9.19/2.77 | Instantiating formula (83) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0, yields: % 9.19/2.77 | (89) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = v0) % 9.19/2.77 | % 9.19/2.77 | Instantiating formula (86) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2, yields: % 9.19/2.77 | (90) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0) % 9.19/2.77 | % 9.19/2.77 | Instantiating formula (83) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2, yields: % 9.19/2.77 | (91) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0) % 9.19/2.77 | % 9.19/2.77 | Instantiating formula (7) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.19/2.77 | (92) all_0_1_1 = 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)) % 9.19/2.77 | % 9.19/2.77 | Instantiating formula (40) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.19/2.77 | (93) all_0_1_1 = 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) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.77 | % 9.19/2.77 | Instantiating formula (41) with all_0_1_1, all_0_1_1, all_0_0_0, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields: % 9.19/2.77 | (94) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.77 | % 9.19/2.77 | Instantiating formula (32) with all_0_1_1, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields: % 9.19/2.77 | (95) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0)) % 9.19/2.77 | % 9.19/2.77 | Instantiating (91) with all_26_0_33 yields: % 9.19/2.77 | (96) ~ (all_26_0_33 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33 % 9.19/2.77 | % 9.19/2.77 | Applying alpha-rule on (96) yields: % 9.19/2.77 | (97) ~ (all_26_0_33 = 0) % 9.19/2.77 | (98) apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33 % 9.19/2.77 | % 9.19/2.77 | Instantiating (90) with all_28_0_34 yields: % 9.19/2.77 | (99) ~ (all_28_0_34 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34 % 9.19/2.77 | % 9.19/2.77 | Applying alpha-rule on (99) yields: % 9.19/2.77 | (100) ~ (all_28_0_34 = 0) % 9.19/2.77 | (101) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34 % 9.19/2.77 | % 9.19/2.77 | Instantiating (89) with all_30_0_35 yields: % 9.19/2.77 | (102) ~ (all_30_0_35 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35 % 9.19/2.77 | % 9.19/2.77 | Applying alpha-rule on (102) yields: % 9.19/2.77 | (103) ~ (all_30_0_35 = 0) % 9.19/2.77 | (104) apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35 % 9.19/2.77 | % 9.19/2.77 | Instantiating (88) with all_32_0_36 yields: % 9.19/2.77 | (105) ~ (all_32_0_36 = 0) & unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36 % 9.19/2.77 | % 9.19/2.77 | Applying alpha-rule on (105) yields: % 9.19/2.77 | (106) ~ (all_32_0_36 = 0) % 9.19/2.77 | (107) unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36 % 9.19/2.77 | % 9.19/2.77 +-Applying beta-rule and splitting (95), into two cases. % 9.19/2.77 |-Branch one: % 9.19/2.77 | (108) all_0_1_1 = 0 % 9.19/2.77 | % 9.19/2.77 | Equations (108) can reduce 50 to: % 9.19/2.77 | (109) $false % 9.19/2.77 | % 9.19/2.77 |-The branch is then unsatisfiable % 9.19/2.77 |-Branch two: % 9.19/2.77 | (50) ~ (all_0_1_1 = 0) % 9.19/2.77 | (111) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0)) % 9.19/2.77 | % 9.19/2.77 +-Applying beta-rule and splitting (92), into two cases. % 9.19/2.77 |-Branch one: % 9.19/2.77 | (108) all_0_1_1 = 0 % 9.19/2.77 | % 9.19/2.78 | Equations (108) can reduce 50 to: % 9.19/2.78 | (109) $false % 9.19/2.78 | % 9.19/2.78 |-The branch is then unsatisfiable % 9.19/2.78 |-Branch two: % 9.19/2.78 | (50) ~ (all_0_1_1 = 0) % 9.19/2.78 | (115) ? [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)) % 9.19/2.78 | % 9.19/2.78 +-Applying beta-rule and splitting (93), into two cases. % 9.19/2.78 |-Branch one: % 9.19/2.78 | (108) all_0_1_1 = 0 % 9.19/2.78 | % 9.19/2.78 | Equations (108) can reduce 50 to: % 9.19/2.78 | (109) $false % 9.19/2.78 | % 9.19/2.78 |-The branch is then unsatisfiable % 9.19/2.78 |-Branch two: % 9.19/2.78 | (50) ~ (all_0_1_1 = 0) % 9.19/2.78 | (119) ? [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) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.78 | % 9.19/2.78 +-Applying beta-rule and splitting (94), into two cases. % 9.19/2.78 |-Branch one: % 9.19/2.78 | (108) all_0_1_1 = 0 % 9.19/2.78 | % 9.19/2.78 | Equations (108) can reduce 50 to: % 9.19/2.78 | (109) $false % 9.19/2.78 | % 9.19/2.78 |-The branch is then unsatisfiable % 9.19/2.78 |-Branch two: % 9.19/2.78 | (50) ~ (all_0_1_1 = 0) % 9.19/2.78 | (123) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (39) with all_32_0_36, all_0_1_1, all_0_3_3, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.19/2.78 | (124) all_32_0_36 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (60) with all_32_0_36, all_0_1_1, all_0_3_3, all_0_2_2, all_0_0_0, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.19/2.78 | (125) all_32_0_36 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (39) with all_28_0_34, all_0_1_1, all_0_3_3, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.19/2.78 | (126) all_28_0_34 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 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_0_2_2) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (49) with all_32_0_36, all_30_0_35, all_0_3_3, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields: % 9.19/2.78 | (127) all_32_0_36 = 0 | all_30_0_35 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (39) with all_28_0_34, all_30_0_35, all_0_3_3, all_0_2_2, all_0_0_0, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, yields: % 9.19/2.78 | (128) all_30_0_35 = 0 | all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (60) with all_28_0_34, all_30_0_35, all_0_3_3, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, yields: % 9.19/2.78 | (129) all_30_0_35 = 0 | all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 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_0_0_0) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (7) with all_0_1_1, all_30_0_35, all_0_2_2, all_0_0_0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.19/2.78 | (130) all_30_0_35 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (40) with all_0_1_1, all_30_0_35, all_0_2_2, all_0_0_0, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 9.19/2.78 | (131) all_30_0_35 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (7) with all_30_0_35, all_30_0_35, all_0_0_0, all_0_0_0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, yields: % 9.19/2.78 | (132) all_30_0_35 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (40) with all_30_0_35, all_30_0_35, all_0_0_0, all_0_0_0, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, yields: % 9.19/2.78 | (133) all_30_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (39) with all_32_0_36, all_26_0_33, all_0_3_3, all_0_0_0, all_0_2_2, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (134) all_32_0_36 = 0 | all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (60) with all_32_0_36, all_26_0_33, all_0_3_3, all_0_2_2, all_0_0_0, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (135) all_32_0_36 = 0 | all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (29) with all_28_0_34, all_26_0_33, all_0_3_3, all_0_0_0, all_0_2_2, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields: % 9.19/2.78 | (136) all_28_0_34 = 0 | all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (39) with all_28_0_34, all_26_0_33, all_0_3_3, all_0_2_2, all_0_2_2, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (137) all_28_0_34 = 0 | all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, 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_2_2) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (41) with all_26_0_33, all_0_1_1, all_0_0_0, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields: % 9.19/2.78 | (138) all_26_0_33 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (41) with all_0_1_1, all_26_0_33, all_0_0_0, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields: % 9.19/2.78 | (139) all_26_0_33 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (40) with all_26_0_33, all_0_1_1, all_0_2_2, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (140) all_26_0_33 = 0 | all_0_1_1 = 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_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (40) with all_0_1_1, all_26_0_33, 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_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (141) all_26_0_33 = 0 | all_0_1_1 = 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_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_4_4) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (40) with all_26_0_33, all_30_0_35, all_0_2_2, all_0_0_0, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (142) all_30_0_35 = 0 | all_26_0_33 = 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_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (40) with all_30_0_35, all_26_0_33, all_0_0_0, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (143) all_30_0_35 = 0 | all_26_0_33 = 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_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (45) with all_26_0_33, all_30_0_35, all_0_0_0, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (144) all_30_0_35 = 0 | all_26_0_33 = 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_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (45) with all_30_0_35, all_26_0_33, all_0_2_2, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields: % 9.19/2.78 | (145) all_30_0_35 = 0 | all_26_0_33 = 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_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (7) with all_26_0_33, all_26_0_33, 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_26_0_33, yields: % 9.19/2.78 | (146) all_26_0_33 = 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)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (41) with all_26_0_33, all_26_0_33, all_0_0_0, 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_26_0_33, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields: % 9.19/2.78 | (147) all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 9.19/2.78 | % 9.19/2.78 | Instantiating formula (40) with all_26_0_33, all_26_0_33, 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_26_0_33, yields: % 9.19/2.78 | (148) all_26_0_33 = 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)) % 9.19/2.78 | % 9.19/2.78 +-Applying beta-rule and splitting (124), into two cases. % 9.19/2.78 |-Branch one: % 9.19/2.78 | (149) all_32_0_36 = 0 % 9.19/2.78 | % 9.19/2.78 | Equations (149) can reduce 106 to: % 9.19/2.78 | (109) $false % 9.19/2.78 | % 9.19/2.78 |-The branch is then unsatisfiable % 9.19/2.78 |-Branch two: % 9.19/2.78 | (106) ~ (all_32_0_36 = 0) % 9.19/2.78 | (152) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0)) % 9.19/2.78 | % 9.19/2.78 +-Applying beta-rule and splitting (148), into two cases. % 9.19/2.78 |-Branch one: % 9.19/2.78 | (153) all_26_0_33 = 0 % 9.19/2.78 | % 9.19/2.78 | Equations (153) can reduce 97 to: % 9.19/2.78 | (109) $false % 9.19/2.78 | % 9.19/2.78 |-The branch is then unsatisfiable % 9.19/2.78 |-Branch two: % 9.19/2.78 | (97) ~ (all_26_0_33 = 0) % 9.19/2.78 | (156) ? [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)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (125), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (149) all_32_0_36 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (149) can reduce 106 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (106) ~ (all_32_0_36 = 0) % 9.19/2.79 | (160) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (152), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (108) all_0_1_1 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (108) can reduce 50 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (50) ~ (all_0_1_1 = 0) % 9.19/2.79 | (164) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (147), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (153) all_26_0_33 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (153) can reduce 97 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (97) ~ (all_26_0_33 = 0) % 9.19/2.79 | (168) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (146), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (153) all_26_0_33 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (153) can reduce 97 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (97) ~ (all_26_0_33 = 0) % 9.19/2.79 | (115) ? [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)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (160), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (108) all_0_1_1 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (108) can reduce 50 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (50) ~ (all_0_1_1 = 0) % 9.19/2.79 | (176) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (129), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (180) all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 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_0_0_0) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (126), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (181) all_28_0_34 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (181) can reduce 100 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (100) ~ (all_28_0_34 = 0) % 9.19/2.79 | (184) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 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_0_2_2) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (132), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (188) ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (133), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (192) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (136), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (181) all_28_0_34 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (181) can reduce 100 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (100) ~ (all_28_0_34 = 0) % 9.19/2.79 | (196) all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (137), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (181) all_28_0_34 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (181) can reduce 100 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (100) ~ (all_28_0_34 = 0) % 9.19/2.79 | (200) all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, 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_2_2) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (134), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (149) all_32_0_36 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (149) can reduce 106 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (106) ~ (all_32_0_36 = 0) % 9.19/2.79 | (204) all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (135), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (149) all_32_0_36 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (149) can reduce 106 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (106) ~ (all_32_0_36 = 0) % 9.19/2.79 | (208) all_26_0_33 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (204), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (153) all_26_0_33 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (153) can reduce 97 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (97) ~ (all_26_0_33 = 0) % 9.19/2.79 | (212) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (208), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (153) all_26_0_33 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (153) can reduce 97 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (97) ~ (all_26_0_33 = 0) % 9.19/2.79 | (216) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (180), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (181) all_28_0_34 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (181) can reduce 100 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (100) ~ (all_28_0_34 = 0) % 9.19/2.79 | (220) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 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_0_0_0) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (128), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (224) all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (138), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (153) all_26_0_33 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (153) can reduce 97 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (97) ~ (all_26_0_33 = 0) % 9.19/2.79 | (228) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (139), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (153) all_26_0_33 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (153) can reduce 97 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (97) ~ (all_26_0_33 = 0) % 9.19/2.79 | (232) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (140), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (153) all_26_0_33 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (153) can reduce 97 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (97) ~ (all_26_0_33 = 0) % 9.19/2.79 | (236) all_0_1_1 = 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_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (141), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (153) all_26_0_33 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (153) can reduce 97 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (97) ~ (all_26_0_33 = 0) % 9.19/2.79 | (240) all_0_1_1 = 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_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_4_4) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (144), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (244) all_26_0_33 = 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_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (130), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (248) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (131), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (252) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (142), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (256) all_26_0_33 = 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_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.79 | % 9.19/2.79 +-Applying beta-rule and splitting (143), into two cases. % 9.19/2.79 |-Branch one: % 9.19/2.79 | (177) all_30_0_35 = 0 % 9.19/2.79 | % 9.19/2.79 | Equations (177) can reduce 103 to: % 9.19/2.79 | (109) $false % 9.19/2.79 | % 9.19/2.79 |-The branch is then unsatisfiable % 9.19/2.79 |-Branch two: % 9.19/2.79 | (103) ~ (all_30_0_35 = 0) % 9.19/2.79 | (260) all_26_0_33 = 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_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (145), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (177) all_30_0_35 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (177) can reduce 103 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (103) ~ (all_30_0_35 = 0) % 9.19/2.80 | (264) all_26_0_33 = 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_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (127), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (149) all_32_0_36 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (149) can reduce 106 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (106) ~ (all_32_0_36 = 0) % 9.19/2.80 | (268) all_30_0_35 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (268), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (177) all_30_0_35 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (177) can reduce 103 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (103) ~ (all_30_0_35 = 0) % 9.19/2.80 | (272) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)) % 9.19/2.80 | % 9.19/2.80 | Instantiating (272) with all_219_0_127 yields: % 9.19/2.80 | (273) (all_219_0_127 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_219_0_127 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (273), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (274) all_219_0_127 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 9.19/2.80 | % 9.19/2.80 | Applying alpha-rule on (274) yields: % 9.19/2.80 | (275) all_219_0_127 = 0 % 9.19/2.80 | (276) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (224), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (181) all_28_0_34 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (181) can reduce 100 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (100) ~ (all_28_0_34 = 0) % 9.19/2.80 | (280) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.80 | % 9.19/2.80 | Instantiating formula (36) with all_0_2_2, all_0_3_3, 0, all_28_0_34 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 9.19/2.80 | (181) all_28_0_34 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (181) can reduce 100 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (283) all_219_0_127 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0 % 9.19/2.80 | % 9.19/2.80 | Applying alpha-rule on (283) yields: % 9.19/2.80 | (275) all_219_0_127 = 0 % 9.19/2.80 | (285) apart_point_and_line(all_0_4_4, all_0_2_2) = 0 % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (236), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (108) all_0_1_1 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (108) can reduce 50 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (50) ~ (all_0_1_1 = 0) % 9.19/2.80 | (289) ? [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_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (248), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (108) all_0_1_1 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (108) can reduce 50 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (50) ~ (all_0_1_1 = 0) % 9.19/2.80 | (293) ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (184), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (108) all_0_1_1 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (108) can reduce 50 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (50) ~ (all_0_1_1 = 0) % 9.19/2.80 | (297) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 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_0_2_2) = v0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (228), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (108) all_0_1_1 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (108) can reduce 50 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (50) ~ (all_0_1_1 = 0) % 9.19/2.80 | (301) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (232), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (108) all_0_1_1 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (108) can reduce 50 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (50) ~ (all_0_1_1 = 0) % 9.19/2.80 | (305) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (240), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (108) all_0_1_1 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (108) can reduce 50 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (50) ~ (all_0_1_1 = 0) % 9.19/2.80 | (309) ? [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_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_4_4) = v0)) % 9.19/2.80 | % 9.19/2.80 +-Applying beta-rule and splitting (252), into two cases. % 9.19/2.80 |-Branch one: % 9.19/2.80 | (108) all_0_1_1 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (108) can reduce 50 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 |-Branch two: % 9.19/2.80 | (50) ~ (all_0_1_1 = 0) % 9.19/2.80 | (313) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 9.19/2.80 | % 9.19/2.80 | Instantiating formula (24) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields: % 9.19/2.80 | (108) all_0_1_1 = 0 % 9.19/2.80 | % 9.19/2.80 | Equations (108) can reduce 50 to: % 9.19/2.80 | (109) $false % 9.19/2.80 | % 9.19/2.80 |-The branch is then unsatisfiable % 9.19/2.80 % SZS output end Proof for theBenchmark % 9.19/2.80 % 9.19/2.80 2187ms %------------------------------------------------------------------------------