%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO180+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 03:48:17 EDT 2022 % Result : Theorem 16.20s 4.56s % Output : Proof 22.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO180+3 : TPTP v8.1.0. Released v4.0.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 11:20:43 EDT 2022 % 0.13/0.34 % CPUTime : % 0.53/0.62 ____ _ % 0.53/0.62 ___ / __ \_____(_)___ ________ __________ % 0.53/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.62 % 0.53/0.62 A Theorem Prover for First-Order Logic % 0.65/0.63 (ePrincess v.1.0) % 0.65/0.63 % 0.65/0.63 (c) Philipp Rümmer, 2009-2015 % 0.65/0.63 (c) Peter Backeman, 2014-2015 % 0.65/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.65/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.65/0.63 Bug reports to peter@backeman.se % 0.65/0.63 % 0.65/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.65/0.63 % 0.65/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.88/1.04 Prover 0: Preprocessing ... % 2.43/1.26 Prover 0: Warning: ignoring some quantifiers % 2.43/1.29 Prover 0: Constructing countermodel ... % 13.84/3.98 Prover 0: gave up % 13.84/3.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 13.84/4.02 Prover 1: Preprocessing ... % 14.53/4.14 Prover 1: Constructing countermodel ... % 14.76/4.20 Prover 1: gave up % 14.76/4.20 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 14.76/4.23 Prover 2: Preprocessing ... % 15.62/4.41 Prover 2: Warning: ignoring some quantifiers % 15.62/4.42 Prover 2: Constructing countermodel ... % 16.20/4.56 Prover 2: proved (358ms) % 16.20/4.56 % 16.20/4.56 No countermodel exists, formula is valid % 16.20/4.56 % SZS status Theorem for theBenchmark % 16.20/4.56 % 16.20/4.56 Generating proof ... Warning: ignoring some quantifiers % 21.08/5.62 found it (size 290) % 21.08/5.62 % 21.08/5.62 % SZS output start Proof for theBenchmark % 21.08/5.62 Assumed formulas after preprocessing and simplification: % 21.08/5.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v1) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v0, v4) = v5 & distinct_points(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ? [v11] : ((v11 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v6, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v7) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v8) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_lines(v9, v8) = v7) | ~ (orthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (incident_point_and_line(v9, v8) = v7) | ~ (incident_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_lines(v9, v8) = v7) | ~ (parallel_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_lines(v9, v8) = v7) | ~ (equal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_points(v9, v8) = v7) | ~ (equal_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (orthogonal_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (incident_point_and_line(v6, v7) = v8) | apart_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (parallel_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_lines(v6, v7) = v8) | distinct_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_points(v6, v7) = v8) | distinct_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | orthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v6, v7) = v8) | incident_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | parallel_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | equal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | equal_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (point(v8) = v7) | ~ (point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (line(v8) = v7) | ~ (line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & point(v8) = 0) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & point(v6) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (orthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (incident_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (parallel_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & orthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & incident_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & point(v8) = 0 & intersection_point(v6, v7) = v8) | ( ~ (v8 = 0) & line(v7) = v8) | ( ~ (v8 = 0) & line(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & parallel_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & line(v8) = 0 & line_connecting(v6, v7) = v8) | ( ~ (v8 = 0) & point(v7) = v8) | ( ~ (v8 = 0) & point(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_points(v6, v7) = v8)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : orthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : incident_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_points(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : orthogonal_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unorthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8 & ? [v6] : ? [v7] : point(v6) = v7 & ? [v6] : ? [v7] : line(v6) = v7) % 21.46/5.70 | 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: % 21.46/5.70 | (1) ~ (all_0_0_0 = 0) & line_connecting(all_0_3_3, all_0_4_4) = all_0_1_1 & line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 % 21.46/5.74 | % 21.46/5.74 | Applying alpha-rule on (1) yields: % 21.46/5.74 | (2) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 % 21.46/5.74 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) % 21.46/5.74 | (4) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 21.46/5.74 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) % 21.46/5.74 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 21.46/5.74 | (7) ! [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))) % 21.46/5.74 | (8) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) % 21.46/5.74 | (9) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 21.46/5.74 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 21.46/5.74 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 21.46/5.74 | (12) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 21.46/5.74 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 21.46/5.74 | (14) ! [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))) % 21.46/5.74 | (15) ! [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))) % 21.46/5.74 | (16) ~ (all_0_0_0 = 0) % 21.46/5.74 | (17) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 21.46/5.74 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 21.46/5.74 | (19) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) % 21.46/5.74 | (20) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 21.46/5.74 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 21.46/5.74 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) % 21.46/5.74 | (23) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 % 21.46/5.74 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) % 21.46/5.74 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 21.46/5.74 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 21.46/5.74 | (27) ! [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))) % 21.46/5.74 | (28) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 21.46/5.74 | (29) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 21.46/5.74 | (30) ! [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))) % 21.46/5.74 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 21.46/5.74 | (32) ! [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))) % 21.46/5.74 | (33) ! [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))) % 21.46/5.74 | (34) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 21.46/5.74 | (35) ! [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))) % 21.46/5.75 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 21.46/5.75 | (37) ! [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)) % 21.46/5.75 | (38) ! [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)) % 21.46/5.75 | (39) ! [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) % 21.46/5.75 | (40) ! [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)) % 21.46/5.75 | (41) ! [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))) % 21.46/5.75 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 21.46/5.75 | (43) ! [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)) % 21.46/5.75 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 21.46/5.75 | (45) ! [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))) % 21.46/5.75 | (46) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 21.46/5.75 | (47) ! [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))) % 21.46/5.75 | (48) ! [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))) % 21.46/5.75 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 21.46/5.75 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 21.46/5.75 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 21.46/5.75 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 21.46/5.75 | (53) ! [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))) % 21.46/5.75 | (54) ! [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)) % 21.46/5.75 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 21.46/5.75 | (56) ! [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))) % 21.46/5.75 | (57) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) % 21.46/5.75 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 21.46/5.75 | (59) apart_point_and_line(all_0_3_3, all_0_2_2) = 0 % 21.46/5.75 | (60) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 21.46/5.75 | (61) ! [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))) % 21.46/5.75 | (62) ! [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))) % 21.46/5.76 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 21.46/5.76 | (64) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 21.46/5.76 | (65) apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0 % 21.46/5.76 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) % 21.46/5.76 | (67) line_connecting(all_0_3_3, all_0_4_4) = all_0_1_1 % 21.46/5.76 | (68) ! [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))) % 21.46/5.76 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 21.46/5.76 | (70) ! [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))) % 21.46/5.76 | (71) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 % 21.46/5.76 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 21.46/5.76 | (73) ! [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) % 21.46/5.76 | (74) ! [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)) % 21.46/5.76 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) % 21.46/5.76 | (76) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 21.46/5.76 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 21.46/5.76 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 21.46/5.76 | (79) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 21.46/5.76 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) % 21.46/5.76 | (81) ! [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))) % 21.46/5.76 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) % 21.46/5.76 | (83) ! [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))) % 21.46/5.76 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 21.46/5.76 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 21.46/5.76 | (86) distinct_points(all_0_5_5, all_0_4_4) = 0 % 21.46/5.76 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 21.46/5.76 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) % 21.46/5.76 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 21.46/5.76 | (90) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 % 21.46/5.76 | (91) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) % 21.46/5.76 | (92) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 21.46/5.76 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 21.46/5.76 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 21.46/5.76 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 21.46/5.76 | (96) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 % 21.46/5.76 | (97) ! [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))) % 21.46/5.77 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 21.46/5.77 | (99) ! [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))) % 21.46/5.77 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 21.46/5.77 | (101) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 21.46/5.77 | (102) ? [v0] : ? [v1] : point(v0) = v1 % 21.46/5.77 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 21.46/5.77 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 21.46/5.77 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 21.46/5.77 | (106) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 % 21.46/5.77 | (107) ! [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))) % 21.46/5.77 | (108) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 21.46/5.77 | (109) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 21.46/5.77 | (110) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 21.46/5.77 | (111) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 21.46/5.77 | (112) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 21.46/5.77 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 21.46/5.77 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) % 21.46/5.77 | (115) ! [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))) % 21.46/5.77 | (116) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) % 21.46/5.77 | (117) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 21.46/5.77 | (118) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 21.46/5.77 | (119) ! [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))) % 21.46/5.77 | (120) ! [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))) % 21.46/5.77 | (121) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) % 21.46/5.77 | (122) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 21.46/5.77 | (123) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 21.46/5.77 | (124) ! [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))) % 21.46/5.77 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 21.46/5.77 | (126) ! [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) % 21.46/5.77 | (127) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 % 21.46/5.77 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 21.46/5.77 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) % 21.46/5.77 | (130) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 % 21.46/5.77 | (131) ! [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))) % 21.46/5.77 | (132) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) % 21.87/5.77 | (133) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 21.87/5.77 | (134) ! [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) % 21.87/5.77 | (135) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) % 21.87/5.77 | (136) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 21.87/5.77 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 21.87/5.77 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) % 21.87/5.77 | (139) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 21.87/5.77 | (140) ! [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))) % 21.87/5.77 | (141) ! [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))) % 21.87/5.77 | (142) ? [v0] : ? [v1] : line(v0) = v1 % 21.87/5.78 | (143) ! [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))) % 21.87/5.78 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 21.87/5.78 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 21.87/5.78 | % 21.87/5.78 | Instantiating formula (68) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_4_4) = all_0_1_1, yields: % 21.87/5.78 | (146) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0)) % 21.87/5.78 | % 21.87/5.78 | Instantiating formula (124) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_4_4) = all_0_1_1, yields: % 21.87/5.78 | (147) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0)) % 21.87/5.78 | % 21.87/5.78 | Instantiating formula (68) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 21.87/5.78 | (148) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 21.87/5.78 | % 21.87/5.78 | Instantiating formula (124) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 21.87/5.78 | (149) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 21.87/5.78 | % 21.87/5.78 | Instantiating formula (56) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 21.87/5.78 | (150) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0)) % 21.87/5.78 | % 21.87/5.78 | Instantiating formula (35) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_1_1, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 21.89/5.78 | (151) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 21.89/5.78 | % 21.89/5.78 | Instantiating formula (143) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 21.89/5.78 | (152) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0)) % 21.89/5.78 | % 21.89/5.78 | Instantiating formula (112) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 21.89/5.78 | (153) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1) % 21.89/5.78 | % 21.89/5.78 | Instantiating formula (79) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 21.89/5.78 | (154) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_5_5, v0) = v1) % 21.89/5.78 | % 21.89/5.78 | Instantiating (154) with all_43_0_55, all_43_1_56 yields: % 21.89/5.78 | (155) ~ (all_43_0_55 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_43_1_56 & apart_point_and_line(all_0_5_5, all_43_1_56) = all_43_0_55 % 21.89/5.78 | % 21.89/5.78 | Applying alpha-rule on (155) yields: % 21.89/5.78 | (156) ~ (all_43_0_55 = 0) % 21.89/5.78 | (157) line_connecting(all_0_5_5, all_0_4_4) = all_43_1_56 % 21.89/5.78 | (158) apart_point_and_line(all_0_5_5, all_43_1_56) = all_43_0_55 % 21.89/5.78 | % 21.89/5.78 | Instantiating (147) with all_48_0_59 yields: % 21.89/5.78 | (159) ( ~ (all_48_0_59 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59) | ( ~ (all_48_0_59 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_48_0_59) % 21.89/5.78 | % 21.89/5.78 | Instantiating (149) with all_49_0_60 yields: % 21.89/5.78 | (160) ( ~ (all_49_0_60 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_49_0_60) | ( ~ (all_49_0_60 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_49_0_60) % 21.89/5.78 | % 21.89/5.78 | Instantiating (146) with all_50_0_61 yields: % 21.89/5.78 | (161) ( ~ (all_50_0_61 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61) | ( ~ (all_50_0_61 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_50_0_61) % 21.89/5.78 | % 21.89/5.78 | Instantiating (153) with all_52_0_63, all_52_1_64 yields: % 21.89/5.78 | (162) ~ (all_52_0_63 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_52_1_64 & apart_point_and_line(all_0_4_4, all_52_1_64) = all_52_0_63 % 21.89/5.78 | % 21.89/5.78 | Applying alpha-rule on (162) yields: % 21.89/5.78 | (163) ~ (all_52_0_63 = 0) % 21.89/5.78 | (164) line_connecting(all_0_5_5, all_0_4_4) = all_52_1_64 % 21.89/5.78 | (165) apart_point_and_line(all_0_4_4, all_52_1_64) = all_52_0_63 % 21.89/5.78 | % 21.89/5.78 | Instantiating (148) with all_54_0_65 yields: % 21.89/5.78 | (166) ( ~ (all_54_0_65 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_54_0_65) | ( ~ (all_54_0_65 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_54_0_65) % 21.89/5.78 | % 21.89/5.78 +-Applying beta-rule and splitting (150), into two cases. % 21.89/5.78 |-Branch one: % 21.89/5.78 | (167) all_0_0_0 = 0 % 21.89/5.78 | % 21.89/5.78 | Equations (167) can reduce 16 to: % 21.89/5.78 | (168) $false % 21.89/5.78 | % 21.89/5.78 |-The branch is then unsatisfiable % 21.89/5.78 |-Branch two: % 21.89/5.78 | (16) ~ (all_0_0_0 = 0) % 21.89/5.78 | (170) ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0)) % 21.89/5.78 | % 21.89/5.78 +-Applying beta-rule and splitting (160), into two cases. % 21.89/5.78 |-Branch one: % 21.89/5.78 | (171) ~ (all_49_0_60 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_49_0_60 % 21.89/5.78 | % 21.89/5.78 | Applying alpha-rule on (171) yields: % 21.89/5.78 | (172) ~ (all_49_0_60 = 0) % 21.89/5.78 | (173) apart_point_and_line(all_0_5_5, all_0_2_2) = all_49_0_60 % 21.89/5.78 | % 21.89/5.78 +-Applying beta-rule and splitting (151), into two cases. % 21.89/5.78 |-Branch one: % 21.89/5.78 | (167) all_0_0_0 = 0 % 21.89/5.78 | % 21.89/5.78 | Equations (167) can reduce 16 to: % 21.89/5.78 | (168) $false % 21.89/5.78 | % 21.89/5.78 |-The branch is then unsatisfiable % 21.89/5.78 |-Branch two: % 21.89/5.78 | (16) ~ (all_0_0_0 = 0) % 21.89/5.78 | (177) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 21.89/5.78 | % 21.89/5.78 +-Applying beta-rule and splitting (166), into two cases. % 21.89/5.78 |-Branch one: % 21.89/5.78 | (178) ~ (all_54_0_65 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_54_0_65 % 21.89/5.78 | % 21.89/5.78 | Applying alpha-rule on (178) yields: % 21.89/5.78 | (179) ~ (all_54_0_65 = 0) % 21.89/5.78 | (180) apart_point_and_line(all_0_4_4, all_0_2_2) = all_54_0_65 % 21.89/5.78 | % 21.89/5.78 +-Applying beta-rule and splitting (152), into two cases. % 21.89/5.78 |-Branch one: % 21.89/5.78 | (167) all_0_0_0 = 0 % 21.89/5.78 | % 21.89/5.78 | Equations (167) can reduce 16 to: % 21.89/5.78 | (168) $false % 21.89/5.78 | % 21.89/5.78 |-The branch is then unsatisfiable % 21.89/5.78 |-Branch two: % 21.89/5.78 | (16) ~ (all_0_0_0 = 0) % 21.89/5.78 | (184) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0)) % 21.89/5.78 | % 21.89/5.78 | Instantiating formula (13) with all_0_5_5, all_0_4_4, all_52_1_64, all_0_2_2 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_52_1_64, line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 21.89/5.78 | (185) all_52_1_64 = all_0_2_2 % 21.89/5.78 | % 21.89/5.78 | Instantiating formula (13) with all_0_5_5, all_0_4_4, all_43_1_56, all_52_1_64 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_52_1_64, line_connecting(all_0_5_5, all_0_4_4) = all_43_1_56, yields: % 21.89/5.78 | (186) all_52_1_64 = all_43_1_56 % 21.89/5.78 | % 21.89/5.78 | Combining equations (185,186) yields a new equation: % 21.89/5.78 | (187) all_43_1_56 = all_0_2_2 % 21.89/5.78 | % 21.89/5.78 | Combining equations (187,186) yields a new equation: % 21.89/5.78 | (185) all_52_1_64 = all_0_2_2 % 21.89/5.78 | % 21.89/5.78 | From (185) and (165) follows: % 21.89/5.78 | (189) apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63 % 21.89/5.78 | % 21.89/5.78 | From (187) and (158) follows: % 21.89/5.78 | (190) apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55 % 21.89/5.78 | % 21.89/5.78 | Instantiating formula (104) with all_0_4_4, all_0_2_2, all_52_0_63, all_54_0_65 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_54_0_65, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.89/5.78 | (191) all_54_0_65 = all_52_0_63 % 21.89/5.78 | % 21.89/5.78 | Instantiating formula (104) with all_0_5_5, all_0_2_2, all_43_0_55, all_49_0_60 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_49_0_60, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.89/5.78 | (192) all_49_0_60 = all_43_0_55 % 21.89/5.78 | % 21.89/5.78 | Equations (191) can reduce 179 to: % 21.89/5.78 | (163) ~ (all_52_0_63 = 0) % 21.89/5.78 | % 21.89/5.78 | Equations (192) can reduce 172 to: % 21.89/5.78 | (156) ~ (all_43_0_55 = 0) % 21.89/5.78 | % 21.89/5.78 | From (191) and (180) follows: % 21.89/5.78 | (189) apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63 % 21.89/5.78 | % 21.89/5.78 | From (192) and (173) follows: % 21.89/5.78 | (190) apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55 % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (73) with all_52_0_63, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = 0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.89/5.79 | (197) all_52_0_63 = 0 | distinct_points(all_0_3_3, all_0_4_4) = 0 % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (35) with all_52_0_63, all_0_0_0, all_0_2_2, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 21.89/5.79 | (198) all_52_0_63 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (35) with all_0_0_0, all_52_0_63, all_0_1_1, 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_52_0_63, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 21.89/5.79 | (199) all_52_0_63 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (131) with all_52_0_63, all_0_0_0, all_0_1_1, 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_52_0_63, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 21.89/5.79 | (200) all_52_0_63 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (131) with all_0_0_0, all_52_0_63, all_0_2_2, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 21.89/5.79 | (201) all_52_0_63 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (115) with all_52_0_63, all_52_0_63, 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_52_0_63, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 21.89/5.79 | (202) all_52_0_63 = 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)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (56) with all_52_0_63, all_52_0_63, 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_52_0_63, yields: % 21.89/5.79 | (203) all_52_0_63 = 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)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (35) with all_52_0_63, all_52_0_63, 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_52_0_63, yields: % 21.89/5.79 | (204) all_52_0_63 = 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)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (143) with all_43_0_55, all_0_0_0, all_0_2_2, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 21.89/5.79 | (205) all_43_0_55 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (143) with all_0_0_0, all_43_0_55, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 21.89/5.79 | (206) all_43_0_55 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (56) with all_43_0_55, all_0_0_0, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.89/5.79 | (207) all_43_0_55 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (56) with all_0_0_0, all_43_0_55, all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.89/5.79 | (208) all_43_0_55 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (35) with all_43_0_55, all_0_0_0, all_0_2_2, all_0_1_1, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.89/5.79 | (209) all_43_0_55 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (35) with all_0_0_0, all_43_0_55, all_0_1_1, 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_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.89/5.79 | (210) all_43_0_55 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (35) with all_43_0_55, all_52_0_63, 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_52_0_63, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.89/5.79 | (211) all_52_0_63 = 0 | all_43_0_55 = 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)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (35) with all_52_0_63, all_43_0_55, 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_52_0_63, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.89/5.79 | (212) all_52_0_63 = 0 | all_43_0_55 = 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)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (143) with all_43_0_55, all_43_0_55, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 21.89/5.79 | (213) all_43_0_55 = 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)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (56) with all_43_0_55, all_43_0_55, 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_43_0_55, yields: % 21.89/5.79 | (214) all_43_0_55 = 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)) % 21.89/5.79 | % 21.89/5.79 | Instantiating formula (35) with all_43_0_55, all_43_0_55, 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_43_0_55, yields: % 21.89/5.79 | (215) all_43_0_55 = 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)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (214), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (216) all_43_0_55 = 0 % 21.89/5.79 | % 21.89/5.79 | Equations (216) can reduce 156 to: % 21.89/5.79 | (168) $false % 21.89/5.79 | % 21.89/5.79 |-The branch is then unsatisfiable % 21.89/5.79 |-Branch two: % 21.89/5.79 | (156) ~ (all_43_0_55 = 0) % 21.89/5.79 | (219) ? [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)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (197), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (220) distinct_points(all_0_3_3, all_0_4_4) = 0 % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (203), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (221) all_52_0_63 = 0 % 21.89/5.79 | % 21.89/5.79 | Equations (221) can reduce 163 to: % 21.89/5.79 | (168) $false % 21.89/5.79 | % 21.89/5.79 |-The branch is then unsatisfiable % 21.89/5.79 |-Branch two: % 21.89/5.79 | (163) ~ (all_52_0_63 = 0) % 21.89/5.79 | (219) ? [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)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (213), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (216) all_43_0_55 = 0 % 21.89/5.79 | % 21.89/5.79 | Equations (216) can reduce 156 to: % 21.89/5.79 | (168) $false % 21.89/5.79 | % 21.89/5.79 |-The branch is then unsatisfiable % 21.89/5.79 |-Branch two: % 21.89/5.79 | (156) ~ (all_43_0_55 = 0) % 21.89/5.79 | (228) ? [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)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (202), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (221) all_52_0_63 = 0 % 21.89/5.79 | % 21.89/5.79 | Equations (221) can reduce 163 to: % 21.89/5.79 | (168) $false % 21.89/5.79 | % 21.89/5.79 |-The branch is then unsatisfiable % 21.89/5.79 |-Branch two: % 21.89/5.79 | (163) ~ (all_52_0_63 = 0) % 21.89/5.79 | (232) ? [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)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (201), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (221) all_52_0_63 = 0 % 21.89/5.79 | % 21.89/5.79 | Equations (221) can reduce 163 to: % 21.89/5.79 | (168) $false % 21.89/5.79 | % 21.89/5.79 |-The branch is then unsatisfiable % 21.89/5.79 |-Branch two: % 21.89/5.79 | (163) ~ (all_52_0_63 = 0) % 21.89/5.79 | (236) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (204), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (221) all_52_0_63 = 0 % 21.89/5.79 | % 21.89/5.79 | Equations (221) can reduce 163 to: % 21.89/5.79 | (168) $false % 21.89/5.79 | % 21.89/5.79 |-The branch is then unsatisfiable % 21.89/5.79 |-Branch two: % 21.89/5.79 | (163) ~ (all_52_0_63 = 0) % 21.89/5.79 | (240) ? [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)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (199), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (221) all_52_0_63 = 0 % 21.89/5.79 | % 21.89/5.79 | Equations (221) can reduce 163 to: % 21.89/5.79 | (168) $false % 21.89/5.79 | % 21.89/5.79 |-The branch is then unsatisfiable % 21.89/5.79 |-Branch two: % 21.89/5.79 | (163) ~ (all_52_0_63 = 0) % 21.89/5.79 | (244) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (200), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (221) all_52_0_63 = 0 % 21.89/5.79 | % 21.89/5.79 | Equations (221) can reduce 163 to: % 21.89/5.79 | (168) $false % 21.89/5.79 | % 21.89/5.79 |-The branch is then unsatisfiable % 21.89/5.79 |-Branch two: % 21.89/5.79 | (163) ~ (all_52_0_63 = 0) % 21.89/5.79 | (248) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 21.89/5.79 | % 21.89/5.79 +-Applying beta-rule and splitting (198), into two cases. % 21.89/5.79 |-Branch one: % 21.89/5.79 | (221) all_52_0_63 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (221) can reduce 163 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (163) ~ (all_52_0_63 = 0) % 21.89/5.80 | (252) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (159), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (253) ~ (all_48_0_59 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59 % 21.89/5.80 | % 21.89/5.80 | Applying alpha-rule on (253) yields: % 21.89/5.80 | (254) ~ (all_48_0_59 = 0) % 21.89/5.80 | (255) apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59 % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (248), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (167) all_0_0_0 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (167) can reduce 16 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (16) ~ (all_0_0_0 = 0) % 21.89/5.80 | (259) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)) % 21.89/5.80 | % 21.89/5.80 | Instantiating (259) with all_145_0_88 yields: % 21.89/5.80 | (260) (all_145_0_88 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_145_0_88 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (all_145_0_88 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_145_0_88) | ( ~ (all_145_0_88 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_145_0_88) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (161), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (261) ~ (all_50_0_61 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61 % 21.89/5.80 | % 21.89/5.80 | Applying alpha-rule on (261) yields: % 21.89/5.80 | (262) ~ (all_50_0_61 = 0) % 21.89/5.80 | (263) apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61 % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (207), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (216) all_43_0_55 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (216) can reduce 156 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (156) ~ (all_43_0_55 = 0) % 21.89/5.80 | (267) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (208), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (216) all_43_0_55 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (216) can reduce 156 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (156) ~ (all_43_0_55 = 0) % 21.89/5.80 | (271) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0)) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (209), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (216) all_43_0_55 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (216) can reduce 156 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (156) ~ (all_43_0_55 = 0) % 21.89/5.80 | (275) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (210), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (216) all_43_0_55 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (216) can reduce 156 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (156) ~ (all_43_0_55 = 0) % 21.89/5.80 | (279) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (260), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (280) (all_145_0_88 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_145_0_88 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (all_145_0_88 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_145_0_88) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (280), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (281) (all_145_0_88 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_145_0_88 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (281), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (282) all_145_0_88 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0 % 21.89/5.80 | % 21.89/5.80 | Applying alpha-rule on (282) yields: % 21.89/5.80 | (283) all_145_0_88 = 0 % 21.89/5.80 | (284) apart_point_and_line(all_0_4_4, all_0_1_1) = 0 % 21.89/5.80 | % 21.89/5.80 | Instantiating formula (104) with all_0_4_4, all_0_1_1, 0, all_50_0_61 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, apart_point_and_line(all_0_4_4, all_0_1_1) = 0, yields: % 21.89/5.80 | (285) all_50_0_61 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (285) can reduce 262 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (287) all_145_0_88 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0 % 21.89/5.80 | % 21.89/5.80 | Applying alpha-rule on (287) yields: % 21.89/5.80 | (283) all_145_0_88 = 0 % 21.89/5.80 | (289) apart_point_and_line(all_0_5_5, all_0_2_2) = 0 % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (215), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (216) all_43_0_55 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (216) can reduce 156 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (156) ~ (all_43_0_55 = 0) % 21.89/5.80 | (293) ? [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)) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (211), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (221) all_52_0_63 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (221) can reduce 163 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (163) ~ (all_52_0_63 = 0) % 21.89/5.80 | (297) all_43_0_55 = 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)) % 21.89/5.80 | % 21.89/5.80 +-Applying beta-rule and splitting (205), into two cases. % 21.89/5.80 |-Branch one: % 21.89/5.80 | (216) all_43_0_55 = 0 % 21.89/5.80 | % 21.89/5.80 | Equations (216) can reduce 156 to: % 21.89/5.80 | (168) $false % 21.89/5.80 | % 21.89/5.80 |-The branch is then unsatisfiable % 21.89/5.80 |-Branch two: % 21.89/5.80 | (156) ~ (all_43_0_55 = 0) % 21.89/5.80 | (301) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)) % 21.99/5.80 | % 21.99/5.80 +-Applying beta-rule and splitting (206), into two cases. % 21.99/5.80 |-Branch one: % 21.99/5.80 | (216) all_43_0_55 = 0 % 21.99/5.80 | % 21.99/5.80 | Equations (216) can reduce 156 to: % 21.99/5.80 | (168) $false % 21.99/5.80 | % 21.99/5.80 |-The branch is then unsatisfiable % 21.99/5.80 |-Branch two: % 21.99/5.80 | (156) ~ (all_43_0_55 = 0) % 21.99/5.80 | (305) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0)) % 21.99/5.80 | % 21.99/5.80 +-Applying beta-rule and splitting (212), into two cases. % 21.99/5.80 |-Branch one: % 21.99/5.80 | (221) all_52_0_63 = 0 % 21.99/5.80 | % 21.99/5.80 | Equations (221) can reduce 163 to: % 21.99/5.80 | (168) $false % 21.99/5.80 | % 21.99/5.80 |-The branch is then unsatisfiable % 21.99/5.80 |-Branch two: % 21.99/5.80 | (163) ~ (all_52_0_63 = 0) % 21.99/5.80 | (309) all_43_0_55 = 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)) % 21.99/5.80 | % 21.99/5.80 +-Applying beta-rule and splitting (297), into two cases. % 21.99/5.80 |-Branch one: % 21.99/5.80 | (216) all_43_0_55 = 0 % 21.99/5.80 | % 21.99/5.80 | Equations (216) can reduce 156 to: % 21.99/5.80 | (168) $false % 21.99/5.80 | % 21.99/5.80 |-The branch is then unsatisfiable % 21.99/5.80 |-Branch two: % 21.99/5.80 | (156) ~ (all_43_0_55 = 0) % 21.99/5.80 | (313) ? [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)) % 21.99/5.80 | % 21.99/5.80 +-Applying beta-rule and splitting (309), into two cases. % 21.99/5.80 |-Branch one: % 21.99/5.80 | (216) all_43_0_55 = 0 % 21.99/5.80 | % 21.99/5.80 | Equations (216) can reduce 156 to: % 21.99/5.80 | (168) $false % 21.99/5.80 | % 21.99/5.80 |-The branch is then unsatisfiable % 21.99/5.80 |-Branch two: % 21.99/5.80 | (156) ~ (all_43_0_55 = 0) % 21.99/5.80 | (317) ? [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)) % 21.99/5.80 | % 21.99/5.80 | Instantiating formula (104) with all_0_5_5, all_0_2_2, 0, all_43_0_55 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields: % 21.99/5.80 | (216) all_43_0_55 = 0 % 21.99/5.80 | % 21.99/5.80 | Equations (216) can reduce 156 to: % 21.99/5.80 | (168) $false % 21.99/5.80 | % 21.99/5.80 |-The branch is then unsatisfiable % 21.99/5.80 |-Branch two: % 21.99/5.80 | (320) ~ (all_145_0_88 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_145_0_88 % 21.99/5.80 | % 21.99/5.80 | Applying alpha-rule on (320) yields: % 21.99/5.80 | (321) ~ (all_145_0_88 = 0) % 21.99/5.80 | (322) distinct_lines(all_0_2_2, all_0_1_1) = all_145_0_88 % 21.99/5.80 | % 21.99/5.80 +-Applying beta-rule and splitting (211), into two cases. % 21.99/5.80 |-Branch one: % 21.99/5.80 | (221) all_52_0_63 = 0 % 21.99/5.80 | % 21.99/5.80 | Equations (221) can reduce 163 to: % 21.99/5.80 | (168) $false % 21.99/5.80 | % 21.99/5.80 |-The branch is then unsatisfiable % 21.99/5.80 |-Branch two: % 21.99/5.80 | (163) ~ (all_52_0_63 = 0) % 21.99/5.80 | (297) all_43_0_55 = 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)) % 21.99/5.80 | % 21.99/5.80 | Instantiating formula (35) with all_48_0_59, all_52_0_63, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.99/5.80 | (327) all_52_0_63 = 0 | all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 21.99/5.80 | % 21.99/5.80 | Instantiating formula (35) with all_52_0_63, all_48_0_59, all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.99/5.81 | (328) all_52_0_63 = 0 | all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (131) with all_48_0_59, all_52_0_63, all_0_2_2, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.99/5.81 | (329) all_52_0_63 = 0 | all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (131) with all_52_0_63, all_48_0_59, all_0_1_1, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.99/5.81 | (330) all_52_0_63 = 0 | all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_48_0_59, all_0_0_0, all_0_1_1, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 21.99/5.81 | (331) all_48_0_59 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_48_0_59, all_43_0_55, all_0_1_1, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.99/5.81 | (332) all_48_0_59 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_43_0_55, all_48_0_59, all_0_2_2, all_0_1_1, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.99/5.81 | (333) all_48_0_59 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (131) with all_48_0_59, all_43_0_55, all_0_2_2, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.99/5.81 | (334) all_48_0_59 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (131) with all_43_0_55, all_48_0_59, all_0_1_1, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.99/5.81 | (335) all_48_0_59 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (56) with all_48_0_59, all_48_0_59, all_0_1_1, all_0_1_1, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, yields: % 21.99/5.81 | (336) all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_48_0_59, all_48_0_59, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, yields: % 21.99/5.81 | (337) all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (56) with all_50_0_61, all_52_0_63, all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.99/5.81 | (338) all_52_0_63 = 0 | all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (56) with all_52_0_63, all_50_0_61, all_0_2_2, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.99/5.81 | (339) all_52_0_63 = 0 | all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_50_0_61, all_52_0_63, all_0_1_1, 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_1_1) = all_50_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.99/5.81 | (340) all_52_0_63 = 0 | all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_52_0_63, all_50_0_61, all_0_2_2, all_0_1_1, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, yields: % 21.99/5.81 | (341) all_52_0_63 = 0 | all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_0_0_0, all_50_0_61, all_0_1_1, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 21.99/5.81 | (342) all_50_0_61 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_43_0_55, all_50_0_61, all_0_2_2, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.99/5.81 | (343) all_50_0_61 = 0 | all_43_0_55 = 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_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (131) with all_43_0_55, all_50_0_61, all_0_1_1, 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_1_1) = all_50_0_61, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields: % 21.99/5.81 | (344) all_50_0_61 = 0 | all_43_0_55 = 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_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (35) with all_48_0_59, all_50_0_61, all_0_1_1, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, yields: % 21.99/5.81 | (345) all_50_0_61 = 0 | all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (56) with all_50_0_61, all_50_0_61, all_0_1_1, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, yields: % 21.99/5.81 | (346) all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (126) with all_145_0_88, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = 0, distinct_lines(all_0_2_2, all_0_1_1) = all_145_0_88, yields: % 21.99/5.81 | (347) all_145_0_88 = 0 | apart_point_and_line(all_0_3_3, all_0_1_1) = 0 % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (54) with all_48_0_59, all_145_0_88, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, distinct_lines(all_0_2_2, all_0_1_1) = all_145_0_88, yields: % 21.99/5.81 | (348) all_145_0_88 = 0 | all_48_0_59 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = v0) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (115) with all_52_0_63, all_52_0_63, all_0_2_2, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, distinct_points(all_0_3_3, all_0_4_4) = 0, yields: % 21.99/5.81 | (349) all_52_0_63 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (115) with all_52_0_63, all_50_0_61, all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, distinct_points(all_0_3_3, all_0_4_4) = 0, yields: % 21.99/5.81 | (350) all_52_0_63 = 0 | all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)) % 21.99/5.81 | % 21.99/5.81 | Instantiating formula (115) with all_50_0_61, all_52_0_63, all_0_1_1, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_52_0_63, distinct_points(all_0_3_3, all_0_4_4) = 0, yields: % 21.99/5.81 | (351) all_52_0_63 = 0 | all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0)) % 21.99/5.81 | % 21.99/5.81 +-Applying beta-rule and splitting (336), into two cases. % 21.99/5.81 |-Branch one: % 21.99/5.81 | (352) all_48_0_59 = 0 % 21.99/5.81 | % 21.99/5.81 | Equations (352) can reduce 254 to: % 21.99/5.81 | (168) $false % 21.99/5.81 | % 21.99/5.81 |-The branch is then unsatisfiable % 21.99/5.81 |-Branch two: % 21.99/5.81 | (254) ~ (all_48_0_59 = 0) % 21.99/5.81 | (170) ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0)) % 21.99/5.81 | % 21.99/5.82 +-Applying beta-rule and splitting (347), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (356) apart_point_and_line(all_0_3_3, all_0_1_1) = 0 % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (346), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (285) all_50_0_61 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (285) can reduce 262 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (262) ~ (all_50_0_61 = 0) % 21.99/5.82 | (170) ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (349), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (221) all_52_0_63 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (221) can reduce 163 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (163) ~ (all_52_0_63 = 0) % 21.99/5.82 | (364) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (337), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (352) all_48_0_59 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (352) can reduce 254 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (254) ~ (all_48_0_59 = 0) % 21.99/5.82 | (368) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (338), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (221) all_52_0_63 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (221) can reduce 163 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (163) ~ (all_52_0_63 = 0) % 21.99/5.82 | (372) all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (341), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (221) all_52_0_63 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (221) can reduce 163 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (163) ~ (all_52_0_63 = 0) % 21.99/5.82 | (376) all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (342), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (285) all_50_0_61 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (285) can reduce 262 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (262) ~ (all_50_0_61 = 0) % 21.99/5.82 | (380) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (343), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (285) all_50_0_61 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (285) can reduce 262 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (262) ~ (all_50_0_61 = 0) % 21.99/5.82 | (384) all_43_0_55 = 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_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (344), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (285) all_50_0_61 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (285) can reduce 262 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (262) ~ (all_50_0_61 = 0) % 21.99/5.82 | (388) all_43_0_55 = 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_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (350), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (221) all_52_0_63 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (221) can reduce 163 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (163) ~ (all_52_0_63 = 0) % 21.99/5.82 | (392) all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (345), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (285) all_50_0_61 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (285) can reduce 262 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (262) ~ (all_50_0_61 = 0) % 21.99/5.82 | (396) all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 21.99/5.82 | % 21.99/5.82 +-Applying beta-rule and splitting (396), into two cases. % 21.99/5.82 |-Branch one: % 21.99/5.82 | (352) all_48_0_59 = 0 % 21.99/5.82 | % 21.99/5.82 | Equations (352) can reduce 254 to: % 21.99/5.82 | (168) $false % 21.99/5.82 | % 21.99/5.82 |-The branch is then unsatisfiable % 21.99/5.82 |-Branch two: % 21.99/5.82 | (254) ~ (all_48_0_59 = 0) % 22.07/5.82 | (400) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (348), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (283) all_145_0_88 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (283) can reduce 321 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (321) ~ (all_145_0_88 = 0) % 22.07/5.82 | (404) all_48_0_59 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = v0) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (339), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (221) all_52_0_63 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (221) can reduce 163 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (163) ~ (all_52_0_63 = 0) % 22.07/5.82 | (408) all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (351), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (221) all_52_0_63 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (221) can reduce 163 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (163) ~ (all_52_0_63 = 0) % 22.07/5.82 | (412) all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0)) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (327), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (221) all_52_0_63 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (221) can reduce 163 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (163) ~ (all_52_0_63 = 0) % 22.07/5.82 | (416) all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (332), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (352) all_48_0_59 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (352) can reduce 254 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (254) ~ (all_48_0_59 = 0) % 22.07/5.82 | (420) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0)) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (330), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (221) all_52_0_63 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (221) can reduce 163 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (163) ~ (all_52_0_63 = 0) % 22.07/5.82 | (424) all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0)) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (331), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (352) all_48_0_59 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (352) can reduce 254 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (254) ~ (all_48_0_59 = 0) % 22.07/5.82 | (428) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0)) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (333), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (352) all_48_0_59 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (352) can reduce 254 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (254) ~ (all_48_0_59 = 0) % 22.07/5.82 | (432) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0)) % 22.07/5.82 | % 22.07/5.82 +-Applying beta-rule and splitting (340), into two cases. % 22.07/5.82 |-Branch one: % 22.07/5.82 | (221) all_52_0_63 = 0 % 22.07/5.82 | % 22.07/5.82 | Equations (221) can reduce 163 to: % 22.07/5.82 | (168) $false % 22.07/5.82 | % 22.07/5.82 |-The branch is then unsatisfiable % 22.07/5.82 |-Branch two: % 22.07/5.82 | (163) ~ (all_52_0_63 = 0) % 22.07/5.82 | (436) all_50_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)) % 22.07/5.82 | % 22.07/5.83 +-Applying beta-rule and splitting (404), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (254) ~ (all_48_0_59 = 0) % 22.07/5.83 | (440) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = v0) % 22.07/5.83 | % 22.07/5.83 +-Applying beta-rule and splitting (328), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (221) all_52_0_63 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (221) can reduce 163 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (163) ~ (all_52_0_63 = 0) % 22.07/5.83 | (444) all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0)) % 22.07/5.83 | % 22.07/5.83 +-Applying beta-rule and splitting (329), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (221) all_52_0_63 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (221) can reduce 163 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (163) ~ (all_52_0_63 = 0) % 22.07/5.83 | (448) all_48_0_59 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 22.07/5.83 | % 22.07/5.83 +-Applying beta-rule and splitting (334), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (254) ~ (all_48_0_59 = 0) % 22.07/5.83 | (452) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0)) % 22.07/5.83 | % 22.07/5.83 +-Applying beta-rule and splitting (335), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (254) ~ (all_48_0_59 = 0) % 22.07/5.83 | (456) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0)) % 22.07/5.83 | % 22.07/5.83 +-Applying beta-rule and splitting (416), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (254) ~ (all_48_0_59 = 0) % 22.07/5.83 | (460) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 22.07/5.83 | % 22.07/5.83 +-Applying beta-rule and splitting (424), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (254) ~ (all_48_0_59 = 0) % 22.07/5.83 | (464) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0)) % 22.07/5.83 | % 22.07/5.83 +-Applying beta-rule and splitting (444), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (254) ~ (all_48_0_59 = 0) % 22.07/5.83 | (468) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0)) % 22.07/5.83 | % 22.07/5.83 +-Applying beta-rule and splitting (448), into two cases. % 22.07/5.83 |-Branch one: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (254) ~ (all_48_0_59 = 0) % 22.07/5.83 | (472) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0)) % 22.07/5.83 | % 22.07/5.83 | Instantiating formula (104) with all_0_3_3, all_0_1_1, 0, all_48_0_59 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_48_0_59, apart_point_and_line(all_0_3_3, all_0_1_1) = 0, yields: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (475) ~ (apart_point_and_line(all_0_3_3, all_0_1_1) = 0) % 22.07/5.83 | (283) all_145_0_88 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (283) can reduce 321 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (478) ~ (all_145_0_88 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_145_0_88 % 22.07/5.83 | % 22.07/5.83 | Applying alpha-rule on (478) yields: % 22.07/5.83 | (321) ~ (all_145_0_88 = 0) % 22.07/5.83 | (480) distinct_points(all_0_5_5, all_0_4_4) = all_145_0_88 % 22.07/5.83 | % 22.07/5.83 | Instantiating formula (18) with all_0_5_5, all_0_4_4, all_145_0_88, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_145_0_88, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 22.07/5.83 | (283) all_145_0_88 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (283) can reduce 321 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (483) ~ (all_50_0_61 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_50_0_61 % 22.07/5.83 | % 22.07/5.83 | Applying alpha-rule on (483) yields: % 22.07/5.83 | (262) ~ (all_50_0_61 = 0) % 22.07/5.83 | (485) distinct_points(all_0_3_3, all_0_4_4) = all_50_0_61 % 22.07/5.83 | % 22.07/5.83 | Instantiating formula (18) with all_0_3_3, all_0_4_4, 0, all_50_0_61 and discharging atoms distinct_points(all_0_3_3, all_0_4_4) = all_50_0_61, distinct_points(all_0_3_3, all_0_4_4) = 0, yields: % 22.07/5.83 | (285) all_50_0_61 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (285) can reduce 262 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (488) ~ (all_48_0_59 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_48_0_59 % 22.07/5.83 | % 22.07/5.83 | Applying alpha-rule on (488) yields: % 22.07/5.83 | (254) ~ (all_48_0_59 = 0) % 22.07/5.83 | (490) distinct_points(all_0_3_3, all_0_4_4) = all_48_0_59 % 22.07/5.83 | % 22.07/5.83 | Instantiating formula (18) with all_0_3_3, all_0_4_4, 0, all_48_0_59 and discharging atoms distinct_points(all_0_3_3, all_0_4_4) = all_48_0_59, distinct_points(all_0_3_3, all_0_4_4) = 0, yields: % 22.07/5.83 | (352) all_48_0_59 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (352) can reduce 254 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (493) ~ (distinct_points(all_0_3_3, all_0_4_4) = 0) % 22.07/5.83 | (221) all_52_0_63 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (221) can reduce 163 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (496) ~ (all_54_0_65 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_54_0_65 % 22.07/5.83 | % 22.07/5.83 | Applying alpha-rule on (496) yields: % 22.07/5.83 | (179) ~ (all_54_0_65 = 0) % 22.07/5.83 | (498) distinct_points(all_0_5_5, all_0_4_4) = all_54_0_65 % 22.07/5.83 | % 22.07/5.83 | Instantiating formula (18) with all_0_5_5, all_0_4_4, all_54_0_65, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_54_0_65, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 22.07/5.83 | (499) all_54_0_65 = 0 % 22.07/5.83 | % 22.07/5.83 | Equations (499) can reduce 179 to: % 22.07/5.83 | (168) $false % 22.07/5.83 | % 22.07/5.83 |-The branch is then unsatisfiable % 22.07/5.83 |-Branch two: % 22.07/5.83 | (501) ~ (all_49_0_60 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_49_0_60 % 22.07/5.83 | % 22.07/5.83 | Applying alpha-rule on (501) yields: % 22.07/5.83 | (172) ~ (all_49_0_60 = 0) % 22.07/5.83 | (503) distinct_points(all_0_5_5, all_0_4_4) = all_49_0_60 % 22.07/5.84 | % 22.07/5.84 | Instantiating formula (18) with all_0_5_5, all_0_4_4, all_49_0_60, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_49_0_60, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 22.07/5.84 | (504) all_49_0_60 = 0 % 22.07/5.84 | % 22.07/5.84 | Equations (504) can reduce 172 to: % 22.07/5.84 | (168) $false % 22.07/5.84 | % 22.07/5.84 |-The branch is then unsatisfiable % 22.07/5.84 % SZS output end Proof for theBenchmark % 22.07/5.84 % 22.07/5.84 5192ms %------------------------------------------------------------------------------