%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO219+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n013.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 03:48:52 EDT 2022 % Result : Theorem 6.31s 2.11s % Output : Proof 9.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO219+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n013.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 13:28:14 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.70/0.93 Prover 0: Preprocessing ... % 2.02/1.08 Prover 0: Warning: ignoring some quantifiers % 2.02/1.10 Prover 0: Constructing countermodel ... % 4.38/1.68 Prover 0: gave up % 4.38/1.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.57/1.70 Prover 1: Preprocessing ... % 4.94/1.79 Prover 1: Constructing countermodel ... % 5.32/1.86 Prover 1: gave up % 5.32/1.86 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.32/1.88 Prover 2: Preprocessing ... % 5.86/2.00 Prover 2: Warning: ignoring some quantifiers % 5.86/2.01 Prover 2: Constructing countermodel ... % 6.31/2.11 Prover 2: proved (253ms) % 6.31/2.11 % 6.31/2.11 No countermodel exists, formula is valid % 6.31/2.11 % SZS status Theorem for theBenchmark % 6.31/2.11 % 6.31/2.11 Generating proof ... Warning: ignoring some quantifiers % 8.50/2.65 found it (size 104) % 8.50/2.65 % 8.50/2.65 % SZS output start Proof for theBenchmark % 8.50/2.65 Assumed formulas after preprocessing and simplification: % 8.50/2.65 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = 0 & unorthogonal_lines(v0, v1) = v3 & convergent_lines(v0, v2) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v5, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v5, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v7, v6) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (convergent_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v5, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v5, v7) = v9) | ~ (convergent_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = 0) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = 0) | unorthogonal_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v7, v6) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | apart_point_and_line(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_points(v5, v7) = v8) | apart_point_and_line(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (unorthogonal_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v6, v8) = 0) | (v9 = 0 & apart_point_and_line(v6, v7) = 0) | (v9 = 0 & apart_point_and_line(v5, v8) = 0) | (v9 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v6) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v5) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v6, v7) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : unorthogonal_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : line_connecting(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : apart_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_points(v6, v5) = v7) % 9.04/2.71 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 9.04/2.71 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_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) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = 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(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, 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(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, 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 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(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) = 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) | ~ (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, 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] : ( ~ (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] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 9.23/2.73 | % 9.23/2.73 | Applying alpha-rule on (1) yields: % 9.23/2.73 | (2) ~ (all_0_1_1 = 0) % 9.23/2.73 | (3) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 9.23/2.73 | (4) ! [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)) % 9.23/2.73 | (5) ! [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))) % 9.23/2.73 | (6) ! [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))) % 9.23/2.73 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 9.23/2.73 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 9.23/2.73 | (9) ! [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))) % 9.23/2.73 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 9.23/2.73 | (11) ! [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))) % 9.23/2.73 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 9.23/2.73 | (13) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 9.23/2.73 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 9.23/2.73 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 9.23/2.73 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 9.23/2.74 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 9.23/2.74 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 9.23/2.74 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 9.23/2.74 | (20) ! [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))) % 9.29/2.74 | (21) ! [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))) % 9.29/2.74 | (22) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 9.29/2.74 | (23) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 9.29/2.74 | (24) ! [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))) % 9.29/2.74 | (25) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 9.29/2.74 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 9.29/2.74 | (27) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 9.29/2.74 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 9.29/2.74 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 9.29/2.74 | (30) ~ (all_0_0_0 = 0) % 9.29/2.74 | (31) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 9.29/2.74 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 9.29/2.74 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 9.29/2.74 | (34) ! [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))) % 9.29/2.74 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 9.29/2.74 | (36) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 9.29/2.74 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 9.29/2.74 | (38) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 9.29/2.74 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 9.29/2.74 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 9.29/2.74 | (41) ! [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))) % 9.29/2.74 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 9.29/2.74 | (43) convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0 % 9.29/2.74 | (44) ! [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))) % 9.29/2.74 | (45) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 9.29/2.74 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 9.29/2.74 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 9.29/2.74 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 9.29/2.75 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 9.29/2.75 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 9.29/2.75 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 9.29/2.75 | (52) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 9.29/2.75 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 9.29/2.75 | (54) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 % 9.29/2.75 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 9.29/2.75 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 9.29/2.75 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) % 9.29/2.75 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) % 9.29/2.75 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 9.29/2.75 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) % 9.29/2.75 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 9.29/2.75 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 9.29/2.75 | (63) ! [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))) % 9.29/2.75 | (64) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1 % 9.29/2.75 | (65) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 9.29/2.75 | (66) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 9.29/2.75 | (67) ! [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))) % 9.29/2.75 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) % 9.29/2.75 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 9.29/2.75 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) % 9.29/2.75 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 9.29/2.75 | (72) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 9.29/2.75 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) % 9.29/2.75 | % 9.29/2.75 | Instantiating formula (21) with 0, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields: % 9.29/2.75 | (74) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 9.29/2.75 | % 9.29/2.75 | Instantiating formula (20) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 9.29/2.75 | (75) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 9.29/2.75 | % 9.29/2.75 | Instantiating formula (4) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 9.29/2.75 | (76) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0) % 9.29/2.75 | % 9.29/2.75 | Instantiating formula (62) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 9.29/2.75 | (77) all_0_1_1 = 0 | convergent_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.75 | % 9.29/2.75 | Instantiating formula (29) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields: % 9.29/2.75 | (78) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 9.29/2.75 | % 9.29/2.75 | Instantiating formula (24) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields: % 9.29/2.75 | (79) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 9.29/2.75 | % 9.29/2.75 | Instantiating formula (9) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields: % 9.29/2.75 | (80) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 9.29/2.75 | % 9.29/2.75 | Instantiating (80) with all_22_0_26 yields: % 9.29/2.75 | (81) (all_22_0_26 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_22_0_26 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26) | ( ~ (all_22_0_26 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26) % 9.29/2.76 | % 9.29/2.76 | Instantiating (75) with all_25_0_29, all_25_1_30 yields: % 9.29/2.76 | (82) (all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_25_1_30 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_25_1_30 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30) % 9.29/2.76 | % 9.29/2.76 | Instantiating (74) with all_26_0_31, all_26_1_32 yields: % 9.29/2.76 | (83) (all_26_0_31 = 0 & all_26_1_32 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_26_1_32 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_26_1_32 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32) % 9.29/2.76 | % 9.29/2.76 | Instantiating (79) with all_29_0_35, all_29_1_36 yields: % 9.29/2.76 | (84) (all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_29_1_36 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_29_1_36 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36) % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (77), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (85) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (84), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (86) (all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_29_1_36 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (86), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (87) all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (87) yields: % 9.29/2.76 | (88) all_29_0_35 = 0 % 9.29/2.76 | (89) all_29_1_36 = 0 % 9.29/2.76 | (90) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.76 | (85) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (76), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (92) all_0_1_1 = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (92) can reduce 2 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (2) ~ (all_0_1_1 = 0) % 9.29/2.76 | (95) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0) % 9.29/2.76 | % 9.29/2.76 | Instantiating formula (39) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields: % 9.29/2.76 | (92) all_0_1_1 = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (92) can reduce 2 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (98) all_29_1_36 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (98) yields: % 9.29/2.76 | (89) all_29_1_36 = 0 % 9.29/2.76 | (100) all_0_0_0 = 0 % 9.29/2.76 | (101) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (100) can reduce 30 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (103) ~ (all_29_1_36 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (103) yields: % 9.29/2.76 | (104) ~ (all_29_1_36 = 0) % 9.29/2.76 | (105) convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36 % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (82), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (106) (all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_25_1_30 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (106), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (107) all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (107) yields: % 9.29/2.76 | (108) all_25_0_29 = 0 % 9.29/2.76 | (109) all_25_1_30 = 0 % 9.29/2.76 | (101) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.76 | (111) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (78), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (100) all_0_0_0 = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (100) can reduce 30 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (30) ~ (all_0_0_0 = 0) % 9.29/2.76 | (115) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 9.29/2.76 | % 9.29/2.76 | Instantiating formula (7) with all_0_4_4, all_0_2_2, 0, all_0_0_0 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields: % 9.29/2.76 | (100) all_0_0_0 = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (100) can reduce 30 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (118) all_25_1_30 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (118) yields: % 9.29/2.76 | (109) all_25_1_30 = 0 % 9.29/2.76 | (92) all_0_1_1 = 0 % 9.29/2.76 | (85) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (92) can reduce 2 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (123) ~ (all_25_1_30 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (123) yields: % 9.29/2.76 | (124) ~ (all_25_1_30 = 0) % 9.29/2.76 | (125) convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30 % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (78), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (100) all_0_0_0 = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (100) can reduce 30 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (30) ~ (all_0_0_0 = 0) % 9.29/2.76 | (115) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (81), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (130) (all_22_0_26 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_22_0_26 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26) % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (130), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (131) (all_22_0_26 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_22_0_26 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 9.29/2.76 | % 9.29/2.76 +-Applying beta-rule and splitting (131), into two cases. % 9.29/2.76 |-Branch one: % 9.29/2.76 | (132) all_22_0_26 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (132) yields: % 9.29/2.76 | (133) all_22_0_26 = 0 % 9.29/2.76 | (100) all_0_0_0 = 0 % 9.29/2.76 | (101) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (100) can reduce 30 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (137) all_22_0_26 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (137) yields: % 9.29/2.76 | (133) all_22_0_26 = 0 % 9.29/2.76 | (92) all_0_1_1 = 0 % 9.29/2.76 | (85) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (92) can reduce 2 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (142) ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (142) yields: % 9.29/2.76 | (143) ~ (all_22_0_26 = 0) % 9.29/2.76 | (144) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26 % 9.29/2.76 | % 9.29/2.76 | Instantiating formula (39) with all_0_3_3, all_0_2_2, all_22_0_26, 0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields: % 9.29/2.76 | (133) all_22_0_26 = 0 % 9.29/2.76 | % 9.29/2.76 | Equations (133) can reduce 143 to: % 9.29/2.76 | (93) $false % 9.29/2.76 | % 9.29/2.76 |-The branch is then unsatisfiable % 9.29/2.76 |-Branch two: % 9.29/2.76 | (147) ~ (all_22_0_26 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26 % 9.29/2.76 | % 9.29/2.76 | Applying alpha-rule on (147) yields: % 9.29/2.76 | (143) ~ (all_22_0_26 = 0) % 9.29/2.77 | (149) convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26 % 9.29/2.77 | % 9.29/2.77 +-Applying beta-rule and splitting (83), into two cases. % 9.29/2.77 |-Branch one: % 9.29/2.77 | (150) (all_26_0_31 = 0 & all_26_1_32 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_26_1_32 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) % 9.29/2.77 | % 9.29/2.77 +-Applying beta-rule and splitting (150), into two cases. % 9.29/2.77 |-Branch one: % 9.29/2.77 | (151) all_26_0_31 = 0 & all_26_1_32 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 9.29/2.77 | % 9.29/2.77 | Applying alpha-rule on (151) yields: % 9.29/2.77 | (152) all_26_0_31 = 0 % 9.29/2.77 | (153) all_26_1_32 = 0 % 9.29/2.77 | (154) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 9.29/2.77 | (155) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 9.29/2.77 | (156) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 |-Branch two: % 9.29/2.77 | (157) all_26_1_32 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 9.29/2.77 | % 9.29/2.77 | Applying alpha-rule on (157) yields: % 9.29/2.77 | (153) all_26_1_32 = 0 % 9.29/2.77 | (159) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (7) with all_0_3_3, all_0_2_2, all_25_1_30, all_29_1_36 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36, convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30, yields: % 9.29/2.77 | (160) all_29_1_36 = all_25_1_30 % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (7) with all_0_3_3, all_0_2_2, all_22_0_26, all_25_1_30 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30, convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, yields: % 9.29/2.77 | (161) all_25_1_30 = all_22_0_26 % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (7) with all_0_3_3, all_0_2_2, 0, all_29_1_36 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 9.29/2.77 | (89) all_29_1_36 = 0 % 9.29/2.77 | % 9.29/2.77 | Combining equations (160,89) yields a new equation: % 9.29/2.77 | (163) all_25_1_30 = 0 % 9.29/2.77 | % 9.29/2.77 | Simplifying 163 yields: % 9.29/2.77 | (109) all_25_1_30 = 0 % 9.29/2.77 | % 9.29/2.77 | Combining equations (161,109) yields a new equation: % 9.29/2.77 | (165) all_22_0_26 = 0 % 9.29/2.77 | % 9.29/2.77 | Simplifying 165 yields: % 9.29/2.77 | (133) all_22_0_26 = 0 % 9.29/2.77 | % 9.29/2.77 | Equations (133) can reduce 143 to: % 9.29/2.77 | (93) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 |-Branch two: % 9.29/2.77 | (168) ~ (all_26_1_32 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32 % 9.29/2.77 | % 9.29/2.77 | Applying alpha-rule on (168) yields: % 9.29/2.77 | (169) ~ (all_26_1_32 = 0) % 9.29/2.77 | (170) convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32 % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (7) with all_0_3_3, all_0_2_2, all_26_1_32, all_29_1_36 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36, convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32, yields: % 9.29/2.77 | (171) all_29_1_36 = all_26_1_32 % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (7) with all_0_3_3, all_0_2_2, all_25_1_30, all_26_1_32 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32, convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30, yields: % 9.29/2.77 | (172) all_26_1_32 = all_25_1_30 % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (7) with all_0_3_3, all_0_2_2, all_22_0_26, all_29_1_36 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36, convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, yields: % 9.29/2.77 | (173) all_29_1_36 = all_22_0_26 % 9.29/2.77 | % 9.29/2.77 | Combining equations (171,173) yields a new equation: % 9.29/2.77 | (174) all_26_1_32 = all_22_0_26 % 9.29/2.77 | % 9.29/2.77 | Simplifying 174 yields: % 9.29/2.77 | (175) all_26_1_32 = all_22_0_26 % 9.29/2.77 | % 9.29/2.77 | Combining equations (175,172) yields a new equation: % 9.29/2.77 | (161) all_25_1_30 = all_22_0_26 % 9.29/2.77 | % 9.29/2.77 | Equations (161) can reduce 124 to: % 9.29/2.77 | (143) ~ (all_22_0_26 = 0) % 9.29/2.77 | % 9.29/2.77 | From (161) and (125) follows: % 9.29/2.77 | (149) convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26 % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (29) with all_22_0_26, all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields: % 9.29/2.77 | (179) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0) % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (29) with all_0_0_0, all_22_0_26, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields: % 9.29/2.77 | (180) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0) % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (51) with all_22_0_26, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 9.29/2.77 | (181) all_22_0_26 = 0 | convergent_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.77 | % 9.29/2.77 +-Applying beta-rule and splitting (179), into two cases. % 9.29/2.77 |-Branch one: % 9.29/2.77 | (133) all_22_0_26 = 0 % 9.29/2.77 | % 9.29/2.77 | Equations (133) can reduce 143 to: % 9.29/2.77 | (93) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 |-Branch two: % 9.29/2.77 | (143) ~ (all_22_0_26 = 0) % 9.29/2.77 | (185) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0) % 9.29/2.77 | % 9.29/2.77 +-Applying beta-rule and splitting (180), into two cases. % 9.29/2.77 |-Branch one: % 9.29/2.77 | (133) all_22_0_26 = 0 % 9.29/2.77 | % 9.29/2.77 | Equations (133) can reduce 143 to: % 9.29/2.77 | (93) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 |-Branch two: % 9.29/2.77 | (143) ~ (all_22_0_26 = 0) % 9.29/2.77 | (189) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0) % 9.29/2.77 | % 9.29/2.77 +-Applying beta-rule and splitting (181), into two cases. % 9.29/2.77 |-Branch one: % 9.29/2.77 | (111) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 9.29/2.77 | % 9.29/2.77 +-Applying beta-rule and splitting (189), into two cases. % 9.29/2.77 |-Branch one: % 9.29/2.77 | (100) all_0_0_0 = 0 % 9.29/2.77 | % 9.29/2.77 | Equations (100) can reduce 30 to: % 9.29/2.77 | (93) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 |-Branch two: % 9.29/2.77 | (30) ~ (all_0_0_0 = 0) % 9.29/2.77 | (194) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0) % 9.29/2.77 | % 9.29/2.77 +-Applying beta-rule and splitting (185), into two cases. % 9.29/2.77 |-Branch one: % 9.29/2.77 | (100) all_0_0_0 = 0 % 9.29/2.77 | % 9.29/2.77 | Equations (100) can reduce 30 to: % 9.29/2.77 | (93) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 |-Branch two: % 9.29/2.77 | (30) ~ (all_0_0_0 = 0) % 9.29/2.77 | (198) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0) % 9.29/2.77 | % 9.29/2.77 | Instantiating formula (7) with all_0_4_4, all_0_2_2, 0, all_0_0_0 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields: % 9.29/2.77 | (100) all_0_0_0 = 0 % 9.29/2.77 | % 9.29/2.77 | Equations (100) can reduce 30 to: % 9.29/2.77 | (93) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 |-Branch two: % 9.29/2.77 | (201) ~ (convergent_lines(all_0_4_4, all_0_2_2) = 0) % 9.29/2.77 | (133) all_22_0_26 = 0 % 9.29/2.77 | % 9.29/2.77 | Equations (133) can reduce 143 to: % 9.29/2.77 | (93) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 |-Branch two: % 9.29/2.77 | (204) ~ (convergent_lines(all_0_4_4, all_0_3_3) = 0) % 9.29/2.77 | (92) all_0_1_1 = 0 % 9.29/2.77 | % 9.29/2.77 | Equations (92) can reduce 2 to: % 9.29/2.77 | (93) $false % 9.29/2.77 | % 9.29/2.77 |-The branch is then unsatisfiable % 9.29/2.77 % SZS output end Proof for theBenchmark % 9.29/2.77 % 9.29/2.77 2181ms %------------------------------------------------------------------------------