%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO218+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 03:48:51 EDT 2022 % Result : Theorem 5.86s 2.02s % Output : Proof 23.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO218+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.33 % Computer : n021.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sat Jun 18 18:20:32 EDT 2022 % 0.14/0.34 % CPUTime : % 0.51/0.57 ____ _ % 0.51/0.57 ___ / __ \_____(_)___ ________ __________ % 0.51/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.57 % 0.51/0.57 A Theorem Prover for First-Order Logic % 0.51/0.57 (ePrincess v.1.0) % 0.51/0.57 % 0.51/0.57 (c) Philipp Rümmer, 2009-2015 % 0.51/0.57 (c) Peter Backeman, 2014-2015 % 0.51/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.57 Bug reports to peter@backeman.se % 0.51/0.57 % 0.51/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.57 % 0.51/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.51/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.61/0.93 Prover 0: Preprocessing ... % 1.92/1.07 Prover 0: Warning: ignoring some quantifiers % 2.01/1.09 Prover 0: Constructing countermodel ... % 3.96/1.61 Prover 0: gave up % 3.96/1.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.96/1.63 Prover 1: Preprocessing ... % 4.47/1.71 Prover 1: Constructing countermodel ... % 4.85/1.77 Prover 1: gave up % 4.85/1.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.85/1.79 Prover 2: Preprocessing ... % 5.26/1.91 Prover 2: Warning: ignoring some quantifiers % 5.26/1.92 Prover 2: Constructing countermodel ... % 5.86/2.02 Prover 2: proved (246ms) % 5.86/2.02 % 5.86/2.02 No countermodel exists, formula is valid % 5.86/2.02 % SZS status Theorem for theBenchmark % 5.86/2.02 % 5.86/2.02 Generating proof ... Warning: ignoring some quantifiers % 22.79/7.04 found it (size 88) % 22.79/7.04 % 22.79/7.04 % SZS output start Proof for theBenchmark % 22.79/7.05 Assumed formulas after preprocessing and simplification: % 22.79/7.05 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = 0 & unorthogonal_lines(v0, v2) = v4 & convergent_lines(v0, v1) = v3 & ! [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) % 22.79/7.11 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 22.79/7.11 | (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_2_2) = all_0_0_0 & convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & ! [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 % 22.79/7.14 | % 22.79/7.14 | Applying alpha-rule on (1) yields: % 22.79/7.14 | (2) ~ (all_0_1_1 = 0) % 22.79/7.14 | (3) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 22.79/7.14 | (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)) % 22.79/7.14 | (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))) % 22.79/7.14 | (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))) % 22.79/7.14 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 22.79/7.14 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 22.79/7.14 | (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))) % 22.79/7.14 | (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))) % 22.79/7.14 | (11) convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1 % 22.79/7.14 | (12) ! [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))) % 22.79/7.14 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 22.79/7.14 | (14) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 22.79/7.14 | (15) ! [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))) % 22.79/7.14 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 22.79/7.14 | (17) ! [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))) % 22.79/7.15 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 22.79/7.15 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 22.79/7.15 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 23.33/7.15 | (21) ! [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))) % 23.33/7.15 | (22) ! [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))) % 23.33/7.15 | (23) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 23.33/7.15 | (24) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 23.33/7.15 | (25) ! [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))) % 23.33/7.15 | (26) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 23.33/7.15 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 23.33/7.15 | (28) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 23.33/7.15 | (29) ! [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))) % 23.33/7.15 | (30) ! [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)) % 23.33/7.15 | (31) ~ (all_0_0_0 = 0) % 23.33/7.15 | (32) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 23.33/7.15 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 23.33/7.15 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 23.33/7.15 | (35) ! [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))) % 23.33/7.15 | (36) ! [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) % 23.33/7.15 | (37) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 23.33/7.15 | (38) ! [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)) % 23.33/7.15 | (39) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 23.33/7.15 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 23.33/7.15 | (41) ! [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))) % 23.33/7.15 | (42) ! [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))) % 23.33/7.16 | (43) ! [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))) % 23.33/7.16 | (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))) % 23.33/7.16 | (45) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 23.33/7.16 | (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) % 23.33/7.16 | (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))) % 23.33/7.16 | (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))) % 23.33/7.16 | (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))) % 23.33/7.16 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 23.33/7.16 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 23.33/7.16 | (52) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 23.33/7.16 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 23.33/7.16 | (54) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 % 23.33/7.16 | (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))) % 23.33/7.16 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 23.33/7.16 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) % 23.33/7.16 | (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)) % 23.33/7.16 | (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)) % 23.33/7.16 | (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) % 23.33/7.16 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 23.33/7.16 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 23.33/7.16 | (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))) % 23.33/7.16 | (64) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 23.33/7.16 | (65) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 23.33/7.16 | (66) ! [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))) % 23.33/7.17 | (67) ! [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)) % 23.33/7.17 | (68) ! [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))) % 23.33/7.17 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) % 23.33/7.17 | (70) ! [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)) % 23.33/7.17 | (71) unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_0_0 % 23.33/7.17 | (72) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 23.33/7.17 | (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) % 23.33/7.17 | % 23.33/7.17 | Instantiating formula (22) 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, unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields: % 23.33/7.17 | (74) ? [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 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 23.33/7.17 | % 23.33/7.17 | Instantiating formula (4) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields: % 23.33/7.17 | (75) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0) % 23.33/7.17 | % 23.33/7.17 | Instantiating formula (62) with all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields: % 23.33/7.17 | (76) all_0_0_0 = 0 | convergent_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.17 | % 23.33/7.17 | Instantiating formula (30) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 23.33/7.17 | (77) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 23.33/7.17 | % 23.33/7.17 | Instantiating formula (66) 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, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 23.33/7.17 | (78) ? [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 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 23.33/7.17 | % 23.33/7.17 | Instantiating formula (44) 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_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 23.33/7.17 | (79) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & unorthogonal_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)) % 23.33/7.17 | % 23.33/7.17 | Instantiating (74) with all_25_0_29, all_25_1_30 yields: % 23.33/7.17 | (80) (all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_25_1_30 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_25_1_30 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30) % 23.33/7.17 | % 23.33/7.17 | Instantiating (79) with all_28_0_34 yields: % 23.33/7.17 | (81) (all_28_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_28_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_28_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_0_34) | ( ~ (all_28_0_34 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_28_0_34) % 23.33/7.17 | % 23.33/7.17 | Instantiating (78) with all_29_0_35, all_29_1_36 yields: % 23.33/7.17 | (82) (all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_29_1_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_29_1_36 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36) % 23.33/7.17 | % 23.33/7.17 +-Applying beta-rule and splitting (76), into two cases. % 23.33/7.17 |-Branch one: % 23.33/7.17 | (83) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.17 | % 23.33/7.17 +-Applying beta-rule and splitting (82), into two cases. % 23.33/7.17 |-Branch one: % 23.33/7.17 | (84) (all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_29_1_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) % 23.33/7.17 | % 23.33/7.17 +-Applying beta-rule and splitting (84), into two cases. % 23.33/7.17 |-Branch one: % 23.33/7.17 | (85) all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.17 | % 23.33/7.17 | Applying alpha-rule on (85) yields: % 23.33/7.17 | (86) all_29_0_35 = 0 % 23.33/7.17 | (87) all_29_1_36 = 0 % 23.33/7.17 | (88) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.17 | (83) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.17 | % 23.33/7.17 +-Applying beta-rule and splitting (75), into two cases. % 23.33/7.17 |-Branch one: % 23.33/7.17 | (90) all_0_0_0 = 0 % 23.33/7.17 | % 23.33/7.18 | Equations (90) can reduce 31 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (31) ~ (all_0_0_0 = 0) % 23.33/7.18 | (93) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0) % 23.33/7.18 | % 23.33/7.18 | Instantiating formula (40) with all_0_4_4, all_0_2_2, 0, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, yields: % 23.33/7.18 | (90) all_0_0_0 = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (90) can reduce 31 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (96) all_29_1_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (96) yields: % 23.33/7.18 | (87) all_29_1_36 = 0 % 23.33/7.18 | (98) all_0_1_1 = 0 % 23.33/7.18 | (99) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (98) can reduce 2 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (101) ~ (all_29_1_36 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (101) yields: % 23.33/7.18 | (102) ~ (all_29_1_36 = 0) % 23.33/7.18 | (103) convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36 % 23.33/7.18 | % 23.33/7.18 +-Applying beta-rule and splitting (80), into two cases. % 23.33/7.18 |-Branch one: % 23.33/7.18 | (104) (all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_25_1_30 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) % 23.33/7.18 | % 23.33/7.18 +-Applying beta-rule and splitting (104), into two cases. % 23.33/7.18 |-Branch one: % 23.33/7.18 | (105) all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (105) yields: % 23.33/7.18 | (106) all_25_0_29 = 0 % 23.33/7.18 | (107) all_25_1_30 = 0 % 23.33/7.18 | (99) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 23.33/7.18 | (109) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 23.33/7.18 | % 23.33/7.18 +-Applying beta-rule and splitting (77), into two cases. % 23.33/7.18 |-Branch one: % 23.33/7.18 | (98) all_0_1_1 = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (98) can reduce 2 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (2) ~ (all_0_1_1 = 0) % 23.33/7.18 | (113) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 23.33/7.18 | % 23.33/7.18 | Instantiating formula (7) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 23.33/7.18 | (98) all_0_1_1 = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (98) can reduce 2 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (116) all_25_1_30 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (116) yields: % 23.33/7.18 | (107) all_25_1_30 = 0 % 23.33/7.18 | (90) all_0_0_0 = 0 % 23.33/7.18 | (83) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (90) can reduce 31 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (121) ~ (all_25_1_30 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (121) yields: % 23.33/7.18 | (122) ~ (all_25_1_30 = 0) % 23.33/7.18 | (123) convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30 % 23.33/7.18 | % 23.33/7.18 +-Applying beta-rule and splitting (77), into two cases. % 23.33/7.18 |-Branch one: % 23.33/7.18 | (98) all_0_1_1 = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (98) can reduce 2 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (2) ~ (all_0_1_1 = 0) % 23.33/7.18 | (113) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 23.33/7.18 | % 23.33/7.18 +-Applying beta-rule and splitting (81), into two cases. % 23.33/7.18 |-Branch one: % 23.33/7.18 | (128) (all_28_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_28_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_28_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_0_34) % 23.33/7.18 | % 23.33/7.18 +-Applying beta-rule and splitting (128), into two cases. % 23.33/7.18 |-Branch one: % 23.33/7.18 | (129) (all_28_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_28_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) % 23.33/7.18 | % 23.33/7.18 +-Applying beta-rule and splitting (129), into two cases. % 23.33/7.18 |-Branch one: % 23.33/7.18 | (130) all_28_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (130) yields: % 23.33/7.18 | (131) all_28_0_34 = 0 % 23.33/7.18 | (90) all_0_0_0 = 0 % 23.33/7.18 | (83) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (90) can reduce 31 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (135) all_28_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (135) yields: % 23.33/7.18 | (131) all_28_0_34 = 0 % 23.33/7.18 | (98) all_0_1_1 = 0 % 23.33/7.18 | (99) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (98) can reduce 2 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (140) ~ (all_28_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_0_34 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (140) yields: % 23.33/7.18 | (141) ~ (all_28_0_34 = 0) % 23.33/7.18 | (142) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_0_34 % 23.33/7.18 | % 23.33/7.18 | Instantiating formula (40) with all_0_3_3, all_0_2_2, all_28_0_34, 0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_0_34, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields: % 23.33/7.18 | (131) all_28_0_34 = 0 % 23.33/7.18 | % 23.33/7.18 | Equations (131) can reduce 141 to: % 23.33/7.18 | (91) $false % 23.33/7.18 | % 23.33/7.18 |-The branch is then unsatisfiable % 23.33/7.18 |-Branch two: % 23.33/7.18 | (145) ~ (all_28_0_34 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_28_0_34 % 23.33/7.18 | % 23.33/7.18 | Applying alpha-rule on (145) yields: % 23.33/7.18 | (141) ~ (all_28_0_34 = 0) % 23.33/7.18 | (147) convergent_lines(all_0_3_3, all_0_2_2) = all_28_0_34 % 23.33/7.18 | % 23.33/7.18 +-Applying beta-rule and splitting (75), into two cases. % 23.33/7.18 |-Branch one: % 23.33/7.18 | (90) all_0_0_0 = 0 % 23.33/7.18 | % 23.33/7.19 | Equations (90) can reduce 31 to: % 23.33/7.19 | (91) $false % 23.33/7.19 | % 23.33/7.19 |-The branch is then unsatisfiable % 23.33/7.19 |-Branch two: % 23.33/7.19 | (31) ~ (all_0_0_0 = 0) % 23.33/7.19 | (93) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0) % 23.33/7.19 | % 23.33/7.19 | Instantiating (93) with all_57_0_45 yields: % 23.33/7.19 | (152) ~ (all_57_0_45 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = all_57_0_45 % 23.33/7.19 | % 23.33/7.19 | Applying alpha-rule on (152) yields: % 23.33/7.19 | (153) ~ (all_57_0_45 = 0) % 23.33/7.19 | (154) convergent_lines(all_0_2_2, all_0_2_2) = all_57_0_45 % 23.33/7.19 | % 23.33/7.19 | Instantiating formula (7) with all_0_3_3, all_0_2_2, all_28_0_34, 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_28_0_34, yields: % 23.33/7.19 | (155) all_29_1_36 = all_28_0_34 % 23.33/7.19 | % 23.33/7.19 | 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: % 23.33/7.19 | (156) all_29_1_36 = all_25_1_30 % 23.33/7.19 | % 23.33/7.19 | Combining equations (155,156) yields a new equation: % 23.33/7.19 | (157) all_28_0_34 = all_25_1_30 % 23.33/7.19 | % 23.33/7.19 | Simplifying 157 yields: % 23.33/7.19 | (158) all_28_0_34 = all_25_1_30 % 23.33/7.19 | % 23.33/7.19 | Equations (158) can reduce 141 to: % 23.33/7.19 | (122) ~ (all_25_1_30 = 0) % 23.33/7.19 | % 23.33/7.19 | From (158) and (147) follows: % 23.33/7.19 | (123) convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30 % 23.33/7.19 | % 23.33/7.19 | Instantiating formula (30) with all_25_1_30, all_57_0_45, all_0_2_2, all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = all_57_0_45, convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30, yields: % 23.33/7.19 | (161) all_57_0_45 = 0 | all_25_1_30 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0) % 23.33/7.19 | % 23.33/7.19 | Instantiating formula (30) with all_25_1_30, all_25_1_30, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30, yields: % 23.33/7.19 | (162) all_25_1_30 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0) % 23.33/7.19 | % 23.33/7.19 | Instantiating formula (16) with all_0_1_1, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 23.33/7.19 | (163) all_0_1_1 = 0 | convergent_lines(all_0_2_2, all_0_3_3) = 0 % 23.33/7.19 | % 23.33/7.19 +-Applying beta-rule and splitting (163), into two cases. % 23.33/7.19 |-Branch one: % 23.33/7.19 | (164) convergent_lines(all_0_2_2, all_0_3_3) = 0 % 23.33/7.19 | % 23.33/7.19 +-Applying beta-rule and splitting (162), into two cases. % 23.33/7.19 |-Branch one: % 23.33/7.19 | (107) all_25_1_30 = 0 % 23.33/7.19 | % 23.33/7.19 | Equations (107) can reduce 122 to: % 23.33/7.19 | (91) $false % 23.33/7.19 | % 23.33/7.19 |-The branch is then unsatisfiable % 23.33/7.19 |-Branch two: % 23.33/7.19 | (122) ~ (all_25_1_30 = 0) % 23.33/7.19 | (168) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0) % 23.33/7.19 | % 23.33/7.19 +-Applying beta-rule and splitting (161), into two cases. % 23.33/7.19 |-Branch one: % 23.33/7.19 | (169) all_57_0_45 = 0 % 23.33/7.19 | % 23.33/7.19 | Equations (169) can reduce 153 to: % 23.33/7.19 | (91) $false % 23.33/7.19 | % 23.33/7.19 |-The branch is then unsatisfiable % 23.33/7.19 |-Branch two: % 23.33/7.19 | (153) ~ (all_57_0_45 = 0) % 23.33/7.19 | (172) all_25_1_30 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0) % 23.33/7.19 | % 23.33/7.19 +-Applying beta-rule and splitting (172), into two cases. % 23.33/7.19 |-Branch one: % 23.33/7.19 | (107) all_25_1_30 = 0 % 23.33/7.19 | % 23.33/7.19 | Equations (107) can reduce 122 to: % 23.33/7.19 | (91) $false % 23.33/7.19 | % 23.33/7.19 |-The branch is then unsatisfiable % 23.33/7.19 |-Branch two: % 23.33/7.19 | (122) ~ (all_25_1_30 = 0) % 23.33/7.19 | (176) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0) % 23.33/7.19 | % 23.33/7.19 | Instantiating (176) with all_197_0_384 yields: % 23.33/7.19 | (177) ~ (all_197_0_384 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_197_0_384 % 23.33/7.19 | % 23.33/7.19 | Applying alpha-rule on (177) yields: % 23.33/7.19 | (178) ~ (all_197_0_384 = 0) % 23.33/7.19 | (179) convergent_lines(all_0_2_2, all_0_3_3) = all_197_0_384 % 23.33/7.19 | % 23.33/7.19 | Instantiating formula (7) with all_0_2_2, all_0_3_3, 0, all_197_0_384 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = all_197_0_384, convergent_lines(all_0_2_2, all_0_3_3) = 0, yields: % 23.33/7.19 | (180) all_197_0_384 = 0 % 23.33/7.19 | % 23.33/7.19 | Equations (180) can reduce 178 to: % 23.33/7.19 | (91) $false % 23.33/7.19 | % 23.33/7.19 |-The branch is then unsatisfiable % 23.33/7.19 |-Branch two: % 23.33/7.19 | (182) ~ (convergent_lines(all_0_2_2, all_0_3_3) = 0) % 23.33/7.19 | (98) all_0_1_1 = 0 % 23.33/7.19 | % 23.33/7.19 | Equations (98) can reduce 2 to: % 23.33/7.19 | (91) $false % 23.33/7.19 | % 23.33/7.19 |-The branch is then unsatisfiable % 23.33/7.19 |-Branch two: % 23.33/7.19 | (185) ~ (convergent_lines(all_0_4_4, all_0_2_2) = 0) % 23.33/7.19 | (90) all_0_0_0 = 0 % 23.33/7.19 | % 23.33/7.19 | Equations (90) can reduce 31 to: % 23.33/7.19 | (91) $false % 23.33/7.19 | % 23.33/7.19 |-The branch is then unsatisfiable % 23.33/7.19 % SZS output end Proof for theBenchmark % 23.33/7.19 % 23.33/7.19 6611ms %------------------------------------------------------------------------------