%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO184+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 03:48:21 EDT 2022 % Result : Theorem 16.93s 4.99s % Output : Proof 18.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : GEO184+3 : TPTP v8.1.0. Released v4.0.0. % 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.33 % Computer : n023.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Sat Jun 18 15:46:49 EDT 2022 % 0.11/0.33 % CPUTime : % 0.19/0.57 ____ _ % 0.19/0.57 ___ / __ \_____(_)___ ________ __________ % 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.57 % 0.59/0.57 A Theorem Prover for First-Order Logic % 0.59/0.57 (ePrincess v.1.0) % 0.59/0.57 % 0.59/0.57 (c) Philipp Rümmer, 2009-2015 % 0.59/0.57 (c) Peter Backeman, 2014-2015 % 0.59/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.57 Bug reports to peter@backeman.se % 0.59/0.57 % 0.59/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.57 % 0.59/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.63/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.81/0.95 Prover 0: Preprocessing ... % 2.20/1.16 Prover 0: Warning: ignoring some quantifiers % 2.47/1.19 Prover 0: Constructing countermodel ... % 15.89/4.78 Prover 0: gave up % 15.89/4.78 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 16.04/4.82 Prover 1: Preprocessing ... % 16.59/4.95 Prover 1: Constructing countermodel ... % 16.93/4.99 Prover 1: proved (212ms) % 16.93/4.99 % 16.93/4.99 No countermodel exists, formula is valid % 16.93/4.99 % SZS status Theorem for theBenchmark % 16.93/4.99 % 16.93/4.99 Generating proof ... found it (size 52) % 17.99/5.27 % 17.99/5.27 % SZS output start Proof for theBenchmark % 17.99/5.27 Assumed formulas after preprocessing and simplification: % 17.99/5.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v1, v2) = 0 & incident_point_and_line(v0, v2) = 0 & equal_lines(v2, v4) = v5 & line_connecting(v0, v1) = v4 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ? [v13] : (unorthogonal_lines(v8, v9) = v13 & apart_point_and_line(v6, v8) = v12 & (v13 = 0 | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (unorthogonal_lines(v7, v8) = v14 & convergent_lines(v7, v8) = v13 & convergent_lines(v6, v8) = v12 & convergent_lines(v6, v7) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | (v12 = 0 & v10 = 0) | (v11 = 0 & v9 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ? [v11] : (apart_point_and_line(v6, v8) = v10 & convergent_lines(v7, v8) = v11 & (v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_lines(v9, v8) = v7) | ~ (orthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (incident_point_and_line(v9, v8) = v7) | ~ (incident_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_lines(v9, v8) = v7) | ~ (parallel_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_lines(v9, v8) = v7) | ~ (equal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_points(v9, v8) = v7) | ~ (equal_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (unorthogonal_lines(v7, v8) = v13 & convergent_lines(v7, v8) = v12 & convergent_lines(v6, v8) = v11 & convergent_lines(v6, v7) = v10 & ( ~ (v10 = 0) | (v13 = 0 & v12 = 0) | (v11 = 0 & v9 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apart_point_and_line(v7, v9) = v13 & apart_point_and_line(v7, v8) = v12 & apart_point_and_line(v6, v9) = v11 & apart_point_and_line(v6, v8) = v10 & (v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (orthogonal_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (incident_point_and_line(v6, v7) = v8) | apart_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (parallel_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_lines(v6, v7) = v8) | distinct_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_points(v6, v7) = v8) | distinct_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (point(v8) = v7) | ~ (point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (line(v8) = v7) | ~ (line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ~ (unorthogonal_lines(v8, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ~ (apart_point_and_line(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (point(v7) = v10 & line(v8) = v11 & line(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ~ (apart_point_and_line(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ~ (convergent_lines(v8, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (point(v7) = v10 & line(v8) = v11 & line(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ (apart_point_and_line(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ (apart_point_and_line(v8, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (point(v8) = v12 & line(v7) = v10 & line(v6) = v9 & convergent_lines(v6, v7) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (apart_point_and_line(v6, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (point(v7) = v10 & point(v6) = v9 & line(v8) = v12 & distinct_points(v6, v7) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v12 = 0))) & ! [v6] : ! [v7] : ( ~ (orthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (incident_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (parallel_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | convergent_lines(v6, v7) = 0) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0)) % 18.40/5.31 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 18.40/5.31 | (1) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_4_4, all_0_3_3) = 0 & incident_point_and_line(all_0_5_5, all_0_3_3) = 0 & equal_lines(all_0_3_3, all_0_1_1) = all_0_0_0 & line_connecting(all_0_5_5, all_0_4_4) = all_0_1_1 & convergent_lines(all_0_3_3, all_0_2_2) = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0))) & ! [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] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 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(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_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(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) % 18.40/5.32 | % 18.40/5.32 | Applying alpha-rule on (1) yields: % 18.40/5.32 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 18.40/5.33 | (3) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 18.40/5.33 | (4) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 18.40/5.33 | (5) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 18.40/5.33 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) % 18.40/5.33 | (7) incident_point_and_line(all_0_5_5, all_0_3_3) = 0 % 18.40/5.33 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 18.40/5.33 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 18.40/5.33 | (10) ! [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)) % 18.40/5.33 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 18.40/5.33 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 18.40/5.33 | (13) incident_point_and_line(all_0_4_4, all_0_3_3) = 0 % 18.40/5.33 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 18.40/5.33 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 18.40/5.33 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 18.40/5.33 | (17) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 18.40/5.33 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 18.40/5.33 | (19) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 18.40/5.33 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 18.40/5.33 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 18.40/5.33 | (22) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 18.40/5.33 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 18.40/5.33 | (24) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 18.40/5.33 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 18.40/5.33 | (26) ! [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) % 18.40/5.33 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 18.40/5.33 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 18.40/5.33 | (29) ~ (all_0_0_0 = 0) % 18.40/5.33 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 18.40/5.33 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 18.40/5.33 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 18.40/5.33 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 18.40/5.34 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 18.40/5.34 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0))) % 18.40/5.34 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 18.40/5.34 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 18.40/5.34 | (38) line_connecting(all_0_5_5, all_0_4_4) = all_0_1_1 % 18.40/5.34 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 18.40/5.34 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 18.40/5.34 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 18.40/5.34 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 18.40/5.34 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 18.40/5.34 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) % 18.40/5.34 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 18.40/5.34 | (46) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 18.40/5.34 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 18.40/5.34 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 18.40/5.34 | (49) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 18.40/5.34 | (50) equal_lines(all_0_3_3, all_0_1_1) = all_0_0_0 % 18.40/5.34 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 18.40/5.34 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 18.40/5.34 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 18.40/5.34 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 18.40/5.34 | (55) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 18.40/5.34 | (56) distinct_points(all_0_5_5, all_0_4_4) = 0 % 18.40/5.34 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 18.40/5.34 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 18.40/5.34 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 18.40/5.34 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 18.40/5.35 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 18.40/5.35 | (62) ! [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) % 18.40/5.35 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (4) with all_0_3_3, all_0_4_4 and discharging atoms incident_point_and_line(all_0_4_4, all_0_3_3) = 0, yields: % 18.40/5.35 | (64) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_3_3) = v0) % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (4) with all_0_3_3, all_0_5_5 and discharging atoms incident_point_and_line(all_0_5_5, all_0_3_3) = 0, yields: % 18.40/5.35 | (65) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = v0) % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (58) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms equal_lines(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 18.40/5.35 | (66) all_0_0_0 = 0 | distinct_lines(all_0_3_3, all_0_1_1) = 0 % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (28) with all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_1_1, yields: % 18.40/5.35 | (67) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_0_4_4) = v1 & point(all_0_5_5) = v0 & line(all_0_1_1) = v3 & distinct_points(all_0_5_5, all_0_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 18.40/5.35 | % 18.40/5.35 | Instantiating (67) with all_16_0_6, all_16_1_7, all_16_2_8, all_16_3_9 yields: % 18.40/5.35 | (68) point(all_0_4_4) = all_16_2_8 & point(all_0_5_5) = all_16_3_9 & line(all_0_1_1) = all_16_0_6 & distinct_points(all_0_5_5, all_0_4_4) = all_16_1_7 & ( ~ (all_16_1_7 = 0) | ~ (all_16_2_8 = 0) | ~ (all_16_3_9 = 0) | all_16_0_6 = 0) % 18.40/5.35 | % 18.40/5.35 | Applying alpha-rule on (68) yields: % 18.40/5.35 | (69) point(all_0_5_5) = all_16_3_9 % 18.40/5.35 | (70) distinct_points(all_0_5_5, all_0_4_4) = all_16_1_7 % 18.40/5.35 | (71) ~ (all_16_1_7 = 0) | ~ (all_16_2_8 = 0) | ~ (all_16_3_9 = 0) | all_16_0_6 = 0 % 18.40/5.35 | (72) point(all_0_4_4) = all_16_2_8 % 18.40/5.35 | (73) line(all_0_1_1) = all_16_0_6 % 18.40/5.35 | % 18.40/5.35 | Instantiating (65) with all_18_0_10 yields: % 18.40/5.35 | (74) ~ (all_18_0_10 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = all_18_0_10 % 18.40/5.35 | % 18.40/5.35 | Applying alpha-rule on (74) yields: % 18.40/5.35 | (75) ~ (all_18_0_10 = 0) % 18.40/5.35 | (76) apart_point_and_line(all_0_5_5, all_0_3_3) = all_18_0_10 % 18.40/5.35 | % 18.40/5.35 | Instantiating (64) with all_20_0_11 yields: % 18.40/5.35 | (77) ~ (all_20_0_11 = 0) & apart_point_and_line(all_0_4_4, all_0_3_3) = all_20_0_11 % 18.40/5.35 | % 18.40/5.35 | Applying alpha-rule on (77) yields: % 18.40/5.35 | (78) ~ (all_20_0_11 = 0) % 18.40/5.35 | (79) apart_point_and_line(all_0_4_4, all_0_3_3) = all_20_0_11 % 18.40/5.35 | % 18.40/5.35 +-Applying beta-rule and splitting (66), into two cases. % 18.40/5.35 |-Branch one: % 18.40/5.35 | (80) distinct_lines(all_0_3_3, all_0_1_1) = 0 % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (31) with all_0_5_5, all_0_4_4, all_16_1_7, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_16_1_7, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 18.40/5.35 | (81) all_16_1_7 = 0 % 18.40/5.35 | % 18.40/5.35 | From (81) and (70) follows: % 18.40/5.35 | (56) distinct_points(all_0_5_5, all_0_4_4) = 0 % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (37) with all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms distinct_lines(all_0_3_3, all_0_1_1) = 0, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 18.40/5.35 | (83) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_4_4, all_0_1_1) = v3 & apart_point_and_line(all_0_4_4, all_0_3_3) = v2 & apart_point_and_line(all_0_5_5, all_0_1_1) = v1 & apart_point_and_line(all_0_5_5, all_0_3_3) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0)) % 18.40/5.35 | % 18.40/5.35 | Instantiating (83) with all_40_0_12, all_40_1_13, all_40_2_14, all_40_3_15 yields: % 18.40/5.35 | (84) apart_point_and_line(all_0_4_4, all_0_1_1) = all_40_0_12 & apart_point_and_line(all_0_4_4, all_0_3_3) = all_40_1_13 & apart_point_and_line(all_0_5_5, all_0_1_1) = all_40_2_14 & apart_point_and_line(all_0_5_5, all_0_3_3) = all_40_3_15 & (all_40_0_12 = 0 | all_40_1_13 = 0 | all_40_2_14 = 0 | all_40_3_15 = 0) % 18.40/5.35 | % 18.40/5.35 | Applying alpha-rule on (84) yields: % 18.40/5.35 | (85) apart_point_and_line(all_0_4_4, all_0_1_1) = all_40_0_12 % 18.40/5.35 | (86) all_40_0_12 = 0 | all_40_1_13 = 0 | all_40_2_14 = 0 | all_40_3_15 = 0 % 18.40/5.35 | (87) apart_point_and_line(all_0_4_4, all_0_3_3) = all_40_1_13 % 18.40/5.35 | (88) apart_point_and_line(all_0_5_5, all_0_1_1) = all_40_2_14 % 18.40/5.35 | (89) apart_point_and_line(all_0_5_5, all_0_3_3) = all_40_3_15 % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (52) with all_0_4_4, all_0_3_3, all_40_1_13, all_20_0_11 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_40_1_13, apart_point_and_line(all_0_4_4, all_0_3_3) = all_20_0_11, yields: % 18.40/5.35 | (90) all_40_1_13 = all_20_0_11 % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (52) with all_0_5_5, all_0_3_3, all_40_3_15, all_18_0_10 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_40_3_15, apart_point_and_line(all_0_5_5, all_0_3_3) = all_18_0_10, yields: % 18.40/5.35 | (91) all_40_3_15 = all_18_0_10 % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (14) with all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_1_1, yields: % 18.40/5.35 | (92) ~ (apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0) % 18.40/5.35 | % 18.40/5.35 | Instantiating formula (2) with all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_1_1, yields: % 18.40/5.35 | (93) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0) % 18.40/5.35 | % 18.40/5.35 +-Applying beta-rule and splitting (93), into two cases. % 18.40/5.35 |-Branch one: % 18.40/5.35 | (94) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) % 18.40/5.35 | % 18.40/5.35 +-Applying beta-rule and splitting (92), into two cases. % 18.40/5.35 |-Branch one: % 18.40/5.35 | (95) ~ (apart_point_and_line(all_0_4_4, all_0_1_1) = 0) % 18.40/5.35 | % 18.40/5.35 | Using (85) and (95) yields: % 18.40/5.35 | (96) ~ (all_40_0_12 = 0) % 18.40/5.35 | % 18.40/5.35 | Using (88) and (94) yields: % 18.40/5.35 | (97) ~ (all_40_2_14 = 0) % 18.40/5.35 | % 18.40/5.35 +-Applying beta-rule and splitting (86), into two cases. % 18.40/5.35 |-Branch one: % 18.40/5.35 | (98) all_40_0_12 = 0 % 18.40/5.35 | % 18.40/5.35 | Equations (98) can reduce 96 to: % 18.40/5.35 | (99) $false % 18.40/5.35 | % 18.40/5.35 |-The branch is then unsatisfiable % 18.40/5.35 |-Branch two: % 18.40/5.35 | (96) ~ (all_40_0_12 = 0) % 18.40/5.35 | (101) all_40_1_13 = 0 | all_40_2_14 = 0 | all_40_3_15 = 0 % 18.40/5.35 | % 18.40/5.35 +-Applying beta-rule and splitting (101), into two cases. % 18.40/5.35 |-Branch one: % 18.40/5.35 | (102) all_40_1_13 = 0 % 18.40/5.36 | % 18.40/5.36 | Combining equations (102,90) yields a new equation: % 18.40/5.36 | (103) all_20_0_11 = 0 % 18.40/5.36 | % 18.40/5.36 | Equations (103) can reduce 78 to: % 18.40/5.36 | (99) $false % 18.40/5.36 | % 18.40/5.36 |-The branch is then unsatisfiable % 18.40/5.36 |-Branch two: % 18.40/5.36 | (105) ~ (all_40_1_13 = 0) % 18.40/5.36 | (106) all_40_2_14 = 0 | all_40_3_15 = 0 % 18.40/5.36 | % 18.40/5.36 +-Applying beta-rule and splitting (106), into two cases. % 18.40/5.36 |-Branch one: % 18.40/5.36 | (107) all_40_2_14 = 0 % 18.40/5.36 | % 18.40/5.36 | Equations (107) can reduce 97 to: % 18.40/5.36 | (99) $false % 18.40/5.36 | % 18.40/5.36 |-The branch is then unsatisfiable % 18.40/5.36 |-Branch two: % 18.40/5.36 | (97) ~ (all_40_2_14 = 0) % 18.40/5.36 | (110) all_40_3_15 = 0 % 18.40/5.36 | % 18.40/5.36 | Combining equations (91,110) yields a new equation: % 18.40/5.36 | (111) all_18_0_10 = 0 % 18.40/5.36 | % 18.40/5.36 | Simplifying 111 yields: % 18.40/5.36 | (112) all_18_0_10 = 0 % 18.40/5.36 | % 18.40/5.36 | Equations (112) can reduce 75 to: % 18.40/5.36 | (99) $false % 18.40/5.36 | % 18.40/5.36 |-The branch is then unsatisfiable % 18.40/5.36 |-Branch two: % 18.40/5.36 | (114) apart_point_and_line(all_0_4_4, all_0_1_1) = 0 % 18.40/5.36 | (115) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0) % 18.40/5.36 | % 18.40/5.36 | Instantiating (115) with all_61_0_16 yields: % 18.40/5.36 | (116) ~ (all_61_0_16 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_61_0_16 % 18.40/5.36 | % 18.40/5.36 | Applying alpha-rule on (116) yields: % 18.40/5.36 | (117) ~ (all_61_0_16 = 0) % 18.40/5.36 | (118) distinct_points(all_0_5_5, all_0_4_4) = all_61_0_16 % 18.40/5.36 | % 18.40/5.36 | Instantiating formula (31) with all_0_5_5, all_0_4_4, all_61_0_16, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_61_0_16, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 18.40/5.36 | (119) all_61_0_16 = 0 % 18.40/5.36 | % 18.40/5.36 | Equations (119) can reduce 117 to: % 18.40/5.36 | (99) $false % 18.40/5.36 | % 18.40/5.36 |-The branch is then unsatisfiable % 18.40/5.36 |-Branch two: % 18.40/5.36 | (121) apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 18.40/5.36 | (115) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0) % 18.40/5.36 | % 18.40/5.36 | Instantiating (115) with all_57_0_17 yields: % 18.40/5.36 | (123) ~ (all_57_0_17 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_57_0_17 % 18.40/5.36 | % 18.40/5.36 | Applying alpha-rule on (123) yields: % 18.40/5.36 | (124) ~ (all_57_0_17 = 0) % 18.40/5.36 | (125) distinct_points(all_0_5_5, all_0_4_4) = all_57_0_17 % 18.40/5.36 | % 18.40/5.36 | Instantiating formula (31) with all_0_5_5, all_0_4_4, all_57_0_17, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_57_0_17, distinct_points(all_0_5_5, all_0_4_4) = 0, yields: % 18.40/5.36 | (126) all_57_0_17 = 0 % 18.40/5.36 | % 18.40/5.36 | Equations (126) can reduce 124 to: % 18.40/5.36 | (99) $false % 18.40/5.36 | % 18.40/5.36 |-The branch is then unsatisfiable % 18.40/5.36 |-Branch two: % 18.40/5.36 | (128) ~ (distinct_lines(all_0_3_3, all_0_1_1) = 0) % 18.40/5.36 | (129) all_0_0_0 = 0 % 18.40/5.36 | % 18.40/5.36 | Equations (129) can reduce 29 to: % 18.40/5.36 | (99) $false % 18.40/5.36 | % 18.40/5.36 |-The branch is then unsatisfiable % 18.40/5.36 % SZS output end Proof for theBenchmark % 18.40/5.36 % 18.40/5.36 4777ms %------------------------------------------------------------------------------