%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO183+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.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 03:48:20 EDT 2022 % Result : Theorem 18.82s 5.62s % Output : Proof 20.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : GEO183+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n011.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sat Jun 18 12:37:53 EDT 2022 % 0.14/0.35 % CPUTime : % 0.58/0.60 ____ _ % 0.58/0.60 ___ / __ \_____(_)___ ________ __________ % 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.60 % 0.58/0.60 A Theorem Prover for First-Order Logic % 0.58/0.60 (ePrincess v.1.0) % 0.58/0.60 % 0.58/0.60 (c) Philipp Rümmer, 2009-2015 % 0.58/0.60 (c) Peter Backeman, 2014-2015 % 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.60 Bug reports to peter@backeman.se % 0.58/0.60 % 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.60 % 0.58/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.77/0.95 Prover 0: Preprocessing ... % 2.12/1.17 Prover 0: Warning: ignoring some quantifiers % 2.46/1.20 Prover 0: Constructing countermodel ... % 17.72/5.37 Prover 0: gave up % 17.72/5.37 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 18.05/5.41 Prover 1: Preprocessing ... % 18.82/5.56 Prover 1: Constructing countermodel ... % 18.82/5.62 Prover 1: proved (248ms) % 18.82/5.62 % 18.82/5.62 No countermodel exists, formula is valid % 18.82/5.62 % SZS status Theorem for theBenchmark % 18.82/5.62 % 18.82/5.62 Generating proof ... found it (size 39) % 20.12/5.83 % 20.12/5.83 % SZS output start Proof for theBenchmark % 20.12/5.83 Assumed formulas after preprocessing and simplification: % 20.12/5.83 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (incident_point_and_line(v1, v2) = v6 & incident_point_and_line(v0, v2) = v5 & equal_lines(v2, v4) = 0 & line_connecting(v0, v1) = v4 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v1) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (unorthogonal_lines(v8, v10) = v12) | ~ (apart_point_and_line(v7, v8) = v11) | ~ (distinct_lines(v8, v9) = 0) | ? [v13] : ? [v14] : (unorthogonal_lines(v9, v10) = v14 & apart_point_and_line(v7, v9) = v13 & (v14 = 0 | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (unorthogonal_lines(v7, v8) = v10) | ? [v12] : ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v11) | ~ (unorthogonal_lines(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (unorthogonal_lines(v8, v9) = v15 & convergent_lines(v8, v9) = v14 & convergent_lines(v7, v9) = v13 & convergent_lines(v7, v8) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | (v13 = 0 & v11 = 0) | (v12 = 0 & v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v11] : ? [v12] : (apart_point_and_line(v7, v9) = v11 & convergent_lines(v8, v9) = v12 & (v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = 0) | ~ (distinct_lines(v8, v9) = v10) | apart_point_and_line(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = 0) | ~ (distinct_points(v7, v9) = v10) | apart_point_and_line(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v8) = 0) | ~ (distinct_lines(v8, v9) = v10) | convergent_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v7, v9) = v10) | ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_points(v7, v9) = v10) | ~ (distinct_points(v7, v8) = 0) | distinct_points(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (orthogonal_lines(v10, v9) = v8) | ~ (orthogonal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (incident_point_and_line(v10, v9) = v8) | ~ (incident_point_and_line(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (parallel_lines(v10, v9) = v8) | ~ (parallel_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_lines(v10, v9) = v8) | ~ (equal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_points(v10, v9) = v8) | ~ (equal_points(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (orthogonal_through_point(v10, v9) = v8) | ~ (orthogonal_through_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unorthogonal_lines(v10, v9) = v8) | ~ (unorthogonal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (parallel_through_point(v10, v9) = v8) | ~ (parallel_through_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection_point(v10, v9) = v8) | ~ (intersection_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (line_connecting(v10, v9) = v8) | ~ (line_connecting(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (apart_point_and_line(v10, v9) = v8) | ~ (apart_point_and_line(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (convergent_lines(v10, v9) = v8) | ~ (convergent_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (distinct_lines(v10, v9) = v8) | ~ (distinct_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (distinct_points(v10, v9) = v8) | ~ (distinct_points(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) | ~ (unorthogonal_lines(v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (unorthogonal_lines(v8, v9) = v14 & convergent_lines(v8, v9) = v13 & convergent_lines(v7, v9) = v12 & convergent_lines(v7, v8) = v11 & ( ~ (v11 = 0) | (v14 = 0 & v13 = 0) | (v12 = 0 & v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (distinct_lines(v9, v10) = 0) | ~ (distinct_points(v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apart_point_and_line(v8, v10) = v14 & apart_point_and_line(v8, v9) = v13 & apart_point_and_line(v7, v10) = v12 & apart_point_and_line(v7, v9) = v11 & (v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (orthogonal_lines(v7, v8) = v9) | unorthogonal_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (incident_point_and_line(v7, v8) = v9) | apart_point_and_line(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (parallel_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_lines(v7, v8) = v9) | distinct_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_points(v7, v8) = v9) | distinct_points(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (point(v9) = v8) | ~ (point(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (line(v9) = v8) | ~ (line(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) | ~ (unorthogonal_lines(v9, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) | ~ (apart_point_and_line(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (point(v8) = v11 & line(v9) = v12 & line(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) | ~ (apart_point_and_line(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) | ~ (convergent_lines(v9, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (point(v8) = v11 & line(v9) = v12 & line(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ~ (apart_point_and_line(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ~ (apart_point_and_line(v9, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (point(v9) = v13 & line(v8) = v11 & line(v7) = v10 & convergent_lines(v7, v8) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ (apart_point_and_line(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ (apart_point_and_line(v7, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (point(v8) = v11 & point(v7) = v10 & line(v9) = v13 & distinct_points(v7, v8) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ( ~ (orthogonal_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (incident_point_and_line(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (parallel_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (equal_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (equal_points(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | convergent_lines(v7, v8) = 0) & ! [v7] : ~ (convergent_lines(v7, v7) = 0) & ! [v7] : ~ (distinct_lines(v7, v7) = 0) & ! [v7] : ~ (distinct_points(v7, v7) = 0) & ( ~ (v6 = 0) | ~ (v5 = 0))) % 20.24/5.87 | 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, all_0_6_6 yields: % 20.24/5.87 | (1) incident_point_and_line(all_0_5_5, all_0_4_4) = all_0_0_0 & incident_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1 & equal_lines(all_0_4_4, all_0_2_2) = 0 & line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2 & convergent_lines(all_0_4_4, all_0_3_3) = 0 & distinct_points(all_0_6_6, all_0_5_5) = 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) & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)) % 20.24/5.88 | % 20.24/5.88 | Applying alpha-rule on (1) yields: % 20.24/5.88 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 20.24/5.88 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 20.24/5.88 | (4) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 20.24/5.88 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 20.24/5.88 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 20.24/5.88 | (7) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 20.24/5.88 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 20.24/5.88 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 20.24/5.88 | (10) ! [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))) % 20.24/5.88 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 20.24/5.88 | (12) ! [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) % 20.24/5.88 | (13) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 20.24/5.88 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 20.24/5.88 | (15) ! [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))) % 20.24/5.88 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 20.24/5.88 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 20.24/5.88 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 20.24/5.88 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 20.24/5.89 | (20) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 20.24/5.89 | (21) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 20.24/5.89 | (22) ! [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)))) % 20.24/5.89 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 20.24/5.89 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 20.24/5.89 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) % 20.24/5.89 | (26) ! [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)))) % 20.24/5.89 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 20.24/5.89 | (28) incident_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1 % 20.24/5.89 | (29) ! [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))) % 20.24/5.89 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 20.24/5.89 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 20.24/5.89 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 20.24/5.89 | (33) line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2 % 20.24/5.89 | (34) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 20.24/5.89 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 20.24/5.89 | (36) distinct_points(all_0_6_6, all_0_5_5) = 0 % 20.24/5.89 | (37) ! [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))) % 20.24/5.89 | (38) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) % 20.24/5.89 | (39) ! [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) % 20.24/5.89 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 20.24/5.89 | (41) ! [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))) % 20.24/5.89 | (42) ! [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))) % 20.24/5.89 | (43) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 20.24/5.89 | (44) incident_point_and_line(all_0_5_5, all_0_4_4) = all_0_0_0 % 20.24/5.89 | (45) equal_lines(all_0_4_4, all_0_2_2) = 0 % 20.24/5.89 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 20.24/5.89 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 20.24/5.89 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 20.24/5.89 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 20.24/5.89 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 20.24/5.89 | (51) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 20.24/5.89 | (52) ! [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)) % 20.24/5.89 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 20.24/5.89 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 20.24/5.89 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 20.24/5.89 | (56) ! [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))) % 20.24/5.89 | (57) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 20.24/5.89 | (58) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 20.24/5.90 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 20.24/5.90 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 20.24/5.90 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 20.24/5.90 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 20.24/5.90 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 20.24/5.90 | % 20.24/5.90 | Instantiating formula (8) with all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms incident_point_and_line(all_0_5_5, all_0_4_4) = all_0_0_0, yields: % 20.24/5.90 | (64) all_0_0_0 = 0 | apart_point_and_line(all_0_5_5, all_0_4_4) = 0 % 20.24/5.90 | % 20.24/5.90 | Instantiating formula (8) with all_0_1_1, all_0_4_4, all_0_6_6 and discharging atoms incident_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, yields: % 20.24/5.90 | (65) all_0_1_1 = 0 | apart_point_and_line(all_0_6_6, all_0_4_4) = 0 % 20.24/5.90 | % 20.24/5.90 | Instantiating formula (13) with all_0_2_2, all_0_4_4 and discharging atoms equal_lines(all_0_4_4, all_0_2_2) = 0, yields: % 20.24/5.90 | (66) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_2_2) = v0) % 20.24/5.90 | % 20.24/5.90 | Instantiating formula (10) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2, yields: % 20.24/5.90 | (67) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_0_5_5) = v1 & point(all_0_6_6) = v0 & line(all_0_2_2) = v3 & distinct_points(all_0_6_6, all_0_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 20.24/5.90 | % 20.24/5.90 | Instantiating (67) with all_16_0_7, all_16_1_8, all_16_2_9, all_16_3_10 yields: % 20.24/5.90 | (68) point(all_0_5_5) = all_16_2_9 & point(all_0_6_6) = all_16_3_10 & line(all_0_2_2) = all_16_0_7 & distinct_points(all_0_6_6, all_0_5_5) = all_16_1_8 & ( ~ (all_16_1_8 = 0) | ~ (all_16_2_9 = 0) | ~ (all_16_3_10 = 0) | all_16_0_7 = 0) % 20.24/5.90 | % 20.24/5.90 | Applying alpha-rule on (68) yields: % 20.24/5.90 | (69) ~ (all_16_1_8 = 0) | ~ (all_16_2_9 = 0) | ~ (all_16_3_10 = 0) | all_16_0_7 = 0 % 20.24/5.90 | (70) distinct_points(all_0_6_6, all_0_5_5) = all_16_1_8 % 20.24/5.90 | (71) point(all_0_6_6) = all_16_3_10 % 20.24/5.90 | (72) line(all_0_2_2) = all_16_0_7 % 20.24/5.90 | (73) point(all_0_5_5) = all_16_2_9 % 20.24/5.90 | % 20.24/5.90 | Instantiating (66) with all_18_0_11 yields: % 20.24/5.90 | (74) ~ (all_18_0_11 = 0) & distinct_lines(all_0_4_4, all_0_2_2) = all_18_0_11 % 20.24/5.90 | % 20.24/5.90 | Applying alpha-rule on (74) yields: % 20.24/5.90 | (75) ~ (all_18_0_11 = 0) % 20.24/5.90 | (76) distinct_lines(all_0_4_4, all_0_2_2) = all_18_0_11 % 20.24/5.90 | % 20.24/5.90 | Instantiating formula (63) with all_0_6_6, all_0_5_5, all_16_1_8, 0 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_16_1_8, distinct_points(all_0_6_6, all_0_5_5) = 0, yields: % 20.24/5.90 | (77) all_16_1_8 = 0 % 20.24/5.90 | % 20.24/5.90 | From (77) and (70) follows: % 20.24/5.90 | (36) distinct_points(all_0_6_6, all_0_5_5) = 0 % 20.24/5.90 | % 20.24/5.90 +-Applying beta-rule and splitting (38), into two cases. % 20.24/5.90 |-Branch one: % 20.24/5.90 | (79) ~ (all_0_0_0 = 0) % 20.24/5.90 | % 20.24/5.90 +-Applying beta-rule and splitting (64), into two cases. % 20.24/5.90 |-Branch one: % 20.24/5.90 | (80) apart_point_and_line(all_0_5_5, all_0_4_4) = 0 % 20.24/5.90 | % 20.24/5.90 | Instantiating formula (39) with all_18_0_11, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_2_2) = all_18_0_11, yields: % 20.24/5.90 | (81) all_18_0_11 = 0 | apart_point_and_line(all_0_5_5, all_0_2_2) = 0 % 20.24/5.90 | % 20.24/5.90 +-Applying beta-rule and splitting (81), into two cases. % 20.24/5.90 |-Branch one: % 20.24/5.90 | (82) apart_point_and_line(all_0_5_5, all_0_2_2) = 0 % 20.24/5.90 | % 20.24/5.90 | Instantiating formula (3) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields: % 20.24/5.90 | (83) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0) % 20.24/5.90 | % 20.24/5.90 | Instantiating (83) with all_59_0_12 yields: % 20.24/5.90 | (84) ~ (all_59_0_12 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_59_0_12 % 20.24/5.90 | % 20.24/5.90 | Applying alpha-rule on (84) yields: % 20.24/5.90 | (85) ~ (all_59_0_12 = 0) % 20.24/5.90 | (86) distinct_points(all_0_6_6, all_0_5_5) = all_59_0_12 % 20.24/5.90 | % 20.24/5.90 | Instantiating formula (63) with all_0_6_6, all_0_5_5, all_59_0_12, 0 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_59_0_12, distinct_points(all_0_6_6, all_0_5_5) = 0, yields: % 20.24/5.90 | (87) all_59_0_12 = 0 % 20.24/5.90 | % 20.24/5.90 | Equations (87) can reduce 85 to: % 20.24/5.90 | (88) $false % 20.24/5.90 | % 20.24/5.90 |-The branch is then unsatisfiable % 20.24/5.90 |-Branch two: % 20.24/5.90 | (89) ~ (apart_point_and_line(all_0_5_5, all_0_2_2) = 0) % 20.24/5.91 | (90) all_18_0_11 = 0 % 20.24/5.91 | % 20.24/5.91 | Equations (90) can reduce 75 to: % 20.24/5.91 | (88) $false % 20.24/5.91 | % 20.24/5.91 |-The branch is then unsatisfiable % 20.24/5.91 |-Branch two: % 20.24/5.91 | (92) ~ (apart_point_and_line(all_0_5_5, all_0_4_4) = 0) % 20.24/5.91 | (93) all_0_0_0 = 0 % 20.24/5.91 | % 20.24/5.91 | Equations (93) can reduce 79 to: % 20.24/5.91 | (88) $false % 20.24/5.91 | % 20.24/5.91 |-The branch is then unsatisfiable % 20.24/5.91 |-Branch two: % 20.24/5.91 | (93) all_0_0_0 = 0 % 20.24/5.91 | (96) ~ (all_0_1_1 = 0) % 20.24/5.91 | % 20.24/5.91 +-Applying beta-rule and splitting (65), into two cases. % 20.24/5.91 |-Branch one: % 20.24/5.91 | (97) apart_point_and_line(all_0_6_6, all_0_4_4) = 0 % 20.24/5.91 | % 20.24/5.91 | Instantiating formula (39) with all_18_0_11, all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_2_2) = all_18_0_11, yields: % 20.24/5.91 | (98) all_18_0_11 = 0 | apart_point_and_line(all_0_6_6, all_0_2_2) = 0 % 20.24/5.91 | % 20.24/5.91 +-Applying beta-rule and splitting (98), into two cases. % 20.24/5.91 |-Branch one: % 20.24/5.91 | (99) apart_point_and_line(all_0_6_6, all_0_2_2) = 0 % 20.24/5.91 | % 20.24/5.91 | Instantiating formula (5) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields: % 20.24/5.91 | (83) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0) % 20.24/5.91 | % 20.24/5.91 | Instantiating (83) with all_65_0_14 yields: % 20.24/5.91 | (101) ~ (all_65_0_14 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_65_0_14 % 20.24/5.91 | % 20.24/5.91 | Applying alpha-rule on (101) yields: % 20.24/5.91 | (102) ~ (all_65_0_14 = 0) % 20.24/5.91 | (103) distinct_points(all_0_6_6, all_0_5_5) = all_65_0_14 % 20.24/5.91 | % 20.24/5.91 | Instantiating formula (63) with all_0_6_6, all_0_5_5, all_65_0_14, 0 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_65_0_14, distinct_points(all_0_6_6, all_0_5_5) = 0, yields: % 20.24/5.91 | (104) all_65_0_14 = 0 % 20.24/5.91 | % 20.24/5.91 | Equations (104) can reduce 102 to: % 20.24/5.91 | (88) $false % 20.24/5.91 | % 20.24/5.91 |-The branch is then unsatisfiable % 20.24/5.91 |-Branch two: % 20.24/5.91 | (106) ~ (apart_point_and_line(all_0_6_6, all_0_2_2) = 0) % 20.24/5.91 | (90) all_18_0_11 = 0 % 20.24/5.91 | % 20.24/5.91 | Equations (90) can reduce 75 to: % 20.24/5.91 | (88) $false % 20.24/5.91 | % 20.24/5.91 |-The branch is then unsatisfiable % 20.24/5.91 |-Branch two: % 20.24/5.91 | (109) ~ (apart_point_and_line(all_0_6_6, all_0_4_4) = 0) % 20.24/5.91 | (110) all_0_1_1 = 0 % 20.24/5.91 | % 20.24/5.91 | Equations (110) can reduce 96 to: % 20.24/5.91 | (88) $false % 20.24/5.91 | % 20.24/5.91 |-The branch is then unsatisfiable % 20.24/5.91 % SZS output end Proof for theBenchmark % 20.24/5.91 % 20.24/5.91 5293ms %------------------------------------------------------------------------------