%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO209+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 03:48:44 EDT 2022 % Result : Theorem 15.48s 4.28s % Output : Proof 17.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO209+3 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n017.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 14:59:12 EDT 2022 % 0.12/0.34 % CPUTime : % 0.55/0.59 ____ _ % 0.55/0.59 ___ / __ \_____(_)___ ________ __________ % 0.55/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.59 % 0.55/0.59 A Theorem Prover for First-Order Logic % 0.55/0.59 (ePrincess v.1.0) % 0.55/0.59 % 0.55/0.59 (c) Philipp Rümmer, 2009-2015 % 0.55/0.59 (c) Peter Backeman, 2014-2015 % 0.55/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.59 Bug reports to peter@backeman.se % 0.55/0.59 % 0.55/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.59 % 0.55/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.79/0.97 Prover 0: Preprocessing ... % 2.32/1.18 Prover 0: Warning: ignoring some quantifiers % 2.42/1.21 Prover 0: Constructing countermodel ... % 14.49/4.07 Prover 0: gave up % 14.49/4.08 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 14.49/4.11 Prover 1: Preprocessing ... % 15.36/4.24 Prover 1: Constructing countermodel ... % 15.48/4.28 Prover 1: proved (209ms) % 15.48/4.28 % 15.48/4.28 No countermodel exists, formula is valid % 15.48/4.28 % SZS status Theorem for theBenchmark % 15.48/4.28 % 15.48/4.28 Generating proof ... found it (size 20) % 16.76/4.58 % 16.76/4.58 % SZS output start Proof for theBenchmark % 16.76/4.58 Assumed formulas after preprocessing and simplification: % 16.76/4.58 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & incident_point_and_line(v0, v3) = 0 & incident_point_and_line(v0, v2) = 0 & parallel_lines(v3, v1) = 0 & parallel_lines(v2, v1) = 0 & equal_lines(v2, v3) = v4 & apart_point_and_line(v0, v1) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ? [v12] : (unorthogonal_lines(v7, v8) = v12 & apart_point_and_line(v5, v7) = v11 & (v12 = 0 | v11 = 0))) & ! [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] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (unorthogonal_lines(v6, v7) = v13 & convergent_lines(v6, v7) = v12 & convergent_lines(v5, v7) = v11 & convergent_lines(v5, v6) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | (v11 = 0 & v9 = 0) | (v10 = 0 & v8 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ? [v10] : (apart_point_and_line(v5, v7) = v9 & convergent_lines(v6, v7) = v10 & (v10 = 0 | v9 = 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(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_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(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, 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 | ~ (orthogonal_lines(v8, v7) = v6) | ~ (orthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (incident_point_and_line(v8, v7) = v6) | ~ (incident_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_lines(v8, v7) = v6) | ~ (parallel_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_lines(v8, v7) = v6) | ~ (equal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_points(v8, v7) = v6) | ~ (equal_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (orthogonal_through_point(v8, v7) = v6) | ~ (orthogonal_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_through_point(v8, v7) = v6) | ~ (parallel_through_point(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(v5, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (unorthogonal_lines(v6, v7) = v12 & convergent_lines(v6, v7) = v11 & convergent_lines(v5, v7) = v10 & convergent_lines(v5, v6) = v9 & ( ~ (v9 = 0) | (v12 = 0 & v11 = 0) | (v10 = 0 & v8 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (apart_point_and_line(v6, v8) = v12 & apart_point_and_line(v6, v7) = v11 & apart_point_and_line(v5, v8) = v10 & apart_point_and_line(v5, v7) = v9 & (v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (orthogonal_lines(v5, v6) = v7) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (incident_point_and_line(v5, v6) = v7) | apart_point_and_line(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (parallel_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_lines(v5, v6) = v7) | distinct_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_points(v5, v6) = v7) | distinct_points(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (point(v7) = v6) | ~ (point(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (line(v7) = v6) | ~ (line(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ~ (unorthogonal_lines(v7, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ~ (apart_point_and_line(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (point(v6) = v9 & line(v7) = v10 & line(v5) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | v10 = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ~ (apart_point_and_line(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ~ (convergent_lines(v7, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (point(v6) = v9 & line(v7) = v10 & line(v5) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | v10 = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ~ (apart_point_and_line(v7, v6) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ~ (apart_point_and_line(v7, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (point(v7) = v11 & line(v6) = v9 & line(v5) = v8 & convergent_lines(v5, v6) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | v11 = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ (apart_point_and_line(v5, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (point(v6) = v9 & point(v5) = v8 & line(v7) = v11 & distinct_points(v5, v6) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | v11 = 0))) & ! [v5] : ! [v6] : ( ~ (orthogonal_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & unorthogonal_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (incident_point_and_line(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (parallel_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (equal_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (equal_points(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (distinct_lines(v5, v6) = 0) | convergent_lines(v5, v6) = 0) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0)) % 17.05/4.62 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 17.05/4.62 | (1) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_4_4, all_0_1_1) = 0 & incident_point_and_line(all_0_4_4, all_0_2_2) = 0 & parallel_lines(all_0_1_1, all_0_3_3) = 0 & parallel_lines(all_0_2_2, all_0_3_3) = 0 & equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 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) % 17.05/4.64 | % 17.05/4.64 | Applying alpha-rule on (1) yields: % 17.05/4.64 | (2) apart_point_and_line(all_0_4_4, all_0_3_3) = 0 % 17.05/4.64 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 17.05/4.64 | (4) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 17.05/4.64 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 17.05/4.64 | (6) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 17.05/4.64 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 17.05/4.64 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 17.05/4.64 | (9) ! [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)))) % 17.05/4.64 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 17.05/4.64 | (11) ! [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)))) % 17.05/4.64 | (12) ! [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))) % 17.05/4.64 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 17.05/4.64 | (14) ! [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)) % 17.05/4.64 | (15) ! [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) % 17.05/4.64 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 17.05/4.64 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 17.05/4.64 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 17.05/4.64 | (19) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 17.05/4.64 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 17.05/4.64 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 17.05/4.64 | (22) ! [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))) % 17.05/4.64 | (23) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 17.05/4.64 | (24) incident_point_and_line(all_0_4_4, all_0_2_2) = 0 % 17.05/4.64 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 17.05/4.64 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 17.05/4.64 | (27) parallel_lines(all_0_2_2, all_0_3_3) = 0 % 17.05/4.64 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 17.05/4.64 | (29) ~ (all_0_0_0 = 0) % 17.05/4.64 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 17.05/4.65 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 17.05/4.65 | (32) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 17.05/4.65 | (33) equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0 % 17.05/4.65 | (34) ! [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))) % 17.05/4.65 | (35) parallel_lines(all_0_1_1, all_0_3_3) = 0 % 17.05/4.65 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) % 17.05/4.65 | (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))) % 17.05/4.65 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 17.05/4.65 | (39) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 17.05/4.65 | (40) ! [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))) % 17.05/4.65 | (41) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 17.05/4.65 | (42) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 17.05/4.65 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 17.05/4.65 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 17.05/4.65 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 17.05/4.65 | (46) incident_point_and_line(all_0_4_4, all_0_1_1) = 0 % 17.05/4.65 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 17.05/4.65 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 17.05/4.65 | (49) ! [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))) % 17.05/4.65 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 17.05/4.65 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 17.05/4.65 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 17.05/4.65 | (53) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 17.05/4.65 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 17.05/4.65 | (55) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 17.05/4.65 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 17.05/4.65 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 17.05/4.65 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 17.05/4.65 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 17.05/4.65 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 17.05/4.65 | (61) ! [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))) % 17.05/4.65 | (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) % 17.05/4.65 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 17.05/4.65 | % 17.05/4.66 | Instantiating formula (6) with all_0_3_3, all_0_1_1 and discharging atoms parallel_lines(all_0_1_1, all_0_3_3) = 0, yields: % 17.05/4.66 | (64) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_1_1, all_0_3_3) = v0) % 17.05/4.66 | % 17.05/4.66 | Instantiating formula (6) with all_0_3_3, all_0_2_2 and discharging atoms parallel_lines(all_0_2_2, all_0_3_3) = 0, yields: % 17.05/4.66 | (65) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0) % 17.05/4.66 | % 17.05/4.66 | Instantiating formula (31) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 17.05/4.66 | (66) all_0_0_0 = 0 | distinct_lines(all_0_2_2, all_0_1_1) = 0 % 17.05/4.66 | % 17.05/4.66 | Instantiating (65) with all_8_0_5 yields: % 17.05/4.66 | (67) ~ (all_8_0_5 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_8_0_5 % 17.05/4.66 | % 17.05/4.66 | Applying alpha-rule on (67) yields: % 17.05/4.66 | (68) ~ (all_8_0_5 = 0) % 17.05/4.66 | (69) convergent_lines(all_0_2_2, all_0_3_3) = all_8_0_5 % 17.05/4.66 | % 17.05/4.66 | Instantiating (64) with all_10_0_6 yields: % 17.05/4.66 | (70) ~ (all_10_0_6 = 0) & convergent_lines(all_0_1_1, all_0_3_3) = all_10_0_6 % 17.05/4.66 | % 17.05/4.66 | Applying alpha-rule on (70) yields: % 17.05/4.66 | (71) ~ (all_10_0_6 = 0) % 17.05/4.66 | (72) convergent_lines(all_0_1_1, all_0_3_3) = all_10_0_6 % 17.05/4.66 | % 17.05/4.66 +-Applying beta-rule and splitting (66), into two cases. % 17.05/4.66 |-Branch one: % 17.05/4.66 | (73) distinct_lines(all_0_2_2, all_0_1_1) = 0 % 17.05/4.66 | % 17.05/4.66 | Instantiating formula (39) with all_0_1_1, all_0_2_2 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, yields: % 17.05/4.66 | (74) convergent_lines(all_0_2_2, all_0_1_1) = 0 % 17.05/4.66 | % 17.05/4.66 | Instantiating formula (3) with all_8_0_5, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = 0, convergent_lines(all_0_2_2, all_0_3_3) = all_8_0_5, yields: % 17.05/4.66 | (75) all_8_0_5 = 0 | convergent_lines(all_0_1_1, all_0_3_3) = 0 % 17.05/4.66 | % 17.05/4.66 +-Applying beta-rule and splitting (75), into two cases. % 17.05/4.66 |-Branch one: % 17.31/4.66 | (76) convergent_lines(all_0_1_1, all_0_3_3) = 0 % 17.31/4.66 | % 17.31/4.66 | Instantiating formula (50) with all_0_1_1, all_0_3_3, 0, all_10_0_6 and discharging atoms convergent_lines(all_0_1_1, all_0_3_3) = all_10_0_6, convergent_lines(all_0_1_1, all_0_3_3) = 0, yields: % 17.31/4.66 | (77) all_10_0_6 = 0 % 17.31/4.66 | % 17.31/4.66 | Equations (77) can reduce 71 to: % 17.31/4.66 | (78) $false % 17.31/4.66 | % 17.31/4.66 |-The branch is then unsatisfiable % 17.31/4.66 |-Branch two: % 17.31/4.66 | (79) ~ (convergent_lines(all_0_1_1, all_0_3_3) = 0) % 17.31/4.66 | (80) all_8_0_5 = 0 % 17.31/4.66 | % 17.31/4.66 | Equations (80) can reduce 68 to: % 17.31/4.66 | (78) $false % 17.31/4.66 | % 17.31/4.66 |-The branch is then unsatisfiable % 17.31/4.66 |-Branch two: % 17.31/4.66 | (82) ~ (distinct_lines(all_0_2_2, all_0_1_1) = 0) % 17.31/4.66 | (83) all_0_0_0 = 0 % 17.31/4.66 | % 17.31/4.66 | Equations (83) can reduce 29 to: % 17.31/4.66 | (78) $false % 17.31/4.66 | % 17.31/4.66 |-The branch is then unsatisfiable % 17.31/4.66 % SZS output end Proof for theBenchmark % 17.31/4.66 % 17.31/4.66 4062ms %------------------------------------------------------------------------------