%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO208+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 14.39s 3.99s % Output : Proof 15.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : GEO208+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n017.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Fri Jun 17 21:46:12 EDT 2022 % 0.11/0.32 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.69/0.97 Prover 0: Preprocessing ... % 2.11/1.18 Prover 0: Warning: ignoring some quantifiers % 2.39/1.20 Prover 0: Constructing countermodel ... % 13.37/3.80 Prover 0: gave up % 13.37/3.80 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 13.61/3.84 Prover 1: Preprocessing ... % 14.05/3.95 Prover 1: Constructing countermodel ... % 14.05/3.99 Prover 1: proved (184ms) % 14.39/3.99 % 14.39/3.99 No countermodel exists, formula is valid % 14.39/3.99 % SZS status Theorem for theBenchmark % 14.39/3.99 % 14.39/3.99 Generating proof ... found it (size 25) % 15.39/4.23 % 15.39/4.23 % SZS output start Proof for theBenchmark % 15.39/4.23 Assumed formulas after preprocessing and simplification: % 15.39/4.23 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & incident_point_and_line(v0, v2) = 0 & incident_point_and_line(v0, v1) = 0 & parallel_lines(v1, v2) = 0 & equal_lines(v1, v2) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (apart_point_and_line(v4, v5) = v8) | ~ (distinct_lines(v5, v6) = 0) | ? [v10] : ? [v11] : (unorthogonal_lines(v6, v7) = v11 & apart_point_and_line(v4, v6) = v10 & (v11 = 0 | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (unorthogonal_lines(v4, v6) = v8) | ~ (unorthogonal_lines(v4, v5) = v7) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v4, v6) = v8) | ~ (unorthogonal_lines(v4, v5) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (unorthogonal_lines(v5, v6) = v12 & convergent_lines(v5, v6) = v11 & convergent_lines(v4, v6) = v10 & convergent_lines(v4, v5) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | (v10 = 0 & v8 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = v7) | ~ (distinct_lines(v5, v6) = 0) | ? [v8] : ? [v9] : (apart_point_and_line(v4, v6) = v8 & convergent_lines(v5, v6) = v9 & (v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = 0) | ~ (distinct_lines(v5, v6) = v7) | apart_point_and_line(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = 0) | ~ (distinct_points(v4, v6) = v7) | apart_point_and_line(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v4, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | convergent_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v4, v5) = 0) | ~ (distinct_lines(v5, v6) = v7) | convergent_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v4, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v4, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (orthogonal_lines(v7, v6) = v5) | ~ (orthogonal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (incident_point_and_line(v7, v6) = v5) | ~ (incident_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (parallel_lines(v7, v6) = v5) | ~ (parallel_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_lines(v7, v6) = v5) | ~ (equal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_points(v7, v6) = v5) | ~ (equal_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (orthogonal_through_point(v7, v6) = v5) | ~ (orthogonal_through_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unorthogonal_lines(v7, v6) = v5) | ~ (unorthogonal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (parallel_through_point(v7, v6) = v5) | ~ (parallel_through_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection_point(v7, v6) = v5) | ~ (intersection_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (line_connecting(v7, v6) = v5) | ~ (line_connecting(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (apart_point_and_line(v7, v6) = v5) | ~ (apart_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (convergent_lines(v7, v6) = v5) | ~ (convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_lines(v7, v6) = v5) | ~ (distinct_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_points(v7, v6) = v5) | ~ (distinct_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v6) = v7) | ~ (unorthogonal_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (unorthogonal_lines(v5, v6) = v11 & convergent_lines(v5, v6) = v10 & convergent_lines(v4, v6) = v9 & convergent_lines(v4, v5) = v8 & ( ~ (v8 = 0) | (v11 = 0 & v10 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ~ (distinct_points(v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (apart_point_and_line(v5, v7) = v11 & apart_point_and_line(v5, v6) = v10 & apart_point_and_line(v4, v7) = v9 & apart_point_and_line(v4, v6) = v8 & (v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (orthogonal_lines(v4, v5) = v6) | unorthogonal_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (incident_point_and_line(v4, v5) = v6) | apart_point_and_line(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (parallel_lines(v4, v5) = v6) | convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_lines(v4, v5) = v6) | distinct_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_points(v4, v5) = v6) | distinct_points(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unorthogonal_lines(v4, v5) = v6) | convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (point(v6) = v5) | ~ (point(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (line(v6) = v5) | ~ (line(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v5, v4) = v6) | ~ (unorthogonal_lines(v6, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v5, v4) = v6) | ~ (apart_point_and_line(v4, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (point(v5) = v8 & line(v6) = v9 & line(v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | ~ (apart_point_and_line(v4, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | ~ (convergent_lines(v6, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (point(v5) = v8 & line(v6) = v9 & line(v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ~ (apart_point_and_line(v6, v5) = 0) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ~ (apart_point_and_line(v6, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (point(v6) = v10 & line(v5) = v8 & line(v4) = v7 & convergent_lines(v4, v5) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ (apart_point_and_line(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ (apart_point_and_line(v4, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (point(v5) = v8 & point(v4) = v7 & line(v6) = v10 & distinct_points(v4, v5) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ( ~ (orthogonal_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & unorthogonal_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (incident_point_and_line(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & apart_point_and_line(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (parallel_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & convergent_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (equal_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & distinct_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (equal_points(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & distinct_points(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | convergent_lines(v4, v5) = 0) & ! [v4] : ~ (convergent_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_points(v4, v4) = 0)) % 15.73/4.28 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 15.73/4.28 | (1) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_3_3, all_0_1_1) = 0 & incident_point_and_line(all_0_3_3, all_0_2_2) = 0 & parallel_lines(all_0_2_2, all_0_1_1) = 0 & equal_lines(all_0_2_2, all_0_1_1) = all_0_0_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) % 15.73/4.29 | % 15.73/4.29 | Applying alpha-rule on (1) yields: % 15.73/4.29 | (2) ! [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))) % 15.73/4.29 | (3) ! [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))) % 15.73/4.29 | (4) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 15.73/4.29 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 15.73/4.29 | (6) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 15.73/4.29 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 15.73/4.29 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 15.73/4.29 | (9) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 15.73/4.29 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 15.73/4.29 | (11) ! [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)) % 15.73/4.29 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 15.73/4.29 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 15.73/4.29 | (14) ! [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))) % 15.73/4.29 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 15.73/4.29 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 15.73/4.29 | (17) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 15.73/4.29 | (18) ~ (all_0_0_0 = 0) % 15.73/4.29 | (19) equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0 % 15.73/4.29 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 15.73/4.30 | (21) ! [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)))) % 15.73/4.30 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 15.73/4.30 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 15.73/4.30 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) % 15.73/4.30 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 15.73/4.30 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 15.73/4.30 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 15.73/4.30 | (28) incident_point_and_line(all_0_3_3, all_0_2_2) = 0 % 15.73/4.30 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 15.73/4.30 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 15.73/4.30 | (31) ! [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))) % 15.73/4.30 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 15.73/4.30 | (33) incident_point_and_line(all_0_3_3, all_0_1_1) = 0 % 15.73/4.30 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 15.73/4.30 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 15.73/4.30 | (36) ! [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))) % 15.73/4.30 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 15.73/4.30 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 15.73/4.30 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 15.73/4.30 | (40) ! [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))) % 15.73/4.30 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 15.73/4.30 | (42) ! [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) % 15.73/4.30 | (43) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 15.73/4.30 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 15.73/4.30 | (45) parallel_lines(all_0_2_2, all_0_1_1) = 0 % 15.73/4.30 | (46) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 15.73/4.30 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 15.73/4.30 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 15.73/4.30 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 15.73/4.30 | (50) ! [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))) % 15.73/4.30 | (51) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 15.73/4.30 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 15.73/4.30 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 15.73/4.30 | (54) ! [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)))) % 15.73/4.31 | (55) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 15.73/4.31 | (56) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 15.73/4.31 | (57) ! [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) % 15.73/4.31 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 15.73/4.31 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 15.73/4.31 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 15.73/4.31 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 15.73/4.31 | % 15.73/4.31 | Instantiating formula (6) with all_0_2_2, all_0_3_3 and discharging atoms incident_point_and_line(all_0_3_3, all_0_2_2) = 0, yields: % 15.73/4.31 | (62) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = v0) % 15.73/4.31 | % 15.73/4.31 | Instantiating formula (46) with all_0_1_1, all_0_2_2 and discharging atoms parallel_lines(all_0_2_2, all_0_1_1) = 0, yields: % 15.73/4.31 | (63) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0) % 15.73/4.31 | % 15.73/4.31 | Instantiating formula (5) 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: % 15.73/4.31 | (64) all_0_0_0 = 0 | distinct_lines(all_0_2_2, all_0_1_1) = 0 % 15.73/4.31 | % 15.73/4.31 | Instantiating (63) with all_8_0_4 yields: % 15.73/4.31 | (65) ~ (all_8_0_4 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_8_0_4 % 15.73/4.31 | % 15.73/4.31 | Applying alpha-rule on (65) yields: % 15.73/4.31 | (66) ~ (all_8_0_4 = 0) % 15.73/4.31 | (67) convergent_lines(all_0_2_2, all_0_1_1) = all_8_0_4 % 15.73/4.31 | % 15.73/4.31 | Instantiating (62) with all_10_0_5 yields: % 15.73/4.31 | (68) ~ (all_10_0_5 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = all_10_0_5 % 15.73/4.31 | % 15.73/4.31 | Applying alpha-rule on (68) yields: % 15.73/4.31 | (69) ~ (all_10_0_5 = 0) % 15.73/4.31 | (70) apart_point_and_line(all_0_3_3, all_0_2_2) = all_10_0_5 % 15.73/4.31 | % 15.73/4.31 +-Applying beta-rule and splitting (64), into two cases. % 15.73/4.31 |-Branch one: % 15.73/4.31 | (71) distinct_lines(all_0_2_2, all_0_1_1) = 0 % 15.73/4.31 | % 15.73/4.31 | Instantiating formula (36) with all_10_0_5, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_10_0_5, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields: % 15.73/4.31 | (72) all_10_0_5 = 0 | ? [v0] : ? [v1] : (apart_point_and_line(all_0_3_3, all_0_1_1) = v0 & convergent_lines(all_0_2_2, all_0_1_1) = v1 & (v1 = 0 | v0 = 0)) % 15.73/4.31 | % 15.73/4.31 | Instantiating formula (17) with all_0_1_1, all_0_2_2 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, yields: % 15.73/4.31 | (73) convergent_lines(all_0_2_2, all_0_1_1) = 0 % 15.73/4.31 | % 15.73/4.31 +-Applying beta-rule and splitting (72), into two cases. % 15.73/4.31 |-Branch one: % 15.73/4.31 | (74) all_10_0_5 = 0 % 15.73/4.31 | % 15.73/4.31 | Equations (74) can reduce 69 to: % 15.73/4.31 | (75) $false % 15.73/4.31 | % 15.73/4.31 |-The branch is then unsatisfiable % 15.73/4.31 |-Branch two: % 15.73/4.31 | (69) ~ (all_10_0_5 = 0) % 15.73/4.31 | (77) ? [v0] : ? [v1] : (apart_point_and_line(all_0_3_3, all_0_1_1) = v0 & convergent_lines(all_0_2_2, all_0_1_1) = v1 & (v1 = 0 | v0 = 0)) % 15.73/4.31 | % 15.73/4.31 | Instantiating (77) with all_36_0_7, all_36_1_8 yields: % 15.73/4.31 | (78) apart_point_and_line(all_0_3_3, all_0_1_1) = all_36_1_8 & convergent_lines(all_0_2_2, all_0_1_1) = all_36_0_7 & (all_36_0_7 = 0 | all_36_1_8 = 0) % 15.73/4.31 | % 15.73/4.31 | Applying alpha-rule on (78) yields: % 15.73/4.31 | (79) apart_point_and_line(all_0_3_3, all_0_1_1) = all_36_1_8 % 15.73/4.31 | (80) convergent_lines(all_0_2_2, all_0_1_1) = all_36_0_7 % 15.73/4.31 | (81) all_36_0_7 = 0 | all_36_1_8 = 0 % 15.73/4.31 | % 15.73/4.31 | Instantiating formula (16) with all_0_2_2, all_0_1_1, all_36_0_7, all_8_0_4 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_36_0_7, convergent_lines(all_0_2_2, all_0_1_1) = all_8_0_4, yields: % 15.73/4.31 | (82) all_36_0_7 = all_8_0_4 % 15.73/4.31 | % 15.73/4.31 | Instantiating formula (16) with all_0_2_2, all_0_1_1, 0, all_36_0_7 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_36_0_7, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields: % 15.73/4.31 | (83) all_36_0_7 = 0 % 15.73/4.31 | % 15.73/4.31 | Combining equations (82,83) yields a new equation: % 15.73/4.31 | (84) all_8_0_4 = 0 % 15.73/4.31 | % 15.73/4.31 | Simplifying 84 yields: % 15.73/4.31 | (85) all_8_0_4 = 0 % 15.73/4.31 | % 15.73/4.31 | Equations (85) can reduce 66 to: % 15.73/4.31 | (75) $false % 15.73/4.31 | % 15.73/4.31 |-The branch is then unsatisfiable % 15.73/4.31 |-Branch two: % 15.73/4.31 | (87) ~ (distinct_lines(all_0_2_2, all_0_1_1) = 0) % 15.73/4.31 | (88) all_0_0_0 = 0 % 15.73/4.31 | % 15.73/4.31 | Equations (88) can reduce 18 to: % 15.73/4.31 | (75) $false % 15.73/4.31 | % 15.73/4.31 |-The branch is then unsatisfiable % 15.73/4.31 % SZS output end Proof for theBenchmark % 15.73/4.31 % 15.73/4.31 3732ms %------------------------------------------------------------------------------