%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 03:48:41 EDT 2022 % Result : Theorem 3.54s 1.54s % Output : Proof 4.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.36 % Computer : n029.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Sat Jun 18 02:18:28 EDT 2022 % 0.15/0.37 % CPUTime : % 0.62/0.63 ____ _ % 0.62/0.63 ___ / __ \_____(_)___ ________ __________ % 0.62/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.62/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.62/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.62/0.63 % 0.62/0.63 A Theorem Prover for First-Order Logic % 0.62/0.63 (ePrincess v.1.0) % 0.62/0.63 % 0.62/0.63 (c) Philipp Rümmer, 2009-2015 % 0.62/0.63 (c) Peter Backeman, 2014-2015 % 0.62/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.62/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.62/0.63 Bug reports to peter@backeman.se % 0.62/0.63 % 0.62/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.62/0.63 % 0.62/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.62/1.00 Prover 0: Preprocessing ... % 1.99/1.15 Prover 0: Warning: ignoring some quantifiers % 1.99/1.17 Prover 0: Constructing countermodel ... % 2.84/1.34 Prover 0: gave up % 2.84/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.84/1.37 Prover 1: Preprocessing ... % 3.37/1.48 Prover 1: Constructing countermodel ... % 3.54/1.54 Prover 1: proved (195ms) % 3.54/1.54 % 3.54/1.54 No countermodel exists, formula is valid % 3.54/1.54 % SZS status Theorem for theBenchmark % 3.54/1.54 % 3.54/1.54 Generating proof ... found it (size 20) % 4.63/1.78 % 4.63/1.78 % SZS output start Proof for theBenchmark % 4.63/1.78 Assumed formulas after preprocessing and simplification: % 4.63/1.78 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & ~ (v3 = 0) & parallel_through_point(v2, v0) = v5 & apart_point_and_line(v0, v1) = v3 & convergent_lines(v1, v2) = v4 & distinct_lines(v1, v5) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ? [v11] : (apart_point_and_line(v6, v8) = v10 & convergent_lines(v7, v8) = v11 & (v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apart_point_and_line(v7, v9) = v13 & apart_point_and_line(v7, v8) = v12 & apart_point_and_line(v6, v9) = v11 & apart_point_and_line(v6, v8) = v10 & (v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ~ (apart_point_and_line(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ~ (convergent_lines(v8, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ (apart_point_and_line(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ (apart_point_and_line(v8, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (apart_point_and_line(v6, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0)) % 4.78/1.82 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 4.78/1.82 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) & parallel_through_point(all_0_3_3, all_0_5_5) = all_0_0_0 & apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2 & convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & distinct_lines(all_0_4_4, all_0_0_0) = 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 | ~ (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] : ( ~ (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] : ( ~ (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] : ( ~ (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] : ( ~ (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] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.78/1.83 | % 4.78/1.83 | Applying alpha-rule on (1) yields: % 4.78/1.83 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 4.78/1.83 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 4.78/1.83 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.78/1.83 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.78/1.83 | (6) ! [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) % 4.78/1.83 | (7) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 4.78/1.83 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 4.78/1.83 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 4.78/1.83 | (10) ! [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) % 4.78/1.83 | (11) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.78/1.83 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 4.78/1.83 | (13) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 4.78/1.83 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 4.78/1.83 | (15) ~ (all_0_2_2 = 0) % 4.78/1.83 | (16) ! [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))) % 4.78/1.83 | (17) ~ (all_0_1_1 = 0) % 4.78/1.83 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 4.78/1.83 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 4.78/1.83 | (20) apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2 % 4.78/1.83 | (21) distinct_lines(all_0_4_4, all_0_0_0) = 0 % 4.78/1.83 | (22) convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1 % 4.78/1.83 | (23) parallel_through_point(all_0_3_3, all_0_5_5) = all_0_0_0 % 4.78/1.83 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 4.78/1.84 | (25) ! [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))) % 4.78/1.84 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 4.78/1.84 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 4.78/1.84 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.87/1.84 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 4.87/1.84 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 4.87/1.84 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.87/1.84 | % 4.87/1.84 | Instantiating formula (16) with all_0_2_2, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2, distinct_lines(all_0_4_4, all_0_0_0) = 0, yields: % 4.87/1.84 | (32) all_0_2_2 = 0 | ? [v0] : ? [v1] : (apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & convergent_lines(all_0_4_4, all_0_0_0) = v1 & (v1 = 0 | v0 = 0)) % 4.87/1.84 | % 4.87/1.84 +-Applying beta-rule and splitting (32), into two cases. % 4.87/1.84 |-Branch one: % 4.87/1.84 | (33) all_0_2_2 = 0 % 4.87/1.84 | % 4.87/1.84 | Equations (33) can reduce 15 to: % 4.87/1.84 | (34) $false % 4.87/1.84 | % 4.87/1.84 |-The branch is then unsatisfiable % 4.87/1.84 |-Branch two: % 4.87/1.84 | (15) ~ (all_0_2_2 = 0) % 4.87/1.84 | (36) ? [v0] : ? [v1] : (apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & convergent_lines(all_0_4_4, all_0_0_0) = v1 & (v1 = 0 | v0 = 0)) % 4.87/1.84 | % 4.87/1.84 | Instantiating (36) with all_18_0_6, all_18_1_7 yields: % 4.87/1.84 | (37) apart_point_and_line(all_0_5_5, all_0_0_0) = all_18_1_7 & convergent_lines(all_0_4_4, all_0_0_0) = all_18_0_6 & (all_18_0_6 = 0 | all_18_1_7 = 0) % 4.87/1.84 | % 4.87/1.84 | Applying alpha-rule on (37) yields: % 4.87/1.84 | (38) apart_point_and_line(all_0_5_5, all_0_0_0) = all_18_1_7 % 4.87/1.84 | (39) convergent_lines(all_0_4_4, all_0_0_0) = all_18_0_6 % 4.87/1.84 | (40) all_18_0_6 = 0 | all_18_1_7 = 0 % 4.87/1.84 | % 4.87/1.84 | Instantiating formula (18) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms parallel_through_point(all_0_3_3, all_0_5_5) = all_0_0_0, yields: % 4.87/1.84 | (41) ~ (apart_point_and_line(all_0_5_5, all_0_0_0) = 0) % 4.87/1.84 | % 4.87/1.85 | Using (38) and (41) yields: % 4.87/1.85 | (42) ~ (all_18_1_7 = 0) % 4.87/1.85 | % 4.87/1.85 +-Applying beta-rule and splitting (40), into two cases. % 4.87/1.85 |-Branch one: % 4.87/1.85 | (43) all_18_0_6 = 0 % 4.87/1.85 | % 4.87/1.85 | From (43) and (39) follows: % 4.87/1.85 | (44) convergent_lines(all_0_4_4, all_0_0_0) = 0 % 4.87/1.85 | % 4.87/1.85 | Instantiating formula (3) with all_0_1_1, all_0_3_3, all_0_0_0, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_0_0) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 4.87/1.85 | (45) all_0_1_1 = 0 | convergent_lines(all_0_0_0, all_0_3_3) = 0 % 4.87/1.85 | % 4.87/1.85 +-Applying beta-rule and splitting (45), into two cases. % 4.87/1.85 |-Branch one: % 4.87/1.85 | (46) convergent_lines(all_0_0_0, all_0_3_3) = 0 % 4.87/1.85 | % 4.87/1.85 | Instantiating formula (9) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms parallel_through_point(all_0_3_3, all_0_5_5) = all_0_0_0, convergent_lines(all_0_0_0, all_0_3_3) = 0, yields: % 4.87/1.85 | (47) $false % 4.87/1.85 | % 4.87/1.85 |-The branch is then unsatisfiable % 4.87/1.85 |-Branch two: % 4.87/1.85 | (48) ~ (convergent_lines(all_0_0_0, all_0_3_3) = 0) % 4.87/1.85 | (49) all_0_1_1 = 0 % 4.87/1.85 | % 4.87/1.85 | Equations (49) can reduce 17 to: % 4.87/1.85 | (34) $false % 4.87/1.85 | % 4.87/1.85 |-The branch is then unsatisfiable % 4.87/1.85 |-Branch two: % 4.87/1.85 | (51) ~ (all_18_0_6 = 0) % 4.87/1.85 | (52) all_18_1_7 = 0 % 4.87/1.85 | % 4.87/1.85 | Equations (52) can reduce 42 to: % 4.87/1.85 | (34) $false % 4.87/1.85 | % 4.87/1.85 |-The branch is then unsatisfiable % 4.87/1.85 % SZS output end Proof for theBenchmark % 4.87/1.85 % 4.87/1.85 1206ms %------------------------------------------------------------------------------