%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO209+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 3.16s 1.42s % Output : Proof 4.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO209+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jun 17 17:46:37 EDT 2022 % 0.13/0.34 % CPUTime : % 0.52/0.59 ____ _ % 0.52/0.59 ___ / __ \_____(_)___ ________ __________ % 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.59 % 0.52/0.59 A Theorem Prover for First-Order Logic % 0.52/0.59 (ePrincess v.1.0) % 0.52/0.59 % 0.52/0.59 (c) Philipp Rümmer, 2009-2015 % 0.52/0.59 (c) Peter Backeman, 2014-2015 % 0.52/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.59 Bug reports to peter@backeman.se % 0.52/0.59 % 0.52/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.59 % 0.52/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.75/0.94 Prover 0: Preprocessing ... % 2.02/1.08 Prover 0: Warning: ignoring some quantifiers % 2.14/1.10 Prover 0: Constructing countermodel ... % 2.75/1.26 Prover 0: gave up % 2.75/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.75/1.28 Prover 1: Preprocessing ... % 3.16/1.38 Prover 1: Constructing countermodel ... % 3.16/1.42 Prover 1: proved (163ms) % 3.16/1.42 % 3.16/1.42 No countermodel exists, formula is valid % 3.16/1.42 % SZS status Theorem for theBenchmark % 3.16/1.42 % 3.16/1.42 Generating proof ... found it (size 21) % 4.27/1.67 % 4.27/1.67 % SZS output start Proof for theBenchmark % 4.27/1.67 Assumed formulas after preprocessing and simplification: % 4.27/1.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & ~ (v5 = 0) & ~ (v4 = 0) & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & apart_point_and_line(v0, v1) = 0 & convergent_lines(v3, v1) = v7 & convergent_lines(v2, v1) = v6 & distinct_lines(v2, v3) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection_point(v8, v9) = v11) | ~ (distinct_points(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (apart_point_and_line(v10, v9) = v15 & apart_point_and_line(v10, v8) = v14 & convergent_lines(v8, v9) = v13 & ( ~ (v13 = 0) | ( ~ (v15 = 0) & ~ (v14 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = v11) | ~ (distinct_lines(v9, v10) = 0) | ? [v12] : ? [v13] : (apart_point_and_line(v8, v10) = v12 & convergent_lines(v9, v10) = v13 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | apart_point_and_line(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_points(v8, v10) = v11) | apart_point_and_line(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_lines(v8, v10) = v11) | ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_points(v8, v10) = v11) | ~ (distinct_points(v8, v9) = 0) | distinct_points(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (parallel_through_point(v11, v10) = v9) | ~ (parallel_through_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection_point(v11, v10) = v9) | ~ (intersection_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (line_connecting(v11, v10) = v9) | ~ (line_connecting(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (apart_point_and_line(v11, v10) = v9) | ~ (apart_point_and_line(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (convergent_lines(v11, v10) = v9) | ~ (convergent_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_lines(v11, v10) = v9) | ~ (distinct_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_points(v11, v10) = v9) | ~ (distinct_points(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v8, v9) = v11) | ~ (apart_point_and_line(v10, v11) = 0) | ? [v12] : ? [v13] : ? [v14] : (distinct_points(v10, v9) = v14 & distinct_points(v10, v8) = v13 & distinct_points(v8, v9) = v12 & ( ~ (v12 = 0) | (v14 = 0 & v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) | ~ (distinct_points(v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (apart_point_and_line(v9, v11) = v15 & apart_point_and_line(v9, v10) = v14 & apart_point_and_line(v8, v11) = v13 & apart_point_and_line(v8, v10) = v12 & (v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (parallel_through_point(v9, v8) = v10) | ~ (apart_point_and_line(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (parallel_through_point(v9, v8) = v10) | ~ (convergent_lines(v10, v9) = 0)) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0)) % 4.46/1.71 | 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, all_0_7_7 yields: % 4.46/1.71 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_3_3 = 0) & apart_point_and_line(all_0_7_7, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3 & apart_point_and_line(all_0_7_7, all_0_6_6) = 0 & convergent_lines(all_0_4_4, all_0_6_6) = all_0_0_0 & convergent_lines(all_0_5_5, all_0_6_6) = all_0_1_1 & distinct_lines(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 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 | ~ (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] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 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 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [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] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.46/1.72 | % 4.46/1.72 | Applying alpha-rule on (1) yields: % 4.46/1.72 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 4.46/1.72 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 4.46/1.72 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))))) % 4.46/1.72 | (5) apart_point_and_line(all_0_7_7, all_0_6_6) = 0 % 4.46/1.72 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.46/1.72 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 4.46/1.72 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.46/1.72 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 4.46/1.72 | (10) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 4.46/1.72 | (11) ~ (all_0_1_1 = 0) % 4.46/1.72 | (12) apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3 % 4.46/1.72 | (13) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 4.46/1.72 | (14) ~ (all_0_0_0 = 0) % 4.46/1.72 | (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))) % 4.46/1.72 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 4.46/1.72 | (17) ~ (all_0_3_3 = 0) % 4.46/1.72 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 4.46/1.72 | (19) ~ (all_0_2_2 = 0) % 4.46/1.72 | (20) ! [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) % 4.46/1.72 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 4.46/1.72 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) % 4.46/1.72 | (23) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.46/1.72 | (24) apart_point_and_line(all_0_7_7, all_0_4_4) = all_0_2_2 % 4.46/1.72 | (25) convergent_lines(all_0_4_4, all_0_6_6) = all_0_0_0 % 4.46/1.72 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 4.46/1.72 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.46/1.73 | (28) ! [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) % 4.46/1.73 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 4.46/1.73 | (30) ! [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))) % 4.46/1.73 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 4.46/1.73 | (32) distinct_lines(all_0_5_5, all_0_4_4) = 0 % 4.46/1.73 | (33) convergent_lines(all_0_5_5, all_0_6_6) = all_0_1_1 % 4.46/1.73 | % 4.46/1.73 | Instantiating formula (30) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3, distinct_lines(all_0_5_5, all_0_4_4) = 0, yields: % 4.46/1.73 | (34) all_0_3_3 = 0 | ? [v0] : ? [v1] : (apart_point_and_line(all_0_7_7, all_0_4_4) = v0 & convergent_lines(all_0_5_5, all_0_4_4) = v1 & (v1 = 0 | v0 = 0)) % 4.46/1.73 | % 4.46/1.73 +-Applying beta-rule and splitting (34), into two cases. % 4.46/1.73 |-Branch one: % 4.46/1.73 | (35) all_0_3_3 = 0 % 4.46/1.73 | % 4.46/1.73 | Equations (35) can reduce 17 to: % 4.46/1.73 | (36) $false % 4.46/1.73 | % 4.46/1.73 |-The branch is then unsatisfiable % 4.46/1.73 |-Branch two: % 4.46/1.73 | (17) ~ (all_0_3_3 = 0) % 4.46/1.73 | (38) ? [v0] : ? [v1] : (apart_point_and_line(all_0_7_7, all_0_4_4) = v0 & convergent_lines(all_0_5_5, all_0_4_4) = v1 & (v1 = 0 | v0 = 0)) % 4.46/1.73 | % 4.46/1.73 | Instantiating (38) with all_22_0_8, all_22_1_9 yields: % 4.46/1.73 | (39) apart_point_and_line(all_0_7_7, all_0_4_4) = all_22_1_9 & convergent_lines(all_0_5_5, all_0_4_4) = all_22_0_8 & (all_22_0_8 = 0 | all_22_1_9 = 0) % 4.46/1.73 | % 4.46/1.73 | Applying alpha-rule on (39) yields: % 4.46/1.73 | (40) apart_point_and_line(all_0_7_7, all_0_4_4) = all_22_1_9 % 4.46/1.73 | (41) convergent_lines(all_0_5_5, all_0_4_4) = all_22_0_8 % 4.46/1.73 | (42) all_22_0_8 = 0 | all_22_1_9 = 0 % 4.46/1.73 | % 4.46/1.73 | Instantiating formula (7) with all_0_7_7, all_0_4_4, all_22_1_9, all_0_2_2 and discharging atoms apart_point_and_line(all_0_7_7, all_0_4_4) = all_22_1_9, apart_point_and_line(all_0_7_7, all_0_4_4) = all_0_2_2, yields: % 4.46/1.73 | (43) all_22_1_9 = all_0_2_2 % 4.46/1.73 | % 4.46/1.73 +-Applying beta-rule and splitting (42), into two cases. % 4.46/1.73 |-Branch one: % 4.46/1.73 | (44) all_22_0_8 = 0 % 4.46/1.73 | % 4.46/1.73 | From (44) and (41) follows: % 4.46/1.73 | (45) convergent_lines(all_0_5_5, all_0_4_4) = 0 % 4.46/1.73 | % 4.46/1.73 | Instantiating formula (31) with all_0_1_1, all_0_6_6, all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, convergent_lines(all_0_5_5, all_0_6_6) = all_0_1_1, yields: % 4.46/1.73 | (46) all_0_1_1 = 0 | convergent_lines(all_0_4_4, all_0_6_6) = 0 % 4.46/1.73 | % 4.46/1.73 +-Applying beta-rule and splitting (46), into two cases. % 4.46/1.73 |-Branch one: % 4.46/1.73 | (47) convergent_lines(all_0_4_4, all_0_6_6) = 0 % 4.46/1.73 | % 4.46/1.73 | Instantiating formula (9) with all_0_4_4, all_0_6_6, 0, all_0_0_0 and discharging atoms convergent_lines(all_0_4_4, all_0_6_6) = all_0_0_0, convergent_lines(all_0_4_4, all_0_6_6) = 0, yields: % 4.46/1.73 | (48) all_0_0_0 = 0 % 4.46/1.73 | % 4.46/1.73 | Equations (48) can reduce 14 to: % 4.46/1.73 | (36) $false % 4.46/1.73 | % 4.46/1.73 |-The branch is then unsatisfiable % 4.46/1.73 |-Branch two: % 4.46/1.73 | (50) ~ (convergent_lines(all_0_4_4, all_0_6_6) = 0) % 4.46/1.73 | (51) all_0_1_1 = 0 % 4.46/1.73 | % 4.46/1.73 | Equations (51) can reduce 11 to: % 4.46/1.73 | (36) $false % 4.46/1.73 | % 4.46/1.73 |-The branch is then unsatisfiable % 4.46/1.73 |-Branch two: % 4.46/1.73 | (53) ~ (all_22_0_8 = 0) % 4.46/1.73 | (54) all_22_1_9 = 0 % 4.46/1.74 | % 4.46/1.74 | Combining equations (54,43) yields a new equation: % 4.46/1.74 | (55) all_0_2_2 = 0 % 4.46/1.74 | % 4.46/1.74 | Equations (55) can reduce 19 to: % 4.46/1.74 | (36) $false % 4.46/1.74 | % 4.46/1.74 |-The branch is then unsatisfiable % 4.46/1.74 % SZS output end Proof for theBenchmark % 4.46/1.74 % 4.46/1.74 1137ms %------------------------------------------------------------------------------