%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO208+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 03:48:43 EDT 2022 % Result : Theorem 3.03s 1.42s % Output : Proof 4.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GEO208+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n004.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 : Sat Jun 18 05:13:38 EDT 2022 % 0.13/0.34 % CPUTime : % 0.65/0.64 ____ _ % 0.65/0.64 ___ / __ \_____(_)___ ________ __________ % 0.65/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.65/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.65/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.65/0.64 % 0.65/0.64 A Theorem Prover for First-Order Logic % 0.65/0.64 (ePrincess v.1.0) % 0.65/0.64 % 0.65/0.64 (c) Philipp Rümmer, 2009-2015 % 0.65/0.64 (c) Peter Backeman, 2014-2015 % 0.65/0.64 (contributions by Angelo Brillout, Peter Baumgartner) % 0.65/0.64 Free software under GNU Lesser General Public License (LGPL). % 0.65/0.64 Bug reports to peter@backeman.se % 0.65/0.64 % 0.65/0.64 For more information, visit http://user.uu.se/~petba168/breu/ % 0.65/0.64 % 0.65/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.78/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.70/0.97 Prover 0: Preprocessing ... % 2.05/1.10 Prover 0: Warning: ignoring some quantifiers % 2.05/1.11 Prover 0: Constructing countermodel ... % 2.57/1.26 Prover 0: gave up % 2.57/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.69/1.29 Prover 1: Preprocessing ... % 3.03/1.39 Prover 1: Constructing countermodel ... % 3.03/1.42 Prover 1: proved (157ms) % 3.03/1.42 % 3.03/1.42 No countermodel exists, formula is valid % 3.03/1.42 % SZS status Theorem for theBenchmark % 3.03/1.42 % 3.03/1.42 Generating proof ... found it (size 18) % 3.84/1.64 % 3.84/1.64 % SZS output start Proof for theBenchmark % 3.84/1.64 Assumed formulas after preprocessing and simplification: % 3.84/1.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v0, v2) = v4 & apart_point_and_line(v0, v1) = v3 & convergent_lines(v1, v2) = v5 & distinct_lines(v1, v2) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (intersection_point(v6, v7) = v9) | ~ (distinct_points(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (apart_point_and_line(v8, v7) = v13 & apart_point_and_line(v8, v6) = v12 & convergent_lines(v6, v7) = v11 & ( ~ (v11 = 0) | ( ~ (v13 = 0) & ~ (v12 = 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 | ~ (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] : ( ~ (line_connecting(v6, v7) = v9) | ~ (apart_point_and_line(v8, v9) = 0) | ? [v10] : ? [v11] : ? [v12] : (distinct_points(v8, v7) = v12 & distinct_points(v8, v6) = v11 & distinct_points(v6, v7) = v10 & ( ~ (v10 = 0) | (v12 = 0 & v11 = 0)))) & ! [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] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [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] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0)) % 4.14/1.68 | 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: % 4.14/1.68 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = all_0_1_1 & 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_0_0 & distinct_lines(all_0_4_4, all_0_3_3) = 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) % 4.30/1.69 | % 4.30/1.69 | Applying alpha-rule on (1) yields: % 4.30/1.69 | (2) ~ (all_0_1_1 = 0) % 4.30/1.69 | (3) convergent_lines(all_0_4_4, all_0_3_3) = all_0_0_0 % 4.30/1.69 | (4) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.30/1.69 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.30/1.69 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 4.30/1.69 | (7) ! [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))))) % 4.30/1.69 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 4.30/1.69 | (9) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 4.30/1.69 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 4.30/1.69 | (11) ! [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) % 4.30/1.69 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 4.30/1.69 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 4.30/1.69 | (14) ~ (all_0_0_0 = 0) % 4.30/1.69 | (15) ! [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) % 4.30/1.69 | (16) ! [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))) % 4.30/1.69 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.30/1.69 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 4.30/1.69 | (19) ! [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))) % 4.30/1.70 | (20) apart_point_and_line(all_0_5_5, all_0_3_3) = all_0_1_1 % 4.30/1.70 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 4.30/1.70 | (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)))) % 4.30/1.70 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 4.30/1.70 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 4.30/1.70 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.30/1.70 | (26) apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2 % 4.30/1.70 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 4.30/1.70 | (28) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 4.30/1.70 | (29) distinct_lines(all_0_4_4, all_0_3_3) = 0 % 4.30/1.70 | (30) ~ (all_0_2_2 = 0) % 4.30/1.70 | % 4.30/1.70 | Instantiating formula (19) with all_0_2_2, all_0_3_3, 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_3_3) = 0, yields: % 4.30/1.70 | (31) all_0_2_2 = 0 | ? [v0] : ? [v1] : (apart_point_and_line(all_0_5_5, all_0_3_3) = v0 & convergent_lines(all_0_4_4, all_0_3_3) = v1 & (v1 = 0 | v0 = 0)) % 4.30/1.70 | % 4.30/1.70 +-Applying beta-rule and splitting (31), into two cases. % 4.30/1.70 |-Branch one: % 4.30/1.70 | (32) all_0_2_2 = 0 % 4.30/1.70 | % 4.30/1.70 | Equations (32) can reduce 30 to: % 4.30/1.70 | (33) $false % 4.30/1.70 | % 4.30/1.70 |-The branch is then unsatisfiable % 4.30/1.70 |-Branch two: % 4.30/1.70 | (30) ~ (all_0_2_2 = 0) % 4.30/1.70 | (35) ? [v0] : ? [v1] : (apart_point_and_line(all_0_5_5, all_0_3_3) = v0 & convergent_lines(all_0_4_4, all_0_3_3) = v1 & (v1 = 0 | v0 = 0)) % 4.30/1.70 | % 4.30/1.70 | Instantiating (35) with all_22_0_6, all_22_1_7 yields: % 4.30/1.70 | (36) apart_point_and_line(all_0_5_5, all_0_3_3) = all_22_1_7 & convergent_lines(all_0_4_4, all_0_3_3) = all_22_0_6 & (all_22_0_6 = 0 | all_22_1_7 = 0) % 4.30/1.70 | % 4.30/1.70 | Applying alpha-rule on (36) yields: % 4.30/1.70 | (37) apart_point_and_line(all_0_5_5, all_0_3_3) = all_22_1_7 % 4.30/1.70 | (38) convergent_lines(all_0_4_4, all_0_3_3) = all_22_0_6 % 4.30/1.70 | (39) all_22_0_6 = 0 | all_22_1_7 = 0 % 4.30/1.70 | % 4.30/1.70 | Instantiating formula (21) with all_0_5_5, all_0_3_3, all_22_1_7, all_0_1_1 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_22_1_7, apart_point_and_line(all_0_5_5, all_0_3_3) = all_0_1_1, yields: % 4.30/1.70 | (40) all_22_1_7 = all_0_1_1 % 4.30/1.70 | % 4.30/1.70 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_22_0_6, all_0_0_0 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_22_0_6, convergent_lines(all_0_4_4, all_0_3_3) = all_0_0_0, yields: % 4.30/1.70 | (41) all_22_0_6 = all_0_0_0 % 4.30/1.70 | % 4.30/1.70 +-Applying beta-rule and splitting (39), into two cases. % 4.30/1.70 |-Branch one: % 4.30/1.70 | (42) all_22_0_6 = 0 % 4.30/1.70 | % 4.30/1.70 | Combining equations (42,41) yields a new equation: % 4.30/1.70 | (43) all_0_0_0 = 0 % 4.30/1.70 | % 4.30/1.70 | Equations (43) can reduce 14 to: % 4.30/1.70 | (33) $false % 4.30/1.71 | % 4.30/1.71 |-The branch is then unsatisfiable % 4.30/1.71 |-Branch two: % 4.30/1.71 | (45) ~ (all_22_0_6 = 0) % 4.30/1.71 | (46) all_22_1_7 = 0 % 4.30/1.71 | % 4.30/1.71 | Combining equations (40,46) yields a new equation: % 4.30/1.71 | (47) all_0_1_1 = 0 % 4.30/1.71 | % 4.30/1.71 | Simplifying 47 yields: % 4.30/1.71 | (48) all_0_1_1 = 0 % 4.30/1.71 | % 4.30/1.71 | Equations (48) can reduce 2 to: % 4.30/1.71 | (33) $false % 4.30/1.71 | % 4.30/1.71 |-The branch is then unsatisfiable % 4.30/1.71 % SZS output end Proof for theBenchmark % 4.30/1.71 % 4.30/1.71 1052ms %------------------------------------------------------------------------------