%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO209+1 : 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 03:48:44 EDT 2022 % Result : Theorem 3.43s 1.60s % Output : Proof 4.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GEO209+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.32 % Computer : n004.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Sat Jun 18 18:17:53 EDT 2022 % 0.12/0.32 % CPUTime : % 0.58/0.59 ____ _ % 0.58/0.59 ___ / __ \_____(_)___ ________ __________ % 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic % 0.58/0.59 (ePrincess v.1.0) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2015 % 0.58/0.59 (c) Peter Backeman, 2014-2015 % 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.59 Bug reports to peter@backeman.se % 0.58/0.59 % 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.61/0.99 Prover 0: Preprocessing ... % 1.96/1.13 Prover 0: Warning: ignoring some quantifiers % 1.96/1.15 Prover 0: Constructing countermodel ... % 2.84/1.38 Prover 0: gave up % 2.84/1.38 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.84/1.41 Prover 1: Preprocessing ... % 3.43/1.54 Prover 1: Constructing countermodel ... % 3.43/1.60 Prover 1: proved (214ms) % 3.43/1.60 % 3.43/1.60 No countermodel exists, formula is valid % 3.43/1.60 % SZS status Theorem for theBenchmark % 3.43/1.60 % 3.43/1.60 Generating proof ... found it (size 21) % 4.67/1.85 % 4.67/1.85 % SZS output start Proof for theBenchmark % 4.67/1.85 Assumed formulas after preprocessing and simplification: % 4.67/1.85 | (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] : (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 | ~ (convergent_lines(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | convergent_lines(v8, 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] : ( ~ (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] : ( ~ (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] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ~ (apart_point_and_line(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ~ (apart_point_and_line(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ (apart_point_and_line(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ (apart_point_and_line(v8, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v8, v9) = v11)) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0)) % 4.67/1.89 | 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: % 4.67/1.89 | (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] : (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) % 4.67/1.90 | % 4.67/1.90 | Applying alpha-rule on (1) yields: % 4.67/1.90 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 4.67/1.90 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 4.67/1.90 | (4) ! [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) % 4.67/1.90 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.67/1.90 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 4.67/1.90 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.67/1.90 | (8) ~ (all_0_1_1 = 0) % 4.67/1.90 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.95/1.90 | (10) ! [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) % 4.95/1.90 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 4.95/1.90 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 4.95/1.90 | (13) ~ (all_0_3_3 = 0) % 4.95/1.90 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 4.95/1.90 | (15) apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3 % 4.95/1.90 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 4.95/1.90 | (17) ~ (all_0_0_0 = 0) % 4.95/1.91 | (18) apart_point_and_line(all_0_7_7, all_0_6_6) = 0 % 4.95/1.91 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 4.95/1.91 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 4.95/1.91 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 4.95/1.91 | (22) ~ (all_0_2_2 = 0) % 4.95/1.91 | (23) ! [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))) % 4.95/1.91 | (24) convergent_lines(all_0_4_4, all_0_6_6) = all_0_0_0 % 4.95/1.91 | (25) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.95/1.91 | (26) distinct_lines(all_0_5_5, all_0_4_4) = 0 % 4.95/1.91 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.95/1.91 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 4.95/1.91 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 4.95/1.91 | (30) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 4.95/1.91 | (31) apart_point_and_line(all_0_7_7, all_0_4_4) = all_0_2_2 % 4.95/1.91 | (32) ! [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))) % 4.95/1.91 | (33) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 4.95/1.91 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 4.95/1.91 | (35) convergent_lines(all_0_5_5, all_0_6_6) = all_0_1_1 % 4.95/1.91 | % 4.95/1.91 | Instantiating formula (23) 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: % 4.95/1.91 | (36) 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)) % 4.95/1.91 | % 4.95/1.91 +-Applying beta-rule and splitting (36), into two cases. % 4.95/1.91 |-Branch one: % 4.95/1.91 | (37) all_0_3_3 = 0 % 4.95/1.91 | % 4.95/1.91 | Equations (37) can reduce 13 to: % 4.95/1.91 | (38) $false % 4.95/1.91 | % 4.95/1.91 |-The branch is then unsatisfiable % 4.95/1.91 |-Branch two: % 4.95/1.91 | (13) ~ (all_0_3_3 = 0) % 4.95/1.92 | (40) ? [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)) % 4.95/1.92 | % 4.95/1.92 | Instantiating (40) with all_22_0_8, all_22_1_9 yields: % 4.95/1.92 | (41) 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) % 4.95/1.92 | % 4.95/1.92 | Applying alpha-rule on (41) yields: % 4.95/1.92 | (42) apart_point_and_line(all_0_7_7, all_0_4_4) = all_22_1_9 % 4.95/1.92 | (43) convergent_lines(all_0_5_5, all_0_4_4) = all_22_0_8 % 4.95/1.92 | (44) all_22_0_8 = 0 | all_22_1_9 = 0 % 4.95/1.92 | % 4.95/1.92 | Instantiating formula (14) 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: % 4.95/1.92 | (45) all_22_1_9 = all_0_2_2 % 4.95/1.92 | % 4.95/1.92 +-Applying beta-rule and splitting (44), into two cases. % 4.95/1.92 |-Branch one: % 4.95/1.92 | (46) all_22_0_8 = 0 % 4.95/1.92 | % 4.95/1.92 | From (46) and (43) follows: % 4.95/1.92 | (47) convergent_lines(all_0_5_5, all_0_4_4) = 0 % 4.95/1.92 | % 4.95/1.92 | Instantiating formula (34) 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: % 4.95/1.92 | (48) all_0_1_1 = 0 | convergent_lines(all_0_4_4, all_0_6_6) = 0 % 4.95/1.92 | % 4.95/1.92 +-Applying beta-rule and splitting (48), into two cases. % 4.95/1.92 |-Branch one: % 4.95/1.92 | (49) convergent_lines(all_0_4_4, all_0_6_6) = 0 % 4.95/1.92 | % 4.95/1.92 | Instantiating formula (11) 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: % 4.95/1.92 | (50) all_0_0_0 = 0 % 4.95/1.92 | % 4.95/1.92 | Equations (50) can reduce 17 to: % 4.95/1.92 | (38) $false % 4.95/1.92 | % 4.95/1.92 |-The branch is then unsatisfiable % 4.95/1.92 |-Branch two: % 4.95/1.92 | (52) ~ (convergent_lines(all_0_4_4, all_0_6_6) = 0) % 4.95/1.92 | (53) all_0_1_1 = 0 % 4.95/1.92 | % 4.95/1.92 | Equations (53) can reduce 8 to: % 4.95/1.92 | (38) $false % 4.95/1.92 | % 4.95/1.92 |-The branch is then unsatisfiable % 4.95/1.92 |-Branch two: % 4.95/1.92 | (55) ~ (all_22_0_8 = 0) % 4.95/1.92 | (56) all_22_1_9 = 0 % 4.95/1.92 | % 4.95/1.92 | Combining equations (56,45) yields a new equation: % 4.95/1.92 | (57) all_0_2_2 = 0 % 4.95/1.92 | % 4.95/1.92 | Equations (57) can reduce 22 to: % 4.95/1.92 | (38) $false % 4.95/1.92 | % 4.95/1.92 |-The branch is then unsatisfiable % 4.95/1.92 % SZS output end Proof for theBenchmark % 4.95/1.92 % 4.95/1.92 1315ms %------------------------------------------------------------------------------