%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO220+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 03:48:53 EDT 2022 % Result : Theorem 4.50s 1.73s % Output : Proof 6.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO220+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n006.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 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sat Jun 18 10:42:25 EDT 2022 % 0.13/0.35 % CPUTime : % 0.57/0.60 ____ _ % 0.57/0.60 ___ / __ \_____(_)___ ________ __________ % 0.57/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.60 % 0.57/0.60 A Theorem Prover for First-Order Logic % 0.57/0.60 (ePrincess v.1.0) % 0.57/0.60 % 0.57/0.60 (c) Philipp Rümmer, 2009-2015 % 0.57/0.60 (c) Peter Backeman, 2014-2015 % 0.57/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.60 Bug reports to peter@backeman.se % 0.57/0.60 % 0.57/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.60 % 0.57/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.69/0.96 Prover 0: Preprocessing ... % 2.07/1.10 Prover 0: Warning: ignoring some quantifiers % 2.07/1.13 Prover 0: Constructing countermodel ... % 3.85/1.59 Prover 0: gave up % 3.85/1.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.85/1.61 Prover 1: Preprocessing ... % 4.50/1.69 Prover 1: Constructing countermodel ... % 4.50/1.73 Prover 1: proved (139ms) % 4.50/1.73 % 4.50/1.73 No countermodel exists, formula is valid % 4.50/1.73 % SZS status Theorem for theBenchmark % 4.50/1.73 % 4.50/1.73 Generating proof ... found it (size 18) % 5.77/2.04 % 5.77/2.04 % SZS output start Proof for theBenchmark % 5.77/2.04 Assumed formulas after preprocessing and simplification: % 5.77/2.04 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v0, v2) = v4 & unorthogonal_lines(v0, v1) = v3 & convergent_lines(v1, v2) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection_point(v5, v6) = v8) | ~ (distinct_points(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (apart_point_and_line(v7, v6) = v12 & apart_point_and_line(v7, v5) = v11 & convergent_lines(v5, v6) = v10 & ( ~ (v10 = 0) | ( ~ (v12 = 0) & ~ (v11 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (unorthogonal_lines(v6, v7) = v13 & convergent_lines(v6, v7) = v12 & convergent_lines(v5, v7) = v11 & convergent_lines(v5, v6) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | (v11 = 0 & v9 = 0) | (v10 = 0 & v8 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | apart_point_and_line(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_points(v5, v7) = v8) | apart_point_and_line(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v8) | ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (distinct_points(v7, v6) = v11 & distinct_points(v7, v5) = v10 & distinct_points(v5, v6) = v9 & ( ~ (v9 = 0) | (v11 = 0 & v10 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (apart_point_and_line(v6, v8) = v12 & apart_point_and_line(v6, v7) = v11 & apart_point_and_line(v5, v8) = v10 & apart_point_and_line(v5, v7) = v9 & (v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8)) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0)) % 6.21/2.08 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 6.21/2.08 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_0_0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & convergent_lines(all_0_3_3, all_0_2_2) = 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] : (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] : ! [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) = 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 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(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 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) % 6.21/2.09 | % 6.21/2.09 | Applying alpha-rule on (1) yields: % 6.21/2.09 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 6.21/2.09 | (3) ! [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))))) % 6.21/2.09 | (4) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 6.34/2.09 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 6.34/2.09 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 6.34/2.10 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 6.34/2.10 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 6.34/2.10 | (9) ~ (all_0_1_1 = 0) % 6.34/2.10 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 6.34/2.10 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 6.34/2.10 | (12) ! [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)))) % 6.34/2.10 | (13) ! [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)) % 6.34/2.10 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 6.34/2.10 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 6.34/2.10 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 6.34/2.10 | (17) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1 % 6.34/2.10 | (18) ! [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))) % 6.34/2.10 | (19) ~ (all_0_0_0 = 0) % 6.34/2.10 | (20) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 6.34/2.10 | (21) ! [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) % 6.34/2.10 | (22) ! [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)))) % 6.34/2.10 | (23) unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_0_0 % 6.34/2.10 | (24) ! [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) % 6.34/2.10 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 6.34/2.10 | (26) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 6.34/2.10 | (27) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 6.34/2.10 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 6.34/2.10 | % 6.34/2.11 | Instantiating formula (13) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 6.34/2.11 | (29) all_0_0_0 = 0 | all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0) % 6.34/2.11 | % 6.34/2.11 | Instantiating formula (13) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 6.34/2.11 | (30) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0) % 6.34/2.11 | % 6.34/2.11 +-Applying beta-rule and splitting (30), into two cases. % 6.34/2.11 |-Branch one: % 6.34/2.11 | (31) all_0_1_1 = 0 % 6.34/2.11 | % 6.34/2.11 | Equations (31) can reduce 9 to: % 6.34/2.11 | (32) $false % 6.34/2.11 | % 6.34/2.11 |-The branch is then unsatisfiable % 6.34/2.11 |-Branch two: % 6.34/2.11 | (9) ~ (all_0_1_1 = 0) % 6.34/2.11 | (34) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0) % 6.34/2.11 | % 6.34/2.11 +-Applying beta-rule and splitting (29), into two cases. % 6.34/2.11 |-Branch one: % 6.34/2.11 | (35) all_0_0_0 = 0 % 6.34/2.11 | % 6.34/2.11 | Equations (35) can reduce 19 to: % 6.34/2.11 | (32) $false % 6.34/2.11 | % 6.34/2.11 |-The branch is then unsatisfiable % 6.34/2.11 |-Branch two: % 6.34/2.11 | (19) ~ (all_0_0_0 = 0) % 6.34/2.11 | (38) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0) % 6.34/2.11 | % 6.34/2.11 +-Applying beta-rule and splitting (38), into two cases. % 6.34/2.11 |-Branch one: % 6.34/2.11 | (31) all_0_1_1 = 0 % 6.34/2.11 | % 6.34/2.11 | Equations (31) can reduce 9 to: % 6.34/2.11 | (32) $false % 6.34/2.11 | % 6.34/2.11 |-The branch is then unsatisfiable % 6.34/2.11 |-Branch two: % 6.34/2.11 | (9) ~ (all_0_1_1 = 0) % 6.34/2.11 | (42) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0) % 6.34/2.11 | % 6.34/2.11 | Instantiating (42) with all_42_0_22 yields: % 6.34/2.11 | (43) ~ (all_42_0_22 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_42_0_22 % 6.34/2.11 | % 6.34/2.11 | Applying alpha-rule on (43) yields: % 6.34/2.11 | (44) ~ (all_42_0_22 = 0) % 6.34/2.11 | (45) convergent_lines(all_0_3_3, all_0_2_2) = all_42_0_22 % 6.34/2.11 | % 6.34/2.11 | Instantiating formula (10) with all_0_3_3, all_0_2_2, all_42_0_22, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_42_0_22, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 6.34/2.11 | (46) all_42_0_22 = 0 % 6.34/2.11 | % 6.34/2.11 | Equations (46) can reduce 44 to: % 6.34/2.11 | (32) $false % 6.34/2.11 | % 6.34/2.11 |-The branch is then unsatisfiable % 6.34/2.11 % SZS output end Proof for theBenchmark % 6.34/2.11 % 6.34/2.11 1501ms %------------------------------------------------------------------------------