%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO210+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 03:48:45 EDT 2022 % Result : Theorem 4.04s 1.54s % Output : Proof 5.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GEO210+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 04:54:57 EDT 2022 % 0.12/0.33 % CPUTime : % 0.59/0.57 ____ _ % 0.59/0.57 ___ / __ \_____(_)___ ________ __________ % 0.59/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.57 % 0.59/0.57 A Theorem Prover for First-Order Logic % 0.59/0.57 (ePrincess v.1.0) % 0.59/0.57 % 0.59/0.57 (c) Philipp Rümmer, 2009-2015 % 0.59/0.57 (c) Peter Backeman, 2014-2015 % 0.59/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.57 Bug reports to peter@backeman.se % 0.59/0.57 % 0.59/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.57 % 0.59/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.59/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.78/0.93 Prover 0: Preprocessing ... % 2.18/1.09 Prover 0: Warning: ignoring some quantifiers % 2.18/1.12 Prover 0: Constructing countermodel ... % 3.07/1.36 Prover 0: gave up % 3.07/1.36 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.29/1.39 Prover 1: Preprocessing ... % 3.80/1.50 Prover 1: Constructing countermodel ... % 4.04/1.54 Prover 1: proved (179ms) % 4.04/1.54 % 4.04/1.54 No countermodel exists, formula is valid % 4.04/1.54 % SZS status Theorem for theBenchmark % 4.04/1.54 % 4.04/1.54 Generating proof ... found it (size 29) % 5.12/1.78 % 5.12/1.78 % SZS output start Proof for theBenchmark % 5.12/1.78 Assumed formulas after preprocessing and simplification: % 5.12/1.78 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & ~ (v3 = 0) & orthogonal_through_point(v2, v0) = v5 & unorthogonal_lines(v1, v2) = v4 & apart_point_and_line(v0, v1) = v3 & distinct_lines(v1, v5) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ? [v13] : (unorthogonal_lines(v8, v9) = v13 & apart_point_and_line(v6, v8) = v12 & (v13 = 0 | v12 = 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 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [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] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (unorthogonal_lines(v7, v8) = v13 & convergent_lines(v7, v8) = v12 & convergent_lines(v6, v8) = v11 & convergent_lines(v6, v7) = v10 & ( ~ (v10 = 0) | (v13 = 0 & v12 = 0) | (v11 = 0 & v9 = 0)))) & ! [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 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ~ (unorthogonal_lines(v8, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ~ (apart_point_and_line(v6, v8) = 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] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0)) % 5.31/1.82 | 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: % 5.31/1.82 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) & orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_0_0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & 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 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 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 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [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] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [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] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 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] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) % 5.31/1.83 | % 5.31/1.83 | Applying alpha-rule on (1) yields: % 5.31/1.83 | (2) ! [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) % 5.31/1.83 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 5.31/1.83 | (4) distinct_lines(all_0_4_4, all_0_0_0) = 0 % 5.31/1.83 | (5) ! [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)))) % 5.31/1.83 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 5.31/1.83 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 5.31/1.84 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 5.31/1.84 | (9) apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2 % 5.31/1.84 | (10) ! [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))))) % 5.31/1.84 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 5.31/1.84 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 5.31/1.84 | (13) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 5.31/1.84 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 5.31/1.84 | (15) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 5.31/1.84 | (16) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 5.31/1.84 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0))) % 5.31/1.84 | (18) ~ (all_0_2_2 = 0) % 5.31/1.84 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 5.31/1.84 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) % 5.31/1.84 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 5.31/1.84 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 5.31/1.84 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 5.31/1.84 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 5.31/1.84 | (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))) % 5.31/1.84 | (26) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1 % 5.31/1.84 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 5.31/1.84 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 5.31/1.84 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 5.31/1.84 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 5.31/1.84 | (31) ! [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) % 5.31/1.84 | (32) orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_0_0 % 5.31/1.85 | (33) ! [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))) % 5.31/1.85 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 5.31/1.85 | (35) ~ (all_0_1_1 = 0) % 5.31/1.85 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 5.31/1.85 | % 5.31/1.85 | Instantiating formula (17) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, 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: % 5.31/1.85 | (37) all_0_1_1 = 0 | all_0_2_2 = 0 | ? [v0] : ? [v1] : (unorthogonal_lines(all_0_0_0, all_0_3_3) = v1 & apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & (v1 = 0 | v0 = 0)) % 5.31/1.85 | % 5.31/1.85 | Instantiating formula (33) 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: % 5.31/1.85 | (38) 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)) % 5.31/1.85 | % 5.31/1.85 +-Applying beta-rule and splitting (38), into two cases. % 5.31/1.85 |-Branch one: % 5.31/1.85 | (39) all_0_2_2 = 0 % 5.31/1.85 | % 5.31/1.85 | Equations (39) can reduce 18 to: % 5.31/1.85 | (40) $false % 5.31/1.85 | % 5.31/1.85 |-The branch is then unsatisfiable % 5.31/1.85 |-Branch two: % 5.31/1.85 | (18) ~ (all_0_2_2 = 0) % 5.31/1.85 | (42) ? [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)) % 5.31/1.85 | % 5.31/1.85 | Instantiating (42) with all_22_0_6, all_22_1_7 yields: % 5.31/1.85 | (43) apart_point_and_line(all_0_5_5, all_0_0_0) = all_22_1_7 & convergent_lines(all_0_4_4, all_0_0_0) = all_22_0_6 & (all_22_0_6 = 0 | all_22_1_7 = 0) % 5.31/1.85 | % 5.31/1.85 | Applying alpha-rule on (43) yields: % 5.31/1.85 | (44) apart_point_and_line(all_0_5_5, all_0_0_0) = all_22_1_7 % 5.31/1.85 | (45) convergent_lines(all_0_4_4, all_0_0_0) = all_22_0_6 % 5.31/1.85 | (46) all_22_0_6 = 0 | all_22_1_7 = 0 % 5.31/1.85 | % 5.31/1.85 +-Applying beta-rule and splitting (37), into two cases. % 5.31/1.85 |-Branch one: % 5.31/1.85 | (47) all_0_1_1 = 0 % 5.31/1.85 | % 5.31/1.85 | Equations (47) can reduce 35 to: % 5.31/1.85 | (40) $false % 5.31/1.85 | % 5.31/1.85 |-The branch is then unsatisfiable % 5.31/1.85 |-Branch two: % 5.31/1.85 | (35) ~ (all_0_1_1 = 0) % 5.31/1.85 | (50) all_0_2_2 = 0 | ? [v0] : ? [v1] : (unorthogonal_lines(all_0_0_0, all_0_3_3) = v1 & apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & (v1 = 0 | v0 = 0)) % 5.31/1.85 | % 5.31/1.85 +-Applying beta-rule and splitting (50), into two cases. % 5.31/1.85 |-Branch one: % 5.31/1.85 | (39) all_0_2_2 = 0 % 5.31/1.85 | % 5.31/1.85 | Equations (39) can reduce 18 to: % 5.31/1.85 | (40) $false % 5.31/1.85 | % 5.31/1.85 |-The branch is then unsatisfiable % 5.31/1.85 |-Branch two: % 5.31/1.85 | (18) ~ (all_0_2_2 = 0) % 5.31/1.85 | (54) ? [v0] : ? [v1] : (unorthogonal_lines(all_0_0_0, all_0_3_3) = v1 & apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & (v1 = 0 | v0 = 0)) % 5.31/1.85 | % 5.31/1.85 | Instantiating (54) with all_31_0_8, all_31_1_9 yields: % 5.31/1.85 | (55) unorthogonal_lines(all_0_0_0, all_0_3_3) = all_31_0_8 & apart_point_and_line(all_0_5_5, all_0_0_0) = all_31_1_9 & (all_31_0_8 = 0 | all_31_1_9 = 0) % 5.31/1.85 | % 5.31/1.85 | Applying alpha-rule on (55) yields: % 5.31/1.85 | (56) unorthogonal_lines(all_0_0_0, all_0_3_3) = all_31_0_8 % 5.31/1.85 | (57) apart_point_and_line(all_0_5_5, all_0_0_0) = all_31_1_9 % 5.31/1.85 | (58) all_31_0_8 = 0 | all_31_1_9 = 0 % 5.31/1.85 | % 5.31/1.85 | Instantiating formula (20) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_0_0, yields: % 5.31/1.86 | (59) ~ (unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) % 5.31/1.86 | % 5.31/1.86 | Instantiating formula (29) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_0_0, yields: % 5.31/1.86 | (60) ~ (apart_point_and_line(all_0_5_5, all_0_0_0) = 0) % 5.31/1.86 | % 5.31/1.86 | Instantiating formula (34) with all_0_5_5, all_0_0_0, all_22_1_7, all_31_1_9 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_31_1_9, apart_point_and_line(all_0_5_5, all_0_0_0) = all_22_1_7, yields: % 5.31/1.86 | (61) all_31_1_9 = all_22_1_7 % 5.31/1.86 | % 5.31/1.86 | From (61) and (57) follows: % 5.31/1.86 | (44) apart_point_and_line(all_0_5_5, all_0_0_0) = all_22_1_7 % 5.31/1.86 | % 5.31/1.86 | Using (56) and (59) yields: % 5.31/1.86 | (63) ~ (all_31_0_8 = 0) % 5.31/1.86 | % 5.31/1.86 | Using (44) and (60) yields: % 5.31/1.86 | (64) ~ (all_22_1_7 = 0) % 5.31/1.86 | % 5.31/1.86 +-Applying beta-rule and splitting (58), into two cases. % 5.31/1.86 |-Branch one: % 5.31/1.86 | (65) all_31_0_8 = 0 % 5.31/1.86 | % 5.31/1.86 | Equations (65) can reduce 63 to: % 5.31/1.86 | (40) $false % 5.31/1.86 | % 5.31/1.86 |-The branch is then unsatisfiable % 5.31/1.86 |-Branch two: % 5.31/1.86 | (63) ~ (all_31_0_8 = 0) % 5.31/1.86 | (68) all_31_1_9 = 0 % 5.31/1.86 | % 5.31/1.86 | Combining equations (68,61) yields a new equation: % 5.31/1.86 | (69) all_22_1_7 = 0 % 5.31/1.86 | % 5.31/1.86 | Equations (69) can reduce 64 to: % 5.31/1.86 | (40) $false % 5.31/1.86 | % 5.31/1.86 |-The branch is then unsatisfiable % 5.31/1.86 % SZS output end Proof for theBenchmark % 5.31/1.86 % 5.31/1.86 1277ms %------------------------------------------------------------------------------