%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO211+1 : 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 03:48:46 EDT 2022 % Result : Theorem 3.60s 1.50s % Output : Proof 4.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : GEO211+1 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.12 % 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 06:37:43 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.66/0.93 Prover 0: Preprocessing ... % 2.07/1.10 Prover 0: Warning: ignoring some quantifiers % 2.07/1.12 Prover 0: Constructing countermodel ... % 2.94/1.34 Prover 0: gave up % 2.94/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.94/1.37 Prover 1: Preprocessing ... % 3.60/1.48 Prover 1: Constructing countermodel ... % 3.60/1.50 Prover 1: proved (161ms) % 3.60/1.50 % 3.60/1.50 No countermodel exists, formula is valid % 3.60/1.50 % SZS status Theorem for theBenchmark % 3.60/1.50 % 3.60/1.50 Generating proof ... found it (size 8) % 4.32/1.68 % 4.32/1.68 % SZS output start Proof for theBenchmark % 4.32/1.68 Assumed formulas after preprocessing and simplification: % 4.32/1.68 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & unorthogonal_lines(v0, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (unorthogonal_lines(v3, v5) = v7) | ~ (apart_point_and_line(v2, v3) = v6) | ~ (distinct_lines(v3, v4) = 0) | ? [v8] : ? [v9] : (unorthogonal_lines(v4, v5) = v9 & apart_point_and_line(v2, v4) = v8 & (v9 = 0 | v8 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = v5) | ~ (distinct_lines(v3, v4) = 0) | ? [v6] : ? [v7] : (apart_point_and_line(v2, v4) = v6 & convergent_lines(v3, v4) = v7 & (v7 = 0 | v6 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = 0) | ~ (distinct_lines(v3, v4) = v5) | apart_point_and_line(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = 0) | ~ (distinct_points(v2, v4) = v5) | apart_point_and_line(v4, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v3) = 0) | ~ (distinct_lines(v3, v4) = v5) | convergent_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v2, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v2, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (orthogonal_through_point(v5, v4) = v3) | ~ (orthogonal_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (unorthogonal_lines(v5, v4) = v3) | ~ (unorthogonal_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (parallel_through_point(v5, v4) = v3) | ~ (parallel_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersection_point(v5, v4) = v3) | ~ (intersection_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (line_connecting(v5, v4) = v3) | ~ (line_connecting(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (apart_point_and_line(v5, v4) = v3) | ~ (apart_point_and_line(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (convergent_lines(v5, v4) = v3) | ~ (convergent_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_lines(v5, v4) = v3) | ~ (distinct_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_points(v5, v4) = v3) | ~ (distinct_points(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v2, v4) = v5) | ~ (unorthogonal_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (unorthogonal_lines(v3, v4) = v9 & convergent_lines(v3, v4) = v8 & convergent_lines(v2, v4) = v7 & convergent_lines(v2, v3) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | ~ (distinct_points(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v3, v5) = v9 & apart_point_and_line(v3, v4) = v8 & apart_point_and_line(v2, v5) = v7 & apart_point_and_line(v2, v4) = v6 & (v9 = 0 | v8 = 0 | v7 = 0 | v6 = 0))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v4) | convergent_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ( ~ (orthogonal_through_point(v3, v2) = v4) | ~ (unorthogonal_lines(v4, v3) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (orthogonal_through_point(v3, v2) = v4) | ~ (apart_point_and_line(v2, v4) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) | ~ (apart_point_and_line(v2, v4) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) | ~ (convergent_lines(v4, v3) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ~ (apart_point_and_line(v4, v3) = 0) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ~ (apart_point_and_line(v4, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ~ (apart_point_and_line(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ~ (apart_point_and_line(v2, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v2, v3) = v5)) & ! [v2] : ~ (convergent_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_points(v2, v2) = 0)) % 4.65/1.74 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 4.65/1.74 | (1) ~ (all_0_0_0 = 0) & unorthogonal_lines(all_0_1_1, all_0_1_1) = all_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] : (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 | ~ (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] : ( ~ (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] : ( ~ (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] : ! [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) % 4.65/1.76 | % 4.65/1.76 | Applying alpha-rule on (1) yields: % 4.65/1.76 | (2) unorthogonal_lines(all_0_1_1, all_0_1_1) = all_0_0_0 % 4.65/1.76 | (3) ! [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))) % 4.65/1.76 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 4.65/1.76 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 4.65/1.76 | (6) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.65/1.76 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.65/1.76 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 4.65/1.76 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 4.65/1.76 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 4.65/1.76 | (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) % 4.65/1.76 | (12) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 4.65/1.76 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 4.65/1.76 | (14) ~ (all_0_0_0 = 0) % 4.65/1.76 | (15) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 4.65/1.76 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 4.65/1.76 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 4.65/1.76 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 4.65/1.76 | (19) ! [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))) % 4.65/1.76 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 4.65/1.76 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 4.65/1.77 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 4.65/1.77 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.65/1.77 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) % 4.65/1.77 | (25) ! [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) % 4.65/1.77 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 4.65/1.77 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 4.65/1.77 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 4.65/1.77 | (29) ! [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))) % 4.65/1.77 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 4.65/1.77 | (31) ! [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)))) % 4.65/1.77 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 4.65/1.77 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.65/1.77 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.65/1.77 | % 4.65/1.77 | Instantiating formula (27) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_1_1) = all_0_0_0, yields: % 4.65/1.77 | (35) all_0_0_0 = 0 | convergent_lines(all_0_1_1, all_0_1_1) = 0 % 4.65/1.77 | % 4.65/1.77 +-Applying beta-rule and splitting (35), into two cases. % 4.65/1.77 |-Branch one: % 4.65/1.77 | (36) convergent_lines(all_0_1_1, all_0_1_1) = 0 % 4.65/1.77 | % 4.65/1.77 | Instantiating formula (15) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields: % 4.65/1.77 | (37) $false % 4.65/1.77 | % 4.65/1.77 |-The branch is then unsatisfiable % 4.65/1.77 |-Branch two: % 4.65/1.77 | (38) ~ (convergent_lines(all_0_1_1, all_0_1_1) = 0) % 4.65/1.77 | (39) all_0_0_0 = 0 % 4.65/1.77 | % 4.65/1.77 | Equations (39) can reduce 14 to: % 4.65/1.77 | (40) $false % 4.65/1.77 | % 4.65/1.77 |-The branch is then unsatisfiable % 4.65/1.77 % SZS output end Proof for theBenchmark % 4.65/1.77 % 4.65/1.77 1193ms %------------------------------------------------------------------------------