%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO216+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 03:48:50 EDT 2022 % Result : Theorem 13.32s 3.74s % Output : Proof 14.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO216+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Fri Jun 17 20:55:12 EDT 2022 % 0.12/0.34 % CPUTime : % 0.20/0.59 ____ _ % 0.20/0.59 ___ / __ \_____(_)___ ________ __________ % 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic % 0.20/0.59 (ePrincess v.1.0) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2015 % 0.20/0.59 (c) Peter Backeman, 2014-2015 % 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.86/0.95 Prover 0: Preprocessing ... % 2.22/1.16 Prover 0: Warning: ignoring some quantifiers % 2.54/1.18 Prover 0: Constructing countermodel ... % 12.27/3.56 Prover 0: gave up % 12.27/3.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 12.65/3.60 Prover 1: Preprocessing ... % 13.32/3.72 Prover 1: Constructing countermodel ... % 13.32/3.74 Prover 1: proved (181ms) % 13.32/3.74 % 13.32/3.74 No countermodel exists, formula is valid % 13.32/3.74 % SZS status Theorem for theBenchmark % 13.32/3.74 % 13.32/3.74 Generating proof ... found it (size 11) % 14.08/3.93 % 14.08/3.93 % SZS output start Proof for theBenchmark % 14.08/3.93 Assumed formulas after preprocessing and simplification: % 14.08/3.93 | (0) ? [v0] : (orthogonal_lines(v0, v0) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (unorthogonal_lines(v2, v4) = v6) | ~ (apart_point_and_line(v1, v2) = v5) | ~ (distinct_lines(v2, v3) = 0) | ? [v7] : ? [v8] : (unorthogonal_lines(v3, v4) = v8 & apart_point_and_line(v1, v3) = v7 & (v8 = 0 | v7 = 0))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (unorthogonal_lines(v1, v2) = v4) | ? [v6] : ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v1, v3) = v5) | ~ (unorthogonal_lines(v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (unorthogonal_lines(v2, v3) = v9 & convergent_lines(v2, v3) = v8 & convergent_lines(v1, v3) = v7 & convergent_lines(v1, v2) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | (v7 = 0 & v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v5] : ? [v6] : (apart_point_and_line(v1, v3) = v5 & convergent_lines(v2, v3) = v6 & (v6 = 0 | v5 = 0))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (apart_point_and_line(v1, v2) = 0) | ~ (distinct_lines(v2, v3) = v4) | apart_point_and_line(v1, v3) = 0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (apart_point_and_line(v1, v2) = 0) | ~ (distinct_points(v1, v3) = v4) | apart_point_and_line(v3, v2) = 0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (convergent_lines(v1, v3) = v4) | ~ (convergent_lines(v1, v2) = 0) | convergent_lines(v2, v3) = 0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (convergent_lines(v1, v2) = 0) | ~ (distinct_lines(v2, v3) = v4) | convergent_lines(v1, v3) = 0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (distinct_lines(v1, v3) = v4) | ~ (distinct_lines(v1, v2) = 0) | distinct_lines(v2, v3) = 0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (distinct_points(v1, v3) = v4) | ~ (distinct_points(v1, v2) = 0) | distinct_points(v2, v3) = 0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (orthogonal_lines(v4, v3) = v2) | ~ (orthogonal_lines(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (incident_point_and_line(v4, v3) = v2) | ~ (incident_point_and_line(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (parallel_lines(v4, v3) = v2) | ~ (parallel_lines(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (equal_lines(v4, v3) = v2) | ~ (equal_lines(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (equal_points(v4, v3) = v2) | ~ (equal_points(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (orthogonal_through_point(v4, v3) = v2) | ~ (orthogonal_through_point(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (unorthogonal_lines(v4, v3) = v2) | ~ (unorthogonal_lines(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (parallel_through_point(v4, v3) = v2) | ~ (parallel_through_point(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (intersection_point(v4, v3) = v2) | ~ (intersection_point(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (line_connecting(v4, v3) = v2) | ~ (line_connecting(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (apart_point_and_line(v4, v3) = v2) | ~ (apart_point_and_line(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (convergent_lines(v4, v3) = v2) | ~ (convergent_lines(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (distinct_lines(v4, v3) = v2) | ~ (distinct_lines(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (distinct_points(v4, v3) = v2) | ~ (distinct_points(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v3) = v4) | ~ (unorthogonal_lines(v1, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v2, v3) = v8 & convergent_lines(v2, v3) = v7 & convergent_lines(v1, v3) = v6 & convergent_lines(v1, v2) = v5 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0) | (v6 = 0 & v4 = 0)))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_lines(v3, v4) = 0) | ~ (distinct_points(v1, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v2, v4) = v8 & apart_point_and_line(v2, v3) = v7 & apart_point_and_line(v1, v4) = v6 & apart_point_and_line(v1, v3) = v5 & (v8 = 0 | v7 = 0 | v6 = 0 | v5 = 0))) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (orthogonal_lines(v1, v2) = v3) | unorthogonal_lines(v1, v2) = 0) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (incident_point_and_line(v1, v2) = v3) | apart_point_and_line(v1, v2) = 0) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (parallel_lines(v1, v2) = v3) | convergent_lines(v1, v2) = 0) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equal_lines(v1, v2) = v3) | distinct_lines(v1, v2) = 0) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equal_points(v1, v2) = v3) | distinct_points(v1, v2) = 0) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v1, v2) = v3) | convergent_lines(v1, v2) = 0) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (point(v3) = v2) | ~ (point(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (line(v3) = v2) | ~ (line(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (orthogonal_through_point(v2, v1) = v3) | ~ (unorthogonal_lines(v3, v2) = 0)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (orthogonal_through_point(v2, v1) = v3) | ~ (apart_point_and_line(v1, v3) = 0)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (orthogonal_through_point(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (point(v2) = v5 & line(v3) = v6 & line(v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (parallel_through_point(v2, v1) = v3) | ~ (apart_point_and_line(v1, v3) = 0)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (parallel_through_point(v2, v1) = v3) | ~ (convergent_lines(v3, v2) = 0)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (parallel_through_point(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (point(v2) = v5 & line(v3) = v6 & line(v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v1, v2) = v3) | ~ (apart_point_and_line(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v1, v2) = v3) | ~ (apart_point_and_line(v3, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (point(v3) = v7 & line(v2) = v5 & line(v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & distinct_points(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (apart_point_and_line(v1, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & distinct_points(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (point(v2) = v5 & point(v1) = v4 & line(v3) = v7 & distinct_points(v1, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0))) & ! [v1] : ! [v2] : ( ~ (orthogonal_lines(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v3)) & ! [v1] : ! [v2] : ( ~ (incident_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3)) & ! [v1] : ! [v2] : ( ~ (parallel_lines(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v1, v2) = v3)) & ! [v1] : ! [v2] : ( ~ (equal_lines(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v1, v2) = v3)) & ! [v1] : ! [v2] : ( ~ (equal_points(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v1, v2) = v3)) & ! [v1] : ! [v2] : ( ~ (distinct_lines(v1, v2) = 0) | convergent_lines(v1, v2) = 0) & ! [v1] : ~ (convergent_lines(v1, v1) = 0) & ! [v1] : ~ (distinct_lines(v1, v1) = 0) & ! [v1] : ~ (distinct_points(v1, v1) = 0)) % 14.08/3.97 | Instantiating (0) with all_0_0_0 yields: % 14.08/3.97 | (1) orthogonal_lines(all_0_0_0, 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 | 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] : ( ~ (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) = 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_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [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 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [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] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 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] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 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] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [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] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) % 14.56/3.98 | % 14.56/3.98 | Applying alpha-rule on (1) yields: % 14.56/3.98 | (2) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 14.56/3.98 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 14.56/3.98 | (4) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 14.56/3.98 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0)) % 14.56/3.98 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 14.56/3.98 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 14.56/3.98 | (8) ! [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) % 14.56/3.98 | (9) ! [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)) % 14.56/3.98 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 14.56/3.98 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 14.56/3.98 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 14.56/3.98 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 14.56/3.98 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) % 14.56/3.98 | (15) ! [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)))) % 14.56/3.98 | (16) ! [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)))) % 14.56/3.98 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 14.56/3.98 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 14.56/3.99 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 14.56/3.99 | (20) orthogonal_lines(all_0_0_0, all_0_0_0) = 0 % 14.56/3.99 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 14.56/3.99 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 14.56/3.99 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 14.56/3.99 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 14.56/3.99 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 14.56/3.99 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 14.56/3.99 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 14.56/3.99 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 14.56/3.99 | (29) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 14.56/3.99 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 14.56/3.99 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 14.56/3.99 | (32) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 14.56/3.99 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 14.56/3.99 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 14.56/3.99 | (35) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 14.56/3.99 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 14.56/3.99 | (37) ! [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))) % 14.56/3.99 | (38) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 14.56/3.99 | (39) ! [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) % 14.56/3.99 | (40) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 14.56/3.99 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 14.56/3.99 | (42) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 14.56/3.99 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 14.56/3.99 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 14.56/3.99 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 14.56/3.99 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 14.56/3.99 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 14.56/3.99 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 14.56/3.99 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 14.56/3.99 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 14.56/4.00 | (51) ! [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))) % 14.56/4.00 | (52) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 14.56/4.00 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 14.56/4.00 | (54) ! [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))) % 14.56/4.00 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) % 14.56/4.00 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 14.56/4.00 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 14.56/4.00 | % 14.56/4.00 | Instantiating formula (38) with all_0_0_0, all_0_0_0 and discharging atoms orthogonal_lines(all_0_0_0, all_0_0_0) = 0, yields: % 14.56/4.00 | (58) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_0_0) = v0) % 14.56/4.00 | % 14.56/4.00 | Instantiating (58) with all_8_0_1 yields: % 14.56/4.00 | (59) ~ (all_8_0_1 = 0) & unorthogonal_lines(all_0_0_0, all_0_0_0) = all_8_0_1 % 14.56/4.00 | % 14.56/4.00 | Applying alpha-rule on (59) yields: % 14.56/4.00 | (60) ~ (all_8_0_1 = 0) % 14.56/4.00 | (61) unorthogonal_lines(all_0_0_0, all_0_0_0) = all_8_0_1 % 14.56/4.00 | % 14.56/4.00 | Instantiating formula (41) with all_8_0_1, all_0_0_0, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_0_0) = all_8_0_1, yields: % 14.56/4.00 | (62) all_8_0_1 = 0 | convergent_lines(all_0_0_0, all_0_0_0) = 0 % 14.56/4.00 | % 14.56/4.00 +-Applying beta-rule and splitting (62), into two cases. % 14.56/4.00 |-Branch one: % 14.56/4.00 | (63) convergent_lines(all_0_0_0, all_0_0_0) = 0 % 14.56/4.00 | % 14.56/4.00 | Instantiating formula (35) with all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_0_0) = 0, yields: % 14.56/4.00 | (64) $false % 14.56/4.00 | % 14.56/4.00 |-The branch is then unsatisfiable % 14.56/4.00 |-Branch two: % 14.56/4.00 | (65) ~ (convergent_lines(all_0_0_0, all_0_0_0) = 0) % 14.56/4.00 | (66) all_8_0_1 = 0 % 14.56/4.00 | % 14.56/4.00 | Equations (66) can reduce 60 to: % 14.56/4.00 | (67) $false % 14.56/4.00 | % 14.56/4.00 |-The branch is then unsatisfiable % 14.56/4.00 % SZS output end Proof for theBenchmark % 14.56/4.00 % 14.56/4.00 3401ms %------------------------------------------------------------------------------