%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO173+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 03:48:09 EDT 2022 % Result : Theorem 14.22s 4.07s % Output : Proof 15.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : GEO173+3 : TPTP v8.1.0. Released v4.0.0. % 0.09/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.36 % Computer : n016.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Sat Jun 18 10:39:07 EDT 2022 % 0.15/0.36 % CPUTime : % 0.61/0.62 ____ _ % 0.61/0.62 ___ / __ \_____(_)___ ________ __________ % 0.61/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.62 % 0.61/0.62 A Theorem Prover for First-Order Logic % 0.61/0.62 (ePrincess v.1.0) % 0.61/0.62 % 0.61/0.62 (c) Philipp Rümmer, 2009-2015 % 0.61/0.62 (c) Peter Backeman, 2014-2015 % 0.61/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.62 Bug reports to peter@backeman.se % 0.61/0.62 % 0.61/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.62 % 0.61/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.98/1.02 Prover 0: Preprocessing ... % 2.63/1.25 Prover 0: Warning: ignoring some quantifiers % 2.63/1.28 Prover 0: Constructing countermodel ... % 14.22/4.06 Prover 0: proved (3391ms) % 14.22/4.07 % 14.22/4.07 No countermodel exists, formula is valid % 14.22/4.07 % SZS status Theorem for theBenchmark % 14.22/4.07 % 14.22/4.07 Generating proof ... Warning: ignoring some quantifiers % 15.41/4.31 found it (size 8) % 15.41/4.31 % 15.41/4.31 % SZS output start Proof for theBenchmark % 15.41/4.31 Assumed formulas after preprocessing and simplification: % 15.41/4.31 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (line_connecting(v0, v1) = v4 & convergent_lines(v2, v3) & distinct_lines(v2, v4) & distinct_points(v0, v1) & ~ apart_point_and_line(v1, v2) & ~ apart_point_and_line(v0, v2) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (orthogonal_through_point(v8, v7) = v6) | ~ (orthogonal_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_through_point(v8, v7) = v6) | ~ (parallel_through_point(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] : ( ~ distinct_lines(v7, v8) | ~ distinct_points(v5, v6) | apart_point_and_line(v6, v8) | apart_point_and_line(v6, v7) | apart_point_and_line(v5, v8) | apart_point_and_line(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ~ unorthogonal_lines(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ~ apart_point_and_line(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v5, v6) = v7) | ~ line(v5) | ~ point(v6) | line(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ~ apart_point_and_line(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ~ convergent_lines(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v5, v6) = v7) | ~ line(v5) | ~ point(v6) | line(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ~ line(v6) | ~ line(v5) | ~ convergent_lines(v5, v6) | point(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ~ apart_point_and_line(v7, v6) | ~ convergent_lines(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ~ apart_point_and_line(v7, v5) | ~ convergent_lines(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ point(v6) | ~ point(v5) | ~ distinct_points(v5, v6) | line(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ apart_point_and_line(v6, v7) | ~ distinct_points(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ apart_point_and_line(v5, v7) | ~ distinct_points(v5, v6)) & ? [v5] : ? [v6] : ! [v7] : ! [v8] : ( ~ distinct_lines(v7, v8) | unorthogonal_lines(v8, v6) | unorthogonal_lines(v7, v6) | apart_point_and_line(v5, v8) | apart_point_and_line(v5, v7)) & ? [v5] : ! [v6] : ! [v7] : ( ~ unorthogonal_lines(v6, v7) | ~ convergent_lines(v6, v7) | unorthogonal_lines(v7, v5) | unorthogonal_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ unorthogonal_lines(v6, v7) | ~ convergent_lines(v6, v7) | unorthogonal_lines(v7, v5) | convergent_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ unorthogonal_lines(v6, v7) | ~ convergent_lines(v6, v7) | unorthogonal_lines(v6, v5) | convergent_lines(v7, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ unorthogonal_lines(v6, v7) | ~ convergent_lines(v6, v7) | unorthogonal_lines(v5, v7) | unorthogonal_lines(v5, v6)) & ? [v5] : ! [v6] : ! [v7] : ( ~ unorthogonal_lines(v6, v7) | ~ convergent_lines(v6, v7) | unorthogonal_lines(v5, v7) | convergent_lines(v5, v6)) & ? [v5] : ! [v6] : ! [v7] : ( ~ unorthogonal_lines(v6, v7) | ~ convergent_lines(v6, v7) | unorthogonal_lines(v5, v6) | convergent_lines(v5, v7)) & ? [v5] : ! [v6] : ! [v7] : ( ~ unorthogonal_lines(v6, v7) | ~ convergent_lines(v6, v7) | convergent_lines(v7, v5) | convergent_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ unorthogonal_lines(v6, v7) | ~ convergent_lines(v6, v7) | convergent_lines(v5, v7) | convergent_lines(v5, v6)) & ? [v5] : ! [v6] : ! [v7] : ( ~ apart_point_and_line(v6, v7) | apart_point_and_line(v6, v5) | distinct_lines(v7, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ apart_point_and_line(v6, v7) | apart_point_and_line(v5, v7) | distinct_points(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | unorthogonal_lines(v5, v7) | unorthogonal_lines(v5, v6)) & ? [v5] : ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | convergent_lines(v7, v5) | convergent_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | convergent_lines(v6, v5) | distinct_lines(v7, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ distinct_lines(v6, v7) | apart_point_and_line(v5, v7) | apart_point_and_line(v5, v6) | convergent_lines(v6, v7)) & ? [v5] : ! [v6] : ! [v7] : ( ~ distinct_lines(v6, v7) | distinct_lines(v7, v5) | distinct_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ distinct_points(v6, v7) | distinct_points(v7, v5) | distinct_points(v6, v5)) & ! [v5] : ! [v6] : ( ~ orthogonal_lines(v5, v6) | ~ unorthogonal_lines(v5, v6)) & ! [v5] : ! [v6] : ( ~ incident_point_and_line(v5, v6) | ~ apart_point_and_line(v5, v6)) & ! [v5] : ! [v6] : ( ~ parallel_lines(v5, v6) | ~ convergent_lines(v5, v6)) & ! [v5] : ! [v6] : ( ~ equal_lines(v5, v6) | ~ distinct_lines(v5, v6)) & ! [v5] : ! [v6] : ( ~ equal_points(v5, v6) | ~ distinct_points(v5, v6)) & ! [v5] : ! [v6] : ( ~ distinct_lines(v5, v6) | convergent_lines(v5, v6)) & ! [v5] : ~ convergent_lines(v5, v5) & ! [v5] : ~ distinct_lines(v5, v5) & ! [v5] : ~ distinct_points(v5, v5) & ? [v5] : ? [v6] : (orthogonal_lines(v5, v6) | unorthogonal_lines(v5, v6)) & ? [v5] : ? [v6] : (incident_point_and_line(v5, v6) | apart_point_and_line(v5, v6)) & ? [v5] : ? [v6] : (parallel_lines(v5, v6) | convergent_lines(v5, v6)) & ? [v5] : ? [v6] : (equal_lines(v5, v6) | distinct_lines(v5, v6)) & ? [v5] : ? [v6] : (equal_points(v5, v6) | distinct_points(v5, v6)) & ? [v5] : ? [v6] : (unorthogonal_lines(v5, v6) | convergent_lines(v5, v6))) % 15.62/4.37 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 15.62/4.37 | (1) line_connecting(all_0_4_4, all_0_3_3) = all_0_0_0 & convergent_lines(all_0_2_2, all_0_1_1) & distinct_lines(all_0_2_2, all_0_0_0) & distinct_points(all_0_4_4, all_0_3_3) & ~ apart_point_and_line(all_0_3_3, all_0_2_2) & ~ apart_point_and_line(all_0_4_4, all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(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] : ( ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ unorthogonal_lines(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ convergent_lines(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ line(v1) | ~ line(v0) | ~ convergent_lines(v0, v1) | point(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ apart_point_and_line(v1, v2) | ~ distinct_points(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ apart_point_and_line(v0, v2) | ~ distinct_points(v0, v1)) & ? [v0] : ? [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | unorthogonal_lines(v3, v1) | unorthogonal_lines(v2, v1) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v2, v0) | unorthogonal_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v2, v0) | convergent_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v1, v0) | convergent_lines(v2, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | unorthogonal_lines(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | convergent_lines(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v1) | convergent_lines(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | convergent_lines(v0, v2) | convergent_lines(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | unorthogonal_lines(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v1, v0) | distinct_lines(v2, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | apart_point_and_line(v0, v2) | apart_point_and_line(v0, v1) | convergent_lines(v1, v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) & ! [v0] : ! [v1] : ( ~ orthogonal_lines(v0, v1) | ~ unorthogonal_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ incident_point_and_line(v0, v1) | ~ apart_point_and_line(v0, v1)) & ! [v0] : ! [v1] : ( ~ parallel_lines(v0, v1) | ~ convergent_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ equal_lines(v0, v1) | ~ distinct_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ equal_points(v0, v1) | ~ distinct_points(v0, v1)) & ! [v0] : ! [v1] : ( ~ distinct_lines(v0, v1) | convergent_lines(v0, v1)) & ! [v0] : ~ convergent_lines(v0, v0) & ! [v0] : ~ distinct_lines(v0, v0) & ! [v0] : ~ distinct_points(v0, v0) & ? [v0] : ? [v1] : (orthogonal_lines(v0, v1) | unorthogonal_lines(v0, v1)) & ? [v0] : ? [v1] : (incident_point_and_line(v0, v1) | apart_point_and_line(v0, v1)) & ? [v0] : ? [v1] : (parallel_lines(v0, v1) | convergent_lines(v0, v1)) & ? [v0] : ? [v1] : (equal_lines(v0, v1) | distinct_lines(v0, v1)) & ? [v0] : ? [v1] : (equal_points(v0, v1) | distinct_points(v0, v1)) & ? [v0] : ? [v1] : (unorthogonal_lines(v0, v1) | convergent_lines(v0, v1)) % 15.62/4.39 | % 15.62/4.39 | Applying alpha-rule on (1) yields: % 15.62/4.39 | (2) ~ apart_point_and_line(all_0_3_3, all_0_2_2) % 15.62/4.39 | (3) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | unorthogonal_lines(v0, v1)) % 15.62/4.39 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) % 15.62/4.39 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ apart_point_and_line(v0, v2) | ~ distinct_points(v0, v1)) % 15.62/4.39 | (6) ! [v0] : ~ distinct_points(v0, v0) % 15.62/4.39 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 15.62/4.39 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) % 15.62/4.39 | (9) ! [v0] : ! [v1] : ( ~ parallel_lines(v0, v1) | ~ convergent_lines(v0, v1)) % 15.62/4.39 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 15.62/4.39 | (11) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | convergent_lines(v0, v1)) % 15.62/4.39 | (12) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v1, v0) | distinct_lines(v2, v0)) % 15.62/4.39 | (13) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) % 15.62/4.39 | (14) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) % 15.62/4.39 | (15) ? [v0] : ? [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | unorthogonal_lines(v3, v1) | unorthogonal_lines(v2, v1) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) % 15.62/4.39 | (16) ? [v0] : ? [v1] : (equal_points(v0, v1) | distinct_points(v0, v1)) % 15.62/4.39 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 15.62/4.39 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 15.62/4.39 | (19) ! [v0] : ! [v1] : ( ~ distinct_lines(v0, v1) | convergent_lines(v0, v1)) % 15.62/4.39 | (20) ! [v0] : ! [v1] : ( ~ equal_lines(v0, v1) | ~ distinct_lines(v0, v1)) % 15.62/4.39 | (21) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0)) % 15.62/4.39 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1)) % 15.62/4.39 | (23) distinct_points(all_0_4_4, all_0_3_3) % 15.62/4.39 | (24) ! [v0] : ~ distinct_lines(v0, v0) % 15.62/4.39 | (25) line_connecting(all_0_4_4, all_0_3_3) = all_0_0_0 % 15.62/4.39 | (26) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v1, v0) | convergent_lines(v2, v0)) % 15.62/4.40 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) % 15.62/4.40 | (28) ! [v0] : ! [v1] : ( ~ orthogonal_lines(v0, v1) | ~ unorthogonal_lines(v0, v1)) % 15.62/4.40 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ line(v1) | ~ line(v0) | ~ convergent_lines(v0, v1) | point(v2)) % 15.62/4.40 | (30) ? [v0] : ? [v1] : (unorthogonal_lines(v0, v1) | convergent_lines(v0, v1)) % 15.62/4.40 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) % 15.62/4.40 | (32) ? [v0] : ? [v1] : (parallel_lines(v0, v1) | convergent_lines(v0, v1)) % 15.62/4.40 | (33) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) % 15.62/4.40 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ unorthogonal_lines(v2, v1)) % 15.62/4.40 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2)) % 15.62/4.40 | (36) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v2, v0) | convergent_lines(v1, v0)) % 15.62/4.40 | (37) ~ apart_point_and_line(all_0_4_4, all_0_2_2) % 15.62/4.40 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ convergent_lines(v2, v1)) % 15.62/4.40 | (39) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | unorthogonal_lines(v0, v1)) % 15.62/4.40 | (40) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0)) % 15.62/4.40 | (41) ? [v0] : ? [v1] : (orthogonal_lines(v0, v1) | unorthogonal_lines(v0, v1)) % 15.62/4.40 | (42) ! [v0] : ! [v1] : ( ~ incident_point_and_line(v0, v1) | ~ apart_point_and_line(v0, v1)) % 15.62/4.40 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) % 15.62/4.40 | (44) ! [v0] : ~ convergent_lines(v0, v0) % 15.62/4.40 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ apart_point_and_line(v1, v2) | ~ distinct_points(v0, v1)) % 15.62/4.40 | (46) distinct_lines(all_0_2_2, all_0_0_0) % 15.62/4.40 | (47) ? [v0] : ? [v1] : (incident_point_and_line(v0, v1) | apart_point_and_line(v0, v1)) % 15.62/4.40 | (48) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v1) | convergent_lines(v0, v2)) % 15.62/4.40 | (49) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | convergent_lines(v0, v2) | convergent_lines(v0, v1)) % 15.96/4.40 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1)) % 15.96/4.40 | (51) convergent_lines(all_0_2_2, all_0_1_1) % 15.96/4.40 | (52) ! [v0] : ! [v1] : ( ~ equal_points(v0, v1) | ~ distinct_points(v0, v1)) % 15.96/4.40 | (53) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | apart_point_and_line(v0, v2) | apart_point_and_line(v0, v1) | convergent_lines(v1, v2)) % 15.96/4.40 | (54) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) % 15.96/4.40 | (55) ? [v0] : ? [v1] : (equal_lines(v0, v1) | distinct_lines(v0, v1)) % 15.96/4.40 | (56) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v2, v0) | unorthogonal_lines(v1, v0)) % 15.96/4.41 | % 15.96/4.41 | Instantiating formula (31) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms distinct_lines(all_0_2_2, all_0_0_0), distinct_points(all_0_4_4, all_0_3_3), ~ apart_point_and_line(all_0_3_3, all_0_2_2), ~ apart_point_and_line(all_0_4_4, all_0_2_2), yields: % 15.96/4.41 | (57) apart_point_and_line(all_0_3_3, all_0_0_0) | apart_point_and_line(all_0_4_4, all_0_0_0) % 15.96/4.41 | % 15.96/4.41 +-Applying beta-rule and splitting (57), into two cases. % 15.96/4.41 |-Branch one: % 15.96/4.41 | (58) apart_point_and_line(all_0_3_3, all_0_0_0) % 15.96/4.41 | % 15.96/4.41 | Instantiating formula (45) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms line_connecting(all_0_4_4, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_3_3, all_0_0_0), distinct_points(all_0_4_4, all_0_3_3), yields: % 15.96/4.41 | (59) $false % 15.96/4.41 | % 15.96/4.41 |-The branch is then unsatisfiable % 15.96/4.41 |-Branch two: % 15.96/4.41 | (60) ~ apart_point_and_line(all_0_3_3, all_0_0_0) % 15.96/4.41 | (61) apart_point_and_line(all_0_4_4, all_0_0_0) % 15.96/4.41 | % 15.96/4.41 | Instantiating formula (5) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms line_connecting(all_0_4_4, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_0_0), distinct_points(all_0_4_4, all_0_3_3), yields: % 15.96/4.41 | (59) $false % 15.96/4.41 | % 15.96/4.41 |-The branch is then unsatisfiable % 15.96/4.41 % SZS output end Proof for theBenchmark % 15.96/4.41 % 15.96/4.41 3779ms %------------------------------------------------------------------------------