%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO207+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 03:48:43 EDT 2022 % Result : Theorem 2.60s 1.27s % Output : Proof 4.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : GEO207+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n021.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 01:54:31 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.75/0.95 Prover 0: Preprocessing ... % 2.15/1.16 Prover 0: Warning: ignoring some quantifiers % 2.45/1.19 Prover 0: Constructing countermodel ... % 2.60/1.27 Prover 0: proved (640ms) % 2.60/1.27 % 2.60/1.27 No countermodel exists, formula is valid % 2.60/1.27 % SZS status Theorem for theBenchmark % 2.60/1.27 % 2.60/1.27 Generating proof ... Warning: ignoring some quantifiers % 3.64/1.50 found it (size 4) % 3.64/1.50 % 3.64/1.50 % SZS output start Proof for theBenchmark % 3.64/1.50 Assumed formulas after preprocessing and simplification: % 3.64/1.50 | (0) ? [v0] : (convergent_lines(v0, v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (orthogonal_through_point(v4, v3) = v2) | ~ (orthogonal_through_point(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] : ( ~ distinct_lines(v3, v4) | ~ distinct_points(v1, v2) | apart_point_and_line(v2, v4) | apart_point_and_line(v2, v3) | apart_point_and_line(v1, v4) | apart_point_and_line(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (orthogonal_through_point(v2, v1) = v3) | ~ unorthogonal_lines(v3, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (orthogonal_through_point(v2, v1) = v3) | ~ apart_point_and_line(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (orthogonal_through_point(v1, v2) = v3) | ~ line(v1) | ~ point(v2) | line(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (parallel_through_point(v2, v1) = v3) | ~ apart_point_and_line(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (parallel_through_point(v2, v1) = v3) | ~ convergent_lines(v3, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (parallel_through_point(v1, v2) = v3) | ~ line(v1) | ~ point(v2) | line(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v1, v2) = v3) | ~ line(v2) | ~ line(v1) | ~ convergent_lines(v1, v2) | point(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v1, v2) = v3) | ~ apart_point_and_line(v3, v2) | ~ convergent_lines(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v1, v2) = v3) | ~ apart_point_and_line(v3, v1) | ~ convergent_lines(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ point(v2) | ~ point(v1) | ~ distinct_points(v1, v2) | line(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ apart_point_and_line(v1, v3) | ~ distinct_points(v1, v2)) & ? [v1] : ? [v2] : ! [v3] : ! [v4] : ( ~ distinct_lines(v3, v4) | unorthogonal_lines(v4, v2) | unorthogonal_lines(v3, v2) | apart_point_and_line(v1, v4) | apart_point_and_line(v1, v3)) & ? [v1] : ! [v2] : ! [v3] : ( ~ unorthogonal_lines(v2, v3) | ~ convergent_lines(v2, v3) | unorthogonal_lines(v3, v1) | unorthogonal_lines(v2, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ unorthogonal_lines(v2, v3) | ~ convergent_lines(v2, v3) | unorthogonal_lines(v3, v1) | convergent_lines(v2, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ unorthogonal_lines(v2, v3) | ~ convergent_lines(v2, v3) | unorthogonal_lines(v2, v1) | convergent_lines(v3, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ unorthogonal_lines(v2, v3) | ~ convergent_lines(v2, v3) | unorthogonal_lines(v1, v3) | unorthogonal_lines(v1, v2)) & ? [v1] : ! [v2] : ! [v3] : ( ~ unorthogonal_lines(v2, v3) | ~ convergent_lines(v2, v3) | unorthogonal_lines(v1, v3) | convergent_lines(v1, v2)) & ? [v1] : ! [v2] : ! [v3] : ( ~ unorthogonal_lines(v2, v3) | ~ convergent_lines(v2, v3) | unorthogonal_lines(v1, v2) | convergent_lines(v1, v3)) & ? [v1] : ! [v2] : ! [v3] : ( ~ unorthogonal_lines(v2, v3) | ~ convergent_lines(v2, v3) | convergent_lines(v3, v1) | convergent_lines(v2, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ unorthogonal_lines(v2, v3) | ~ convergent_lines(v2, v3) | convergent_lines(v1, v3) | convergent_lines(v1, v2)) & ? [v1] : ! [v2] : ! [v3] : ( ~ apart_point_and_line(v2, v3) | apart_point_and_line(v2, v1) | distinct_lines(v3, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ apart_point_and_line(v2, v3) | apart_point_and_line(v1, v3) | distinct_points(v2, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ convergent_lines(v2, v3) | unorthogonal_lines(v1, v3) | unorthogonal_lines(v1, v2)) & ? [v1] : ! [v2] : ! [v3] : ( ~ convergent_lines(v2, v3) | convergent_lines(v3, v1) | convergent_lines(v2, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ convergent_lines(v2, v3) | convergent_lines(v2, v1) | distinct_lines(v3, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | convergent_lines(v2, v3)) & ? [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | distinct_lines(v3, v1) | distinct_lines(v2, v1)) & ? [v1] : ! [v2] : ! [v3] : ( ~ distinct_points(v2, v3) | distinct_points(v3, v1) | distinct_points(v2, v1)) & ! [v1] : ! [v2] : ( ~ orthogonal_lines(v1, v2) | ~ unorthogonal_lines(v1, v2)) & ! [v1] : ! [v2] : ( ~ incident_point_and_line(v1, v2) | ~ apart_point_and_line(v1, v2)) & ! [v1] : ! [v2] : ( ~ parallel_lines(v1, v2) | ~ convergent_lines(v1, v2)) & ! [v1] : ! [v2] : ( ~ equal_lines(v1, v2) | ~ distinct_lines(v1, v2)) & ! [v1] : ! [v2] : ( ~ equal_points(v1, v2) | ~ distinct_points(v1, v2)) & ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | convergent_lines(v1, v2)) & ! [v1] : ~ convergent_lines(v1, v1) & ! [v1] : ~ distinct_lines(v1, v1) & ! [v1] : ~ distinct_points(v1, v1) & ? [v1] : ? [v2] : (orthogonal_lines(v1, v2) | unorthogonal_lines(v1, v2)) & ? [v1] : ? [v2] : (incident_point_and_line(v1, v2) | apart_point_and_line(v1, v2)) & ? [v1] : ? [v2] : (parallel_lines(v1, v2) | convergent_lines(v1, v2)) & ? [v1] : ? [v2] : (equal_lines(v1, v2) | distinct_lines(v1, v2)) & ? [v1] : ? [v2] : (equal_points(v1, v2) | distinct_points(v1, v2)) & ? [v1] : ? [v2] : (unorthogonal_lines(v1, v2) | convergent_lines(v1, v2))) % 3.64/1.56 | Instantiating (0) with all_0_0_0 yields: % 3.64/1.56 | (1) convergent_lines(all_0_0_0, all_0_0_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 | ~ (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)) % 4.08/1.57 | % 4.08/1.57 | Applying alpha-rule on (1) yields: % 4.08/1.57 | (2) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | unorthogonal_lines(v0, v1)) % 4.08/1.57 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) % 4.08/1.57 | (4) ! [v0] : ~ distinct_points(v0, v0) % 4.08/1.57 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ apart_point_and_line(v1, v2) | ~ distinct_points(v0, v1)) % 4.08/1.57 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1)) % 4.08/1.57 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.08/1.57 | (8) ! [v0] : ! [v1] : ( ~ parallel_lines(v0, v1) | ~ convergent_lines(v0, v1)) % 4.08/1.57 | (9) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | convergent_lines(v0, v1)) % 4.08/1.57 | (10) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v1, v0) | distinct_lines(v2, v0)) % 4.08/1.57 | (11) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) % 4.08/1.57 | (12) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) % 4.08/1.58 | (13) ? [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)) % 4.08/1.58 | (14) ? [v0] : ? [v1] : (equal_points(v0, v1) | distinct_points(v0, v1)) % 4.08/1.58 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.08/1.58 | (16) ! [v0] : ! [v1] : ( ~ distinct_lines(v0, v1) | convergent_lines(v0, v1)) % 4.08/1.58 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) % 4.08/1.58 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) % 4.08/1.58 | (19) ! [v0] : ! [v1] : ( ~ equal_lines(v0, v1) | ~ distinct_lines(v0, v1)) % 4.08/1.58 | (20) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0)) % 4.08/1.58 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) % 4.08/1.58 | (22) ! [v0] : ~ distinct_lines(v0, v0) % 4.08/1.58 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 4.08/1.58 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1)) % 4.08/1.58 | (25) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v1, v0) | convergent_lines(v2, v0)) % 4.08/1.58 | (26) convergent_lines(all_0_0_0, all_0_0_0) % 4.08/1.58 | (27) ! [v0] : ! [v1] : ( ~ orthogonal_lines(v0, v1) | ~ unorthogonal_lines(v0, v1)) % 4.08/1.58 | (28) ? [v0] : ? [v1] : (unorthogonal_lines(v0, v1) | convergent_lines(v0, v1)) % 4.08/1.58 | (29) ! [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)) % 4.08/1.58 | (30) ? [v0] : ? [v1] : (parallel_lines(v0, v1) | convergent_lines(v0, v1)) % 4.08/1.58 | (31) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) % 4.08/1.58 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ unorthogonal_lines(v2, v1)) % 4.08/1.58 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2)) % 4.08/1.58 | (34) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v2, v0) | convergent_lines(v1, v0)) % 4.08/1.58 | (35) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v2) | unorthogonal_lines(v0, v1)) % 4.08/1.58 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 4.08/1.58 | (37) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0)) % 4.08/1.58 | (38) ? [v0] : ? [v1] : (orthogonal_lines(v0, v1) | unorthogonal_lines(v0, v1)) % 4.08/1.58 | (39) ! [v0] : ! [v1] : ( ~ incident_point_and_line(v0, v1) | ~ apart_point_and_line(v0, v1)) % 4.08/1.58 | (40) ! [v0] : ~ convergent_lines(v0, v0) % 4.08/1.58 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ convergent_lines(v2, v1)) % 4.08/1.58 | (42) ? [v0] : ? [v1] : (incident_point_and_line(v0, v1) | apart_point_and_line(v0, v1)) % 4.08/1.58 | (43) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v0, v1) | convergent_lines(v0, v2)) % 4.08/1.58 | (44) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | convergent_lines(v0, v2) | convergent_lines(v0, v1)) % 4.08/1.59 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ line(v1) | ~ line(v0) | ~ convergent_lines(v0, v1) | point(v2)) % 4.08/1.59 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ apart_point_and_line(v0, v2) | ~ distinct_points(v0, v1)) % 4.08/1.59 | (47) ! [v0] : ! [v1] : ( ~ equal_points(v0, v1) | ~ distinct_points(v0, v1)) % 4.08/1.59 | (48) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | apart_point_and_line(v0, v2) | apart_point_and_line(v0, v1) | convergent_lines(v1, v2)) % 4.08/1.59 | (49) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) % 4.08/1.59 | (50) ? [v0] : ? [v1] : (equal_lines(v0, v1) | distinct_lines(v0, v1)) % 4.08/1.59 | (51) ? [v0] : ! [v1] : ! [v2] : ( ~ unorthogonal_lines(v1, v2) | ~ convergent_lines(v1, v2) | unorthogonal_lines(v2, v0) | unorthogonal_lines(v1, v0)) % 4.08/1.59 | % 4.08/1.59 | Instantiating formula (40) with all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_0_0), yields: % 4.08/1.59 | (52) $false % 4.08/1.59 | % 4.08/1.59 |-The branch is then unsatisfiable % 4.08/1.59 % SZS output end Proof for theBenchmark % 4.08/1.59 % 4.08/1.59 1001ms %------------------------------------------------------------------------------