%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO228+1 : TPTP v8.1.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n003.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 03:48:59 EDT 2022 % Result : Theorem 3.12s 1.40s % Output : Proof 4.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO228+1 : TPTP v8.1.0. Bugfixed v6.4.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n003.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 08:35:43 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.58 ____ _ % 0.53/0.58 ___ / __ \_____(_)___ ________ __________ % 0.53/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.58 % 0.53/0.58 A Theorem Prover for First-Order Logic % 0.53/0.58 (ePrincess v.1.0) % 0.53/0.58 % 0.53/0.58 (c) Philipp Rümmer, 2009-2015 % 0.53/0.58 (c) Peter Backeman, 2014-2015 % 0.53/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.58 Bug reports to peter@backeman.se % 0.53/0.58 % 0.53/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.58 % 0.53/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.83/0.98 Prover 0: Preprocessing ... % 2.57/1.24 Prover 0: Warning: ignoring some quantifiers % 2.64/1.28 Prover 0: Constructing countermodel ... % 3.12/1.40 Prover 0: proved (770ms) % 3.12/1.40 % 3.12/1.40 No countermodel exists, formula is valid % 3.12/1.40 % SZS status Theorem for theBenchmark % 3.12/1.40 % 3.12/1.40 Generating proof ... Warning: ignoring some quantifiers % 4.54/1.69 found it (size 14) % 4.54/1.69 % 4.54/1.69 % SZS output start Proof for theBenchmark % 4.54/1.69 Assumed formulas after preprocessing and simplification: % 4.54/1.69 | (0) ? [v0] : ? [v1] : ? [v2] : (reverse_line(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v6) = v8) | ~ (reverse_line(v5) = v7) | ~ distinct_lines(v5, v6) | ~ distinct_points(v3, v4) | left_apart_point(v4, v8) | left_apart_point(v4, v7) | left_apart_point(v4, v6) | left_apart_point(v4, v5) | left_apart_point(v3, v8) | left_apart_point(v3, v7) | left_apart_point(v3, v6) | left_apart_point(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ (reverse_line(v3) = v6) | ~ distinct_points(v4, v5) | before_on_line(v3, v4, v5) | unequally_directed_lines(v3, v7) | left_apart_point(v5, v6) | left_apart_point(v5, v3) | left_apart_point(v4, v6) | left_apart_point(v4, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ (reverse_line(v3) = v6) | ~ before_on_line(v3, v4, v5) | ~ unequally_directed_lines(v3, v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ (reverse_line(v3) = v6) | ~ before_on_line(v3, v4, v5) | ~ left_apart_point(v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ (reverse_line(v3) = v6) | ~ before_on_line(v3, v4, v5) | ~ left_apart_point(v5, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ (reverse_line(v3) = v6) | ~ before_on_line(v3, v4, v5) | ~ left_apart_point(v4, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ (reverse_line(v3) = v6) | ~ before_on_line(v3, v4, v5) | ~ left_apart_point(v4, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ (reverse_line(v3) = v6) | ~ before_on_line(v3, v4, v5) | distinct_points(v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v5) = v7) | ~ (reverse_line(v4) = v6) | ~ unequally_directed_lines(v3, v6) | ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v7) | unequally_directed_lines(v3, v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v5) = v7) | ~ (reverse_line(v4) = v6) | ~ unequally_directed_lines(v3, v6) | ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v7) | unequally_directed_lines(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v5) = v7) | ~ (reverse_line(v4) = v6) | ~ unequally_directed_lines(v3, v6) | ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v5) | unequally_directed_lines(v3, v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v5) = v7) | ~ (reverse_line(v4) = v6) | ~ unequally_directed_lines(v3, v6) | ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v5) | unequally_directed_lines(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (parallel_through_point(v6, v5) = v4) | ~ (parallel_through_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection_point(v6, v5) = v4) | ~ (intersection_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (line_connecting(v6, v5) = v4) | ~ (line_connecting(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v3, v4) = v6) | ~ distinct_points(v3, v4) | ~ left_apart_point(v3, v5) | left_convergent_lines(v6, v5) | left_apart_point(v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ divides_points(v5, v3, v4) | left_apart_point(v4, v6) | left_apart_point(v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ divides_points(v5, v3, v4) | left_apart_point(v4, v6) | left_apart_point(v3, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ divides_points(v5, v3, v4) | left_apart_point(v4, v5) | left_apart_point(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ divides_points(v5, v3, v4) | left_apart_point(v3, v6) | left_apart_point(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ unequally_directed_lines(v4, v5) | ~ left_apart_point(v3, v4) | distinct_lines(v4, v5) | left_apart_point(v3, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ left_apart_point(v4, v6) | ~ left_apart_point(v3, v5) | divides_points(v5, v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ left_apart_point(v4, v5) | ~ left_apart_point(v3, v6) | divides_points(v5, v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_on_line(v3, v4, v5, v6) | before_on_line(v3, v6, v5) | before_on_line(v3, v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_on_line(v3, v4, v5, v6) | before_on_line(v3, v6, v5) | before_on_line(v3, v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_on_line(v3, v4, v5, v6) | before_on_line(v3, v5, v6) | before_on_line(v3, v5, v4)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ between_on_line(v3, v4, v5, v6) | before_on_line(v3, v5, v4) | before_on_line(v3, v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ before_on_line(v3, v6, v5) | ~ before_on_line(v3, v5, v4) | between_on_line(v3, v4, v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ before_on_line(v3, v5, v6) | ~ before_on_line(v3, v4, v5) | between_on_line(v3, v4, v5, v6)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (reverse_line(v5) = v4) | ~ (reverse_line(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) | ~ unequally_directed_lines(v5, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) | ~ apart_point_and_line(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v3, v4) = v5) | ~ point(v4) | ~ line(v3) | line(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection_point(v3, v4) = v5) | ~ line(v4) | ~ line(v3) | ~ unequally_directed_lines(v3, v4) | point(v5) | ? [v6] : (reverse_line(v4) = v6 & ~ unequally_directed_lines(v3, v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection_point(v3, v4) = v5) | ~ unequally_directed_lines(v3, v4) | ~ apart_point_and_line(v5, v4) | ? [v6] : (reverse_line(v4) = v6 & ~ unequally_directed_lines(v3, v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection_point(v3, v4) = v5) | ~ unequally_directed_lines(v3, v4) | ~ apart_point_and_line(v5, v3) | ? [v6] : (reverse_line(v4) = v6 & ~ unequally_directed_lines(v3, v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v4, v3) = v5) | ? [v6] : ? [v7] : (line_connecting(v3, v4) = v6 & reverse_line(v5) = v7 & ~ unequally_directed_lines(v6, v7))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ~ point(v4) | ~ point(v3) | ~ distinct_points(v3, v4) | line(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ~ distinct_points(v3, v4) | ~ apart_point_and_line(v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ~ distinct_points(v3, v4) | ~ apart_point_and_line(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ? [v6] : ? [v7] : (line_connecting(v4, v3) = v6 & reverse_line(v6) = v7 & ~ unequally_directed_lines(v5, v7))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ left_convergent_lines(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ line(v4) | ~ line(v3) | unequally_directed_lines(v3, v5) | unequally_directed_lines(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ unequally_directed_lines(v3, v5) | ~ unequally_directed_lines(v3, v4) | left_convergent_lines(v3, v5) | left_convergent_lines(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ unequally_directed_lines(v3, v5) | ~ unequally_directed_lines(v3, v4) | convergent_lines(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ convergent_lines(v3, v4) | unequally_directed_lines(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ convergent_lines(v3, v4) | unequally_directed_lines(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ left_apart_point(v3, v5) | apart_point_and_line(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ left_apart_point(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ left_apart_point(v3, v4) | apart_point_and_line(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ apart_point_and_line(v3, v4) | left_apart_point(v3, v5) | left_apart_point(v3, v4)) & ? [v3] : ! [v4] : ! [v5] : ( ~ left_convergent_lines(v4, v5) | left_convergent_lines(v4, v3) | unequally_directed_lines(v5, v3)) & ? [v3] : ! [v4] : ! [v5] : ( ~ distinct_lines(v4, v5) | distinct_lines(v5, v3) | distinct_lines(v4, v3)) & ? [v3] : ! [v4] : ! [v5] : ( ~ distinct_points(v4, v5) | distinct_points(v5, v3) | distinct_points(v4, v3)) & ? [v3] : ! [v4] : ! [v5] : ( ~ unequally_directed_lines(v4, v5) | unequally_directed_lines(v5, v3) | unequally_directed_lines(v4, v3)) & ? [v3] : ! [v4] : ! [v5] : ( ~ left_apart_point(v4, v5) | distinct_points(v4, v3) | left_apart_point(v3, v5)) & ! [v3] : ! [v4] : ( ~ (reverse_line(v3) = v4) | ~ line(v3) | line(v4)) & ! [v3] : ! [v4] : ( ~ (reverse_line(v3) = v4) | ~ distinct_lines(v3, v4)) & ! [v3] : ! [v4] : ~ left_convergent_lines(v3, v4) & ! [v3] : ! [v4] : ~ left_apart_point(v3, v4) & ! [v3] : ~ distinct_lines(v3, v3) & ! [v3] : ~ distinct_points(v3, v3) & ! [v3] : ~ unequally_directed_lines(v3, v3) & ((unequally_directed_lines(v0, v2) & unequally_directed_lines(v0, v1) & ~ convergent_lines(v0, v1)) | (convergent_lines(v0, v1) & ( ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1))))) % 4.54/1.75 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 4.54/1.75 | (1) reverse_line(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v3) = v5) | ~ (reverse_line(v2) = v4) | ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | left_apart_point(v1, v5) | left_apart_point(v1, v4) | left_apart_point(v1, v3) | left_apart_point(v1, v2) | left_apart_point(v0, v5) | left_apart_point(v0, v4) | left_apart_point(v0, v3) | left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ distinct_points(v1, v2) | before_on_line(v0, v1, v2) | unequally_directed_lines(v0, v4) | left_apart_point(v2, v3) | left_apart_point(v2, v0) | left_apart_point(v1, v3) | left_apart_point(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ unequally_directed_lines(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v2)) & ! [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] : ( ~ (line_connecting(v0, v1) = v3) | ~ distinct_points(v0, v1) | ~ left_apart_point(v0, v2) | left_convergent_lines(v3, v2) | left_apart_point(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v0, v3) | left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ unequally_directed_lines(v1, v2) | ~ left_apart_point(v0, v1) | distinct_lines(v1, v2) | left_apart_point(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v1, v3) | ~ left_apart_point(v0, v2) | divides_points(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v1, v2) | ~ left_apart_point(v0, v3) | divides_points(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ unequally_directed_lines(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ point(v1) | ~ line(v0) | line(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ line(v1) | ~ line(v0) | ~ unequally_directed_lines(v0, v1) | point(v2) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ unequally_directed_lines(v0, v1) | ~ apart_point_and_line(v2, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ unequally_directed_lines(v0, v1) | ~ apart_point_and_line(v2, v0) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & ~ unequally_directed_lines(v3, v4))) & ! [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) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & ~ unequally_directed_lines(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ line(v1) | ~ line(v0) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1) | left_convergent_lines(v0, v2) | left_convergent_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1) | convergent_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | apart_point_and_line(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v2) | left_apart_point(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0)) & ? [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] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1)) & ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1) & ! [v0] : ! [v1] : ~ left_apart_point(v0, v1) & ! [v0] : ~ distinct_lines(v0, v0) & ! [v0] : ~ distinct_points(v0, v0) & ! [v0] : ~ unequally_directed_lines(v0, v0) & ((unequally_directed_lines(all_0_2_2, all_0_0_0) & unequally_directed_lines(all_0_2_2, all_0_1_1) & ~ convergent_lines(all_0_2_2, all_0_1_1)) | (convergent_lines(all_0_2_2, all_0_1_1) & ( ~ unequally_directed_lines(all_0_2_2, all_0_0_0) | ~ unequally_directed_lines(all_0_2_2, all_0_1_1)))) % 4.91/1.77 | % 4.91/1.77 | Applying alpha-rule on (1) yields: % 4.91/1.77 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3)) % 4.91/1.77 | (3) ! [v0] : ~ unequally_directed_lines(v0, v0) % 4.91/1.77 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) % 4.91/1.77 | (5) ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0)) % 4.91/1.77 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.91/1.77 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v2)) % 4.91/1.77 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ unequally_directed_lines(v2, v1)) % 4.91/1.77 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v1, v0)) % 4.91/1.77 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ unequally_directed_lines(v1, v2) | ~ left_apart_point(v0, v1) | distinct_lines(v1, v2) | left_apart_point(v0, v3)) % 4.91/1.77 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2)) % 4.91/1.77 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1) | left_convergent_lines(v0, v2) | left_convergent_lines(v0, v1)) % 4.91/1.77 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v1, v2)) % 4.91/1.77 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 4.91/1.77 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ unequally_directed_lines(v0, v1) | ~ apart_point_and_line(v2, v0) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) % 4.91/1.77 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v2)) % 4.91/1.77 | (17) ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1) % 4.91/1.77 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3)) % 4.91/1.77 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v0, v3)) % 4.91/1.77 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v1, v3) | ~ left_apart_point(v0, v2) | divides_points(v2, v0, v1)) % 4.98/1.78 | (21) (unequally_directed_lines(all_0_2_2, all_0_0_0) & unequally_directed_lines(all_0_2_2, all_0_1_1) & ~ convergent_lines(all_0_2_2, all_0_1_1)) | (convergent_lines(all_0_2_2, all_0_1_1) & ( ~ unequally_directed_lines(all_0_2_2, all_0_0_0) | ~ unequally_directed_lines(all_0_2_2, all_0_1_1))) % 4.98/1.78 | (22) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1)) % 4.98/1.78 | (23) ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0)) % 4.98/1.78 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1)) % 4.98/1.78 | (25) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) % 4.98/1.78 | (26) ! [v0] : ~ distinct_lines(v0, v0) % 4.98/1.78 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v2)) % 4.98/1.78 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ line(v1) | ~ line(v0) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1)) % 4.98/1.78 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & ~ unequally_directed_lines(v2, v4))) % 4.98/1.78 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2)) % 4.98/1.78 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2)) % 4.98/1.78 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v2, v3)) % 4.98/1.78 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v4)) % 4.98/1.78 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2)) % 4.98/1.78 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v1, v2) | ~ left_apart_point(v0, v3) | divides_points(v2, v0, v1)) % 4.98/1.78 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v4)) % 4.98/1.78 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ distinct_points(v1, v2) | before_on_line(v0, v1, v2) | unequally_directed_lines(v0, v4) | left_apart_point(v2, v3) | left_apart_point(v2, v0) | left_apart_point(v1, v3) | left_apart_point(v1, v0)) % 4.98/1.78 | (38) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1)) % 4.98/1.78 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ unequally_directed_lines(v0, v1) | ~ apart_point_and_line(v2, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) % 4.98/1.78 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2)) % 4.98/1.78 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2)) % 4.98/1.78 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v2) | left_apart_point(v0, v1)) % 4.98/1.78 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v3) = v5) | ~ (reverse_line(v2) = v4) | ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | left_apart_point(v1, v5) | left_apart_point(v1, v4) | left_apart_point(v1, v3) | left_apart_point(v1, v2) | left_apart_point(v0, v5) | left_apart_point(v0, v4) | left_apart_point(v0, v3) | left_apart_point(v0, v2)) % 4.98/1.78 | (44) ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2)) % 4.98/1.78 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ line(v1) | ~ line(v0) | ~ unequally_directed_lines(v0, v1) | point(v2) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) % 4.98/1.78 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ unequally_directed_lines(v0, v4)) % 4.98/1.78 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2)) % 4.98/1.79 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | apart_point_and_line(v0, v1)) % 4.98/1.79 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1) | convergent_lines(v0, v1)) % 4.98/1.79 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2)) % 4.98/1.79 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3)) % 4.98/1.79 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ distinct_points(v0, v1) | ~ left_apart_point(v0, v2) | left_convergent_lines(v3, v2) | left_apart_point(v1, v2)) % 4.98/1.79 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v1, v3)) % 4.98/1.79 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1)) % 4.98/1.79 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2)) % 4.98/1.79 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ point(v1) | ~ line(v0) | line(v2)) % 4.98/1.79 | (57) ! [v0] : ! [v1] : ~ left_apart_point(v0, v1) % 4.98/1.79 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.98/1.79 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 4.98/1.79 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v2, v0)) % 4.98/1.79 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & ~ unequally_directed_lines(v3, v4))) % 4.98/1.79 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v0, v3) | left_apart_point(v0, v2)) % 4.98/1.79 | (63) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) % 4.98/1.79 | (64) ! [v0] : ~ distinct_points(v0, v0) % 4.98/1.79 | (65) reverse_line(all_0_1_1) = all_0_0_0 % 4.98/1.79 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1)) % 4.98/1.79 | % 4.98/1.79 +-Applying beta-rule and splitting (21), into two cases. % 4.98/1.79 |-Branch one: % 4.98/1.79 | (67) unequally_directed_lines(all_0_2_2, all_0_0_0) & unequally_directed_lines(all_0_2_2, all_0_1_1) & ~ convergent_lines(all_0_2_2, all_0_1_1) % 4.98/1.79 | % 4.98/1.79 | Applying alpha-rule on (67) yields: % 4.98/1.79 | (68) unequally_directed_lines(all_0_2_2, all_0_0_0) % 4.98/1.79 | (69) unequally_directed_lines(all_0_2_2, all_0_1_1) % 4.98/1.79 | (70) ~ convergent_lines(all_0_2_2, all_0_1_1) % 4.98/1.79 | % 4.98/1.79 | Instantiating formula (49) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms reverse_line(all_0_1_1) = all_0_0_0, unequally_directed_lines(all_0_2_2, all_0_0_0), unequally_directed_lines(all_0_2_2, all_0_1_1), ~ convergent_lines(all_0_2_2, all_0_1_1), yields: % 4.98/1.79 | (71) $false % 4.98/1.79 | % 4.98/1.80 |-The branch is then unsatisfiable % 4.98/1.80 |-Branch two: % 4.98/1.80 | (72) convergent_lines(all_0_2_2, all_0_1_1) & ( ~ unequally_directed_lines(all_0_2_2, all_0_0_0) | ~ unequally_directed_lines(all_0_2_2, all_0_1_1)) % 4.98/1.80 | % 4.98/1.80 | Applying alpha-rule on (72) yields: % 4.98/1.80 | (73) convergent_lines(all_0_2_2, all_0_1_1) % 4.98/1.80 | (74) ~ unequally_directed_lines(all_0_2_2, all_0_0_0) | ~ unequally_directed_lines(all_0_2_2, all_0_1_1) % 4.98/1.80 | % 4.98/1.80 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms reverse_line(all_0_1_1) = all_0_0_0, convergent_lines(all_0_2_2, all_0_1_1), yields: % 4.98/1.80 | (68) unequally_directed_lines(all_0_2_2, all_0_0_0) % 4.98/1.80 | % 4.98/1.80 | Instantiating formula (24) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms reverse_line(all_0_1_1) = all_0_0_0, convergent_lines(all_0_2_2, all_0_1_1), yields: % 4.98/1.80 | (69) unequally_directed_lines(all_0_2_2, all_0_1_1) % 4.98/1.80 | % 4.98/1.80 +-Applying beta-rule and splitting (74), into two cases. % 4.98/1.80 |-Branch one: % 4.98/1.80 | (77) ~ unequally_directed_lines(all_0_2_2, all_0_0_0) % 4.98/1.80 | % 4.98/1.80 | Using (68) and (77) yields: % 4.98/1.80 | (71) $false % 4.98/1.80 | % 4.98/1.80 |-The branch is then unsatisfiable % 4.98/1.80 |-Branch two: % 4.98/1.80 | (68) unequally_directed_lines(all_0_2_2, all_0_0_0) % 4.98/1.80 | (80) ~ unequally_directed_lines(all_0_2_2, all_0_1_1) % 4.98/1.80 | % 4.98/1.80 | Using (69) and (80) yields: % 4.98/1.80 | (71) $false % 4.98/1.80 | % 4.98/1.80 |-The branch is then unsatisfiable % 4.98/1.80 % SZS output end Proof for theBenchmark % 4.98/1.80 % 4.98/1.80 1208ms %------------------------------------------------------------------------------