%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO258+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 03:49:17 EDT 2022 % Result : Theorem 3.67s 1.52s % Output : Proof 5.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO258+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 13:21:02 EDT 2022 % 0.13/0.34 % CPUTime : % 0.59/0.59 ____ _ % 0.59/0.59 ___ / __ \_____(_)___ ________ __________ % 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.59 % 0.59/0.59 A Theorem Prover for First-Order Logic % 0.59/0.59 (ePrincess v.1.0) % 0.59/0.59 % 0.59/0.59 (c) Philipp Rümmer, 2009-2015 % 0.59/0.59 (c) Peter Backeman, 2014-2015 % 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.59 Bug reports to peter@backeman.se % 0.59/0.59 % 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.59 % 0.59/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.77/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.90/0.98 Prover 0: Preprocessing ... % 2.52/1.26 Prover 0: Warning: ignoring some quantifiers % 2.85/1.29 Prover 0: Constructing countermodel ... % 3.67/1.52 Prover 0: proved (880ms) % 3.67/1.52 % 3.67/1.52 No countermodel exists, formula is valid % 3.67/1.52 % SZS status Theorem for theBenchmark % 3.67/1.52 % 3.67/1.52 Generating proof ... Warning: ignoring some quantifiers % 5.10/1.82 found it (size 20) % 5.10/1.82 % 5.10/1.82 % SZS output start Proof for theBenchmark % 5.10/1.82 Assumed formulas after preprocessing and simplification: % 5.10/1.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (between_on_line(v0, v1, v2, v3) & ~ between_on_line(v0, v3, v2, v1) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v7) = v9) | ~ (reverse_line(v6) = v8) | ~ distinct_lines(v6, v7) | ~ distinct_points(v4, v5) | left_apart_point(v5, v9) | left_apart_point(v5, v8) | left_apart_point(v5, v7) | left_apart_point(v5, v6) | left_apart_point(v4, v9) | left_apart_point(v4, v8) | left_apart_point(v4, v7) | left_apart_point(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v6) = v8) | ~ (reverse_line(v5) = v7) | ~ unequally_directed_lines(v4, v7) | ~ unequally_directed_lines(v4, v5) | unequally_directed_lines(v5, v8) | unequally_directed_lines(v4, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v6) = v8) | ~ (reverse_line(v5) = v7) | ~ unequally_directed_lines(v4, v7) | ~ unequally_directed_lines(v4, v5) | unequally_directed_lines(v5, v8) | unequally_directed_lines(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v6) = v8) | ~ (reverse_line(v5) = v7) | ~ unequally_directed_lines(v4, v7) | ~ unequally_directed_lines(v4, v5) | unequally_directed_lines(v5, v6) | unequally_directed_lines(v4, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v6) = v8) | ~ (reverse_line(v5) = v7) | ~ unequally_directed_lines(v4, v7) | ~ unequally_directed_lines(v4, v5) | unequally_directed_lines(v5, v6) | unequally_directed_lines(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (parallel_through_point(v7, v6) = v5) | ~ (parallel_through_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection_point(v7, v6) = v5) | ~ (intersection_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (line_connecting(v7, v6) = v5) | ~ (line_connecting(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ incident_point_and_line(v6, v4) | ~ incident_point_and_line(v5, v4) | ~ distinct_points(v5, v6) | ~ equally_directed_lines(v4, v7) | before_on_line(v4, v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ before_on_line(v4, v5, v6) | incident_point_and_line(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ before_on_line(v4, v5, v6) | incident_point_and_line(v5, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ before_on_line(v4, v5, v6) | distinct_points(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ before_on_line(v4, v5, v6) | equally_directed_lines(v4, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ distinct_points(v4, v5) | ~ left_apart_point(v4, v6) | left_convergent_lines(v7, v6) | left_apart_point(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ left_apart_point(v4, v5) | ~ unequally_directed_lines(v5, v6) | distinct_lines(v5, v6) | left_apart_point(v4, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ between_on_line(v4, v5, v6, v7) | before_on_line(v4, v7, v6) | before_on_line(v4, v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ between_on_line(v4, v5, v6, v7) | before_on_line(v4, v7, v6) | before_on_line(v4, v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ between_on_line(v4, v5, v6, v7) | before_on_line(v4, v6, v7) | before_on_line(v4, v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ between_on_line(v4, v5, v6, v7) | before_on_line(v4, v6, v5) | before_on_line(v4, v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ before_on_line(v4, v7, v6) | ~ before_on_line(v4, v6, v5) | between_on_line(v4, v5, v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ before_on_line(v4, v6, v7) | ~ before_on_line(v4, v5, v6) | between_on_line(v4, v5, v6, v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (reverse_line(v6) = v5) | ~ (reverse_line(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | ~ apart_point_and_line(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | equally_directed_lines(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v4, v5) = v6) | ~ line(v4) | ~ point(v5) | line(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ~ line(v5) | ~ line(v4) | ~ unequally_directed_lines(v4, v5) | point(v6) | ? [v7] : (reverse_line(v5) = v7 & ~ unequally_directed_lines(v4, v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ~ apart_point_and_line(v6, v5) | ~ unequally_directed_lines(v4, v5) | ? [v7] : (reverse_line(v5) = v7 & ~ unequally_directed_lines(v4, v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ~ apart_point_and_line(v6, v4) | ~ unequally_directed_lines(v4, v5) | ? [v7] : (reverse_line(v5) = v7 & ~ unequally_directed_lines(v4, v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v5, v4) = v6) | ~ distinct_points(v4, v5) | ? [v7] : ? [v8] : (line_connecting(v4, v5) = v7 & reverse_line(v6) = v8 & equally_directed_lines(v7, v8))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ point(v5) | ~ point(v4) | ~ distinct_points(v4, v5) | line(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ distinct_points(v4, v5) | ~ apart_point_and_line(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ distinct_points(v4, v5) | ~ apart_point_and_line(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ distinct_points(v4, v5) | ? [v7] : ? [v8] : (line_connecting(v5, v4) = v7 & reverse_line(v7) = v8 & equally_directed_lines(v6, v8))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ left_convergent_lines(v4, v6) | right_convergent_lines(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ left_convergent_lines(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ right_convergent_lines(v4, v5) | left_convergent_lines(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ left_apart_point(v4, v6) | right_apart_point(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ left_apart_point(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ right_apart_point(v4, v5) | left_apart_point(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ unequally_directed_lines(v4, v6) | ~ unequally_directed_lines(v4, v5) | left_convergent_lines(v4, v6) | left_convergent_lines(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ unequally_directed_lines(v4, v6) | unequally_directed_opposite_lines(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ unequally_directed_opposite_lines(v4, v5) | unequally_directed_lines(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ divides_points(v6, v4, v5) | left_apart_point(v5, v6) | left_apart_point(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ divides_points(v6, v4, v5) | left_apart_point(v5, v6) | right_apart_point(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ divides_points(v6, v4, v5) | left_apart_point(v4, v6) | right_apart_point(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ divides_points(v6, v4, v5) | right_apart_point(v5, v6) | right_apart_point(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ left_apart_point(v5, v6) | ~ right_apart_point(v4, v6) | divides_points(v6, v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ left_apart_point(v4, v6) | ~ right_apart_point(v5, v6) | divides_points(v6, v4, v5)) & ? [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | unequally_directed_lines(v4, v6) | unequally_directed_lines(v4, v5)) & ? [v4] : ! [v5] : ! [v6] : ( ~ distinct_lines(v5, v6) | distinct_lines(v6, v4) | distinct_lines(v5, v4)) & ? [v4] : ! [v5] : ! [v6] : ( ~ distinct_points(v5, v6) | distinct_points(v6, v4) | distinct_points(v5, v4)) & ? [v4] : ! [v5] : ! [v6] : ( ~ left_convergent_lines(v5, v6) | left_convergent_lines(v5, v4) | unequally_directed_lines(v6, v4)) & ? [v4] : ! [v5] : ! [v6] : ( ~ left_apart_point(v5, v6) | distinct_points(v5, v4) | left_apart_point(v4, v6)) & ? [v4] : ! [v5] : ! [v6] : ( ~ unequally_directed_lines(v5, v6) | unequally_directed_lines(v6, v4) | unequally_directed_lines(v5, v4)) & ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ line(v4) | line(v5)) & ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ distinct_lines(v4, v5)) & ! [v4] : ! [v5] : ( ~ convergent_lines(v4, v5) | unequally_directed_lines(v4, v5)) & ! [v4] : ! [v5] : ( ~ convergent_lines(v4, v5) | unequally_directed_opposite_lines(v4, v5)) & ! [v4] : ! [v5] : ( ~ apart_point_and_line(v4, v5) | left_apart_point(v4, v5) | right_apart_point(v4, v5)) & ! [v4] : ! [v5] : ( ~ equally_directed_opposite_lines(v4, v5) | ~ unequally_directed_opposite_lines(v4, v5)) & ! [v4] : ! [v5] : ( ~ equally_directed_lines(v4, v5) | ~ unequally_directed_lines(v4, v5)) & ! [v4] : ! [v5] : ~ left_convergent_lines(v4, v5) & ! [v4] : ! [v5] : ( ~ left_apart_point(v4, v5) | apart_point_and_line(v4, v5)) & ! [v4] : ! [v5] : ~ left_apart_point(v4, v5) & ! [v4] : ! [v5] : ( ~ right_apart_point(v4, v5) | apart_point_and_line(v4, v5)) & ! [v4] : ! [v5] : ( ~ unequally_directed_lines(v4, v5) | ~ unequally_directed_opposite_lines(v4, v5) | convergent_lines(v4, v5)) & ! [v4] : ~ distinct_lines(v4, v4) & ! [v4] : ~ distinct_points(v4, v4) & ? [v4] : ? [v5] : (equally_directed_opposite_lines(v4, v5) | unequally_directed_opposite_lines(v4, v5)) & ? [v4] : ? [v5] : (equally_directed_lines(v4, v5) | unequally_directed_lines(v4, v5)) & ? [v4] : equally_directed_lines(v4, v4)) % 5.40/1.88 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 5.40/1.88 | (1) between_on_line(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0) & ~ between_on_line(all_0_3_3, all_0_0_0, all_0_1_1, all_0_2_2) & ! [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] : ( ~ (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(v1, v2) = v3) | ~ incident_point_and_line(v2, v0) | ~ incident_point_and_line(v1, v0) | ~ distinct_points(v1, v2) | ~ equally_directed_lines(v0, v3) | before_on_line(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | equally_directed_lines(v0, v3)) & ! [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) | ~ left_apart_point(v0, v1) | ~ unequally_directed_lines(v1, v2) | distinct_lines(v1, v2) | left_apart_point(v0, v3)) & ! [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) | ~ apart_point_and_line(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_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) | ~ 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) | ~ apart_point_and_line(v2, v1) | ~ unequally_directed_lines(v0, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v0) | ~ unequally_directed_lines(v0, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ~ distinct_points(v0, v1) | ? [v3] : ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & equally_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) | ~ distinct_points(v0, v1) | ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & equally_directed_lines(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2) | right_convergent_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_convergent_lines(v0, v1) | left_convergent_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | right_apart_point(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_apart_point(v0, v1) | left_apart_point(v0, v2)) & ! [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_opposite_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_opposite_lines(v0, v1) | unequally_directed_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | right_apart_point(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v0, v2) | right_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | right_apart_point(v1, v2) | right_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | ~ right_apart_point(v0, v2) | divides_points(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v0, v2) | ~ right_apart_point(v1, v2) | divides_points(v2, v0, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1)) & ? [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] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v1) | right_apart_point(v0, v1)) & ! [v0] : ! [v1] : ( ~ equally_directed_opposite_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ equally_directed_lines(v0, v1) | ~ unequally_directed_lines(v0, v1)) & ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1) & ! [v0] : ! [v1] : ( ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1)) & ! [v0] : ! [v1] : ~ left_apart_point(v0, v1) & ! [v0] : ! [v1] : ( ~ right_apart_point(v0, v1) | apart_point_and_line(v0, v1)) & ! [v0] : ! [v1] : ( ~ unequally_directed_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1) | convergent_lines(v0, v1)) & ! [v0] : ~ distinct_lines(v0, v0) & ! [v0] : ~ distinct_points(v0, v0) & ? [v0] : ? [v1] : (equally_directed_opposite_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) & ? [v0] : ? [v1] : (equally_directed_lines(v0, v1) | unequally_directed_lines(v0, v1)) & ? [v0] : equally_directed_lines(v0, v0) % 5.46/1.90 | % 5.46/1.90 | Applying alpha-rule on (1) yields: % 5.46/1.90 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2)) % 5.46/1.90 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3)) % 5.46/1.90 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1)) % 5.46/1.90 | (5) ! [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)) % 5.46/1.90 | (6) ! [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)) % 5.46/1.90 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2)) % 5.46/1.90 | (8) ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2)) % 5.46/1.90 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v0, v2) | right_apart_point(v0, v2)) % 5.46/1.90 | (10) ! [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)) % 5.46/1.90 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2)) % 5.46/1.90 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2)) % 5.46/1.90 | (13) ! [v0] : ! [v1] : ( ~ equally_directed_opposite_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1)) % 5.46/1.90 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) % 5.46/1.90 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | right_apart_point(v1, v2) | right_apart_point(v0, v2)) % 5.46/1.90 | (16) ! [v0] : ! [v1] : ( ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1)) % 5.46/1.90 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_opposite_lines(v0, v1) | unequally_directed_lines(v0, v2)) % 5.46/1.90 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | unequally_directed_opposite_lines(v0, v1)) % 5.46/1.90 | (19) ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0)) % 5.46/1.90 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | right_apart_point(v1, v2)) % 5.46/1.90 | (21) ! [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)) % 5.46/1.90 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2)) % 5.46/1.90 | (23) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1)) % 5.46/1.90 | (24) ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1) % 5.46/1.90 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v2, v0)) % 5.46/1.90 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 5.46/1.90 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 5.46/1.90 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v1) | ~ unequally_directed_lines(v0, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) % 5.46/1.90 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2)) % 5.46/1.91 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v0, v2) | ~ right_apart_point(v1, v2) | divides_points(v2, v0, v1)) % 5.46/1.91 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ~ distinct_points(v0, v1) | ? [v3] : ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & equally_directed_lines(v3, v4))) % 5.46/1.91 | (32) ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0)) % 5.46/1.91 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v1, v0)) % 5.46/1.91 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 5.46/1.91 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ incident_point_and_line(v2, v0) | ~ incident_point_and_line(v1, v0) | ~ distinct_points(v1, v2) | ~ equally_directed_lines(v0, v3) | before_on_line(v0, v1, v2)) % 5.46/1.91 | (36) ? [v0] : ? [v1] : (equally_directed_lines(v0, v1) | unequally_directed_lines(v0, v1)) % 5.46/1.91 | (37) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1)) % 5.46/1.91 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1)) % 5.46/1.91 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v0) | ~ unequally_directed_lines(v0, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) % 5.46/1.91 | (40) ! [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)) % 5.46/1.91 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | equally_directed_lines(v0, v3)) % 5.46/1.91 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2)) % 5.46/1.91 | (43) ! [v0] : ! [v1] : ( ~ right_apart_point(v0, v1) | apart_point_and_line(v0, v1)) % 5.46/1.91 | (44) between_on_line(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0) % 5.46/1.91 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) % 5.46/1.91 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_apart_point(v0, v1) | left_apart_point(v0, v2)) % 5.46/1.91 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | right_apart_point(v0, v1)) % 5.46/1.91 | (48) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) % 5.46/1.91 | (49) ! [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))) % 5.46/1.91 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & equally_directed_lines(v2, v4))) % 5.56/1.91 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v0, v1) | ~ unequally_directed_lines(v1, v2) | distinct_lines(v1, v2) | left_apart_point(v0, v3)) % 5.56/1.91 | (52) ? [v0] : equally_directed_lines(v0, v0) % 5.56/1.91 | (53) ! [v0] : ! [v1] : ( ~ unequally_directed_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1) | convergent_lines(v0, v1)) % 5.56/1.91 | (54) ? [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1)) % 5.56/1.91 | (55) ! [v0] : ! [v1] : ( ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v1) | right_apart_point(v0, v1)) % 5.56/1.91 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 5.56/1.91 | (57) ! [v0] : ! [v1] : ~ left_apart_point(v0, v1) % 5.56/1.91 | (58) ? [v0] : ? [v1] : (equally_directed_opposite_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) % 5.56/1.91 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3)) % 5.56/1.91 | (60) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) % 5.56/1.91 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | ~ right_apart_point(v0, v2) | divides_points(v2, v0, v1)) % 5.56/1.91 | (62) ! [v0] : ~ distinct_points(v0, v0) % 5.56/1.91 | (63) ! [v0] : ! [v1] : ( ~ equally_directed_lines(v0, v1) | ~ unequally_directed_lines(v0, v1)) % 5.56/1.92 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2)) % 5.56/1.92 | (65) ! [v0] : ~ distinct_lines(v0, v0) % 5.56/1.92 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2)) % 5.56/1.92 | (67) ! [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)) % 5.56/1.92 | (68) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) % 5.56/1.92 | (69) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1)) % 5.56/1.92 | (70) ~ between_on_line(all_0_3_3, all_0_0_0, all_0_1_1, all_0_2_2) % 5.56/1.92 | (71) ! [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)) % 5.56/1.92 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_convergent_lines(v0, v1) | left_convergent_lines(v0, v2)) % 5.59/1.92 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2) | right_convergent_lines(v0, v1)) % 5.59/1.92 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3)) % 5.59/1.92 | % 5.59/1.92 | Instantiating formula (59) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms between_on_line(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0), yields: % 5.59/1.92 | (75) before_on_line(all_0_3_3, all_0_0_0, all_0_1_1) | before_on_line(all_0_3_3, all_0_1_1, all_0_0_0) % 5.59/1.92 | % 5.59/1.92 | Instantiating formula (29) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms between_on_line(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0), yields: % 5.59/1.92 | (76) before_on_line(all_0_3_3, all_0_0_0, all_0_1_1) | before_on_line(all_0_3_3, all_0_2_2, all_0_1_1) % 5.59/1.92 | % 5.59/1.92 | Instantiating formula (38) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms between_on_line(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0), yields: % 5.59/1.92 | (77) before_on_line(all_0_3_3, all_0_1_1, all_0_0_0) | before_on_line(all_0_3_3, all_0_1_1, all_0_2_2) % 5.59/1.92 | % 5.59/1.92 | Instantiating formula (66) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms between_on_line(all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0), yields: % 5.59/1.92 | (78) before_on_line(all_0_3_3, all_0_1_1, all_0_2_2) | before_on_line(all_0_3_3, all_0_2_2, all_0_1_1) % 5.59/1.92 | % 5.59/1.92 +-Applying beta-rule and splitting (78), into two cases. % 5.59/1.92 |-Branch one: % 5.59/1.92 | (79) before_on_line(all_0_3_3, all_0_1_1, all_0_2_2) % 5.59/1.92 | % 5.59/1.92 +-Applying beta-rule and splitting (75), into two cases. % 5.59/1.92 |-Branch one: % 5.59/1.92 | (80) before_on_line(all_0_3_3, all_0_0_0, all_0_1_1) % 5.59/1.92 | % 5.59/1.92 | Instantiating formula (3) with all_0_2_2, all_0_1_1, all_0_0_0, all_0_3_3 and discharging atoms before_on_line(all_0_3_3, all_0_0_0, all_0_1_1), before_on_line(all_0_3_3, all_0_1_1, all_0_2_2), ~ between_on_line(all_0_3_3, all_0_0_0, all_0_1_1, all_0_2_2), yields: % 5.59/1.92 | (81) $false % 5.59/1.92 | % 5.59/1.92 |-The branch is then unsatisfiable % 5.59/1.92 |-Branch two: % 5.59/1.92 | (82) ~ before_on_line(all_0_3_3, all_0_0_0, all_0_1_1) % 5.59/1.92 | (83) before_on_line(all_0_3_3, all_0_1_1, all_0_0_0) % 5.59/1.92 | % 5.59/1.92 +-Applying beta-rule and splitting (76), into two cases. % 5.59/1.92 |-Branch one: % 5.59/1.92 | (80) before_on_line(all_0_3_3, all_0_0_0, all_0_1_1) % 5.59/1.92 | % 5.59/1.93 | Using (80) and (82) yields: % 5.59/1.93 | (81) $false % 5.59/1.93 | % 5.59/1.93 |-The branch is then unsatisfiable % 5.59/1.93 |-Branch two: % 5.59/1.93 | (82) ~ before_on_line(all_0_3_3, all_0_0_0, all_0_1_1) % 5.59/1.93 | (87) before_on_line(all_0_3_3, all_0_2_2, all_0_1_1) % 5.59/1.93 | % 5.59/1.93 | Instantiating formula (74) with all_0_2_2, all_0_1_1, all_0_0_0, all_0_3_3 and discharging atoms before_on_line(all_0_3_3, all_0_1_1, all_0_0_0), before_on_line(all_0_3_3, all_0_2_2, all_0_1_1), ~ between_on_line(all_0_3_3, all_0_0_0, all_0_1_1, all_0_2_2), yields: % 5.59/1.93 | (81) $false % 5.59/1.93 | % 5.59/1.93 |-The branch is then unsatisfiable % 5.59/1.93 |-Branch two: % 5.59/1.93 | (89) ~ before_on_line(all_0_3_3, all_0_1_1, all_0_2_2) % 5.59/1.93 | (87) before_on_line(all_0_3_3, all_0_2_2, all_0_1_1) % 5.59/1.93 | % 5.59/1.93 +-Applying beta-rule and splitting (77), into two cases. % 5.59/1.93 |-Branch one: % 5.59/1.93 | (83) before_on_line(all_0_3_3, all_0_1_1, all_0_0_0) % 5.59/1.93 | % 5.59/1.93 | Instantiating formula (74) with all_0_2_2, all_0_1_1, all_0_0_0, all_0_3_3 and discharging atoms before_on_line(all_0_3_3, all_0_1_1, all_0_0_0), before_on_line(all_0_3_3, all_0_2_2, all_0_1_1), ~ between_on_line(all_0_3_3, all_0_0_0, all_0_1_1, all_0_2_2), yields: % 5.59/1.93 | (81) $false % 5.59/1.93 | % 5.59/1.93 |-The branch is then unsatisfiable % 5.59/1.93 |-Branch two: % 5.59/1.93 | (93) ~ before_on_line(all_0_3_3, all_0_1_1, all_0_0_0) % 5.59/1.93 | (79) before_on_line(all_0_3_3, all_0_1_1, all_0_2_2) % 5.59/1.93 | % 5.59/1.93 | Using (79) and (89) yields: % 5.59/1.93 | (81) $false % 5.59/1.93 | % 5.59/1.93 |-The branch is then unsatisfiable % 5.59/1.93 % SZS output end Proof for theBenchmark % 5.59/1.93 % 5.59/1.93 1331ms %------------------------------------------------------------------------------