TSTP Solution File: GEO247+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO247+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 03:49:10 EDT 2022
% Result : Theorem 3.10s 1.38s
% Output : Proof 4.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO247+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 20:23:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.50/0.63 ____ _
% 0.50/0.63 ___ / __ \_____(_)___ ________ __________
% 0.50/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.63
% 0.50/0.63 A Theorem Prover for First-Order Logic
% 0.66/0.63 (ePrincess v.1.0)
% 0.66/0.63
% 0.66/0.63 (c) Philipp Rümmer, 2009-2015
% 0.66/0.63 (c) Peter Backeman, 2014-2015
% 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.63 Bug reports to peter@backeman.se
% 0.66/0.63
% 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.63
% 0.66/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.79/1.02 Prover 0: Preprocessing ...
% 2.66/1.28 Prover 0: Warning: ignoring some quantifiers
% 2.66/1.31 Prover 0: Constructing countermodel ...
% 3.10/1.37 Prover 0: proved (684ms)
% 3.10/1.38
% 3.10/1.38 No countermodel exists, formula is valid
% 3.10/1.38 % SZS status Theorem for theBenchmark
% 3.10/1.38
% 3.10/1.38 Generating proof ... Warning: ignoring some quantifiers
% 3.94/1.64 found it (size 4)
% 3.94/1.64
% 3.94/1.64 % SZS output start Proof for theBenchmark
% 3.94/1.64 Assumed formulas after preprocessing and simplification:
% 3.94/1.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (left_apart_point(v3, v5) & left_apart_point(v2, v4) & left_apart_point(v0, v5) & left_apart_point(v0, v4) & right_apart_point(v3, v4) & right_apart_point(v2, v5) & right_apart_point(v1, v5) & right_apart_point(v1, v4) & ~ convergent_lines(v4, v5) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v9) = v11) | ~ (reverse_line(v8) = v10) | ~ distinct_lines(v8, v9) | ~ distinct_points(v6, v7) | left_apart_point(v7, v11) | left_apart_point(v7, v10) | left_apart_point(v7, v9) | left_apart_point(v7, v8) | left_apart_point(v6, v11) | left_apart_point(v6, v10) | left_apart_point(v6, v9) | left_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v8) = v10) | ~ (reverse_line(v7) = v9) | ~ unequally_directed_lines(v6, v9) | ~ unequally_directed_lines(v6, v7) | unequally_directed_lines(v7, v10) | unequally_directed_lines(v6, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v8) = v10) | ~ (reverse_line(v7) = v9) | ~ unequally_directed_lines(v6, v9) | ~ unequally_directed_lines(v6, v7) | unequally_directed_lines(v7, v10) | unequally_directed_lines(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v8) = v10) | ~ (reverse_line(v7) = v9) | ~ unequally_directed_lines(v6, v9) | ~ unequally_directed_lines(v6, v7) | unequally_directed_lines(v7, v8) | unequally_directed_lines(v6, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v8) = v10) | ~ (reverse_line(v7) = v9) | ~ unequally_directed_lines(v6, v9) | ~ unequally_directed_lines(v6, v7) | unequally_directed_lines(v7, v8) | unequally_directed_lines(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ incident_point_and_line(v8, v6) | ~ incident_point_and_line(v7, v6) | ~ distinct_points(v7, v8) | ~ equally_directed_lines(v6, v9) | before_on_line(v6, v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ before_on_line(v6, v7, v8) | incident_point_and_line(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ before_on_line(v6, v7, v8) | incident_point_and_line(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ before_on_line(v6, v7, v8) | distinct_points(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ before_on_line(v6, v7, v8) | equally_directed_lines(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v6, v7) = v9) | ~ distinct_points(v6, v7) | ~ left_apart_point(v6, v8) | left_convergent_lines(v9, v8) | left_apart_point(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ left_apart_point(v6, v7) | ~ unequally_directed_lines(v7, v8) | distinct_lines(v7, v8) | left_apart_point(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ between_on_line(v6, v7, v8, v9) | before_on_line(v6, v9, v8) | before_on_line(v6, v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ between_on_line(v6, v7, v8, v9) | before_on_line(v6, v9, v8) | before_on_line(v6, v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ between_on_line(v6, v7, v8, v9) | before_on_line(v6, v8, v9) | before_on_line(v6, v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ between_on_line(v6, v7, v8, v9) | before_on_line(v6, v8, v7) | before_on_line(v6, v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ before_on_line(v6, v9, v8) | ~ before_on_line(v6, v8, v7) | between_on_line(v6, v7, v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ before_on_line(v6, v8, v9) | ~ before_on_line(v6, v7, v8) | between_on_line(v6, v7, v8, v9)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (reverse_line(v8) = v7) | ~ (reverse_line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ~ apart_point_and_line(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | equally_directed_lines(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ~ line(v6) | ~ point(v7) | line(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ line(v7) | ~ line(v6) | ~ unequally_directed_lines(v6, v7) | point(v8) | ? [v9] : (reverse_line(v7) = v9 & ~ unequally_directed_lines(v6, v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ apart_point_and_line(v8, v7) | ~ unequally_directed_lines(v6, v7) | ? [v9] : (reverse_line(v7) = v9 & ~ unequally_directed_lines(v6, v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ apart_point_and_line(v8, v6) | ~ unequally_directed_lines(v6, v7) | ? [v9] : (reverse_line(v7) = v9 & ~ unequally_directed_lines(v6, v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v7, v6) = v8) | ~ distinct_points(v6, v7) | ? [v9] : ? [v10] : (line_connecting(v6, v7) = v9 & reverse_line(v8) = v10 & equally_directed_lines(v9, v10))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ point(v7) | ~ point(v6) | ~ distinct_points(v6, v7) | line(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ distinct_points(v6, v7) | ~ apart_point_and_line(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ distinct_points(v6, v7) | ~ apart_point_and_line(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ distinct_points(v6, v7) | ? [v9] : ? [v10] : (line_connecting(v7, v6) = v9 & reverse_line(v9) = v10 & equally_directed_lines(v8, v10))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ left_convergent_lines(v6, v8) | right_convergent_lines(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ left_convergent_lines(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ right_convergent_lines(v6, v7) | left_convergent_lines(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ left_apart_point(v6, v8) | right_apart_point(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ left_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ right_apart_point(v6, v7) | left_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ unequally_directed_lines(v6, v8) | ~ unequally_directed_lines(v6, v7) | left_convergent_lines(v6, v8) | left_convergent_lines(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ unequally_directed_lines(v6, v8) | unequally_directed_opposite_lines(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ unequally_directed_opposite_lines(v6, v7) | unequally_directed_lines(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ divides_points(v8, v6, v7) | left_apart_point(v7, v8) | left_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ divides_points(v8, v6, v7) | left_apart_point(v7, v8) | right_apart_point(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ divides_points(v8, v6, v7) | left_apart_point(v6, v8) | right_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ divides_points(v8, v6, v7) | right_apart_point(v7, v8) | right_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ left_apart_point(v7, v8) | ~ right_apart_point(v6, v8) | divides_points(v8, v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ left_apart_point(v6, v8) | ~ right_apart_point(v7, v8) | divides_points(v8, v6, v7)) & ? [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | unequally_directed_lines(v6, v8) | unequally_directed_lines(v6, v7)) & ? [v6] : ! [v7] : ! [v8] : ( ~ distinct_lines(v7, v8) | distinct_lines(v8, v6) | distinct_lines(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ distinct_points(v7, v8) | distinct_points(v8, v6) | distinct_points(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ left_convergent_lines(v7, v8) | left_convergent_lines(v7, v6) | unequally_directed_lines(v8, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ left_apart_point(v7, v8) | distinct_points(v7, v6) | left_apart_point(v6, v8)) & ? [v6] : ! [v7] : ! [v8] : ( ~ unequally_directed_lines(v7, v8) | unequally_directed_lines(v8, v6) | unequally_directed_lines(v7, v6)) & ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ line(v6) | line(v7)) & ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ distinct_lines(v6, v7)) & ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | unequally_directed_lines(v6, v7)) & ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | unequally_directed_opposite_lines(v6, v7)) & ! [v6] : ! [v7] : ( ~ apart_point_and_line(v6, v7) | left_apart_point(v6, v7) | right_apart_point(v6, v7)) & ! [v6] : ! [v7] : ( ~ equally_directed_opposite_lines(v6, v7) | ~ unequally_directed_opposite_lines(v6, v7)) & ! [v6] : ! [v7] : ( ~ equally_directed_lines(v6, v7) | ~ unequally_directed_lines(v6, v7)) & ! [v6] : ! [v7] : ~ left_convergent_lines(v6, v7) & ! [v6] : ! [v7] : ( ~ left_apart_point(v6, v7) | apart_point_and_line(v6, v7)) & ! [v6] : ! [v7] : ~ left_apart_point(v6, v7) & ! [v6] : ! [v7] : ( ~ right_apart_point(v6, v7) | apart_point_and_line(v6, v7)) & ! [v6] : ! [v7] : ( ~ unequally_directed_lines(v6, v7) | ~ unequally_directed_opposite_lines(v6, v7) | convergent_lines(v6, v7)) & ! [v6] : ~ distinct_lines(v6, v6) & ! [v6] : ~ distinct_points(v6, v6) & ? [v6] : ? [v7] : (equally_directed_opposite_lines(v6, v7) | unequally_directed_opposite_lines(v6, v7)) & ? [v6] : ? [v7] : (equally_directed_lines(v6, v7) | unequally_directed_lines(v6, v7)) & ? [v6] : equally_directed_lines(v6, v6))
% 4.50/1.71 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 4.50/1.71 | (1) left_apart_point(all_0_2_2, all_0_0_0) & left_apart_point(all_0_3_3, all_0_1_1) & left_apart_point(all_0_5_5, all_0_0_0) & left_apart_point(all_0_5_5, all_0_1_1) & right_apart_point(all_0_2_2, all_0_1_1) & right_apart_point(all_0_3_3, all_0_0_0) & right_apart_point(all_0_4_4, all_0_0_0) & right_apart_point(all_0_4_4, all_0_1_1) & ~ convergent_lines(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] : ( ~ (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)
% 4.50/1.73 |
% 4.50/1.73 | Applying alpha-rule on (1) yields:
% 4.50/1.73 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 4.50/1.73 | (3) ? [v0] : ? [v1] : (equally_directed_opposite_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1))
% 4.50/1.73 | (4) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.50/1.73 | (5) ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1)
% 4.50/1.73 | (6) ! [v0] : ! [v1] : ( ~ right_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.50/1.73 | (7) left_apart_point(all_0_2_2, all_0_0_0)
% 4.50/1.73 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2))
% 4.50/1.73 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | ~ right_apart_point(v0, v2) | divides_points(v2, v0, v1))
% 4.50/1.73 | (10) ! [v0] : ! [v1] : ( ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v1) | right_apart_point(v0, v1))
% 4.50/1.73 | (11) ! [v0] : ~ distinct_lines(v0, v0)
% 4.50/1.73 | (12) right_apart_point(all_0_3_3, all_0_0_0)
% 4.50/1.73 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2))
% 4.50/1.73 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2))
% 4.50/1.73 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2))
% 4.50/1.73 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | equally_directed_lines(v0, v3))
% 4.50/1.73 | (17) right_apart_point(all_0_4_4, all_0_0_0)
% 4.50/1.74 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2))
% 4.50/1.74 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3))
% 4.50/1.74 | (20) left_apart_point(all_0_5_5, all_0_1_1)
% 4.50/1.74 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 4.50/1.74 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_apart_point(v0, v1) | left_apart_point(v0, v2))
% 4.50/1.74 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | right_apart_point(v0, v1))
% 4.50/1.74 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2))
% 4.50/1.74 | (25) ! [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))
% 4.50/1.74 | (26) ? [v0] : equally_directed_lines(v0, v0)
% 4.50/1.74 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 4.50/1.74 | (28) right_apart_point(all_0_4_4, all_0_1_1)
% 4.50/1.74 | (29) ! [v0] : ! [v1] : ( ~ unequally_directed_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1) | convergent_lines(v0, v1))
% 4.50/1.74 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v0, v2) | right_apart_point(v0, v2))
% 4.50/1.74 | (31) ! [v0] : ! [v1] : ~ left_apart_point(v0, v1)
% 4.50/1.74 | (32) ? [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1))
% 4.50/1.74 | (33) ~ convergent_lines(all_0_1_1, all_0_0_0)
% 4.50/1.74 | (34) ! [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))
% 4.50/1.74 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | right_apart_point(v1, v2))
% 4.50/1.74 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3))
% 4.50/1.74 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v0, v2) | ~ right_apart_point(v1, v2) | divides_points(v2, v0, v1))
% 4.50/1.74 | (38) ! [v0] : ~ distinct_points(v0, v0)
% 4.50/1.74 | (39) ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0))
% 4.50/1.74 | (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, v2) | unequally_directed_lines(v0, v4))
% 4.50/1.74 | (41) ! [v0] : ! [v1] : ( ~ equally_directed_opposite_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1))
% 4.50/1.74 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1))
% 4.50/1.74 | (43) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 4.50/1.74 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2))
% 4.50/1.75 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v1, v0))
% 4.50/1.75 | (46) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1))
% 4.50/1.75 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3))
% 4.50/1.75 | (48) ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2))
% 4.50/1.75 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v2, v0))
% 4.50/1.75 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_opposite_lines(v0, v1) | unequally_directed_lines(v0, v2))
% 4.50/1.75 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | unequally_directed_opposite_lines(v0, v1))
% 4.50/1.75 | (52) left_apart_point(all_0_3_3, all_0_1_1)
% 4.50/1.75 | (53) ! [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)))
% 4.50/1.75 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_convergent_lines(v0, v1) | left_convergent_lines(v0, v2))
% 4.50/1.75 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2) | right_convergent_lines(v0, v1))
% 4.50/1.75 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2))
% 4.50/1.75 | (57) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1))
% 4.50/1.75 | (58) ! [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))
% 4.82/1.75 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1))
% 4.82/1.75 | (60) right_apart_point(all_0_2_2, all_0_1_1)
% 4.82/1.75 | (61) ! [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)))
% 4.82/1.75 | (62) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1))
% 4.82/1.75 | (63) ? [v0] : ? [v1] : (equally_directed_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.82/1.75 | (64) ! [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))
% 4.82/1.75 | (65) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 4.82/1.76 | (66) ! [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))
% 4.82/1.76 | (67) ! [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))
% 4.82/1.76 | (68) ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0))
% 4.82/1.76 | (69) left_apart_point(all_0_5_5, all_0_0_0)
% 4.82/1.76 | (70) ! [v0] : ! [v1] : ( ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.82/1.76 | (71) ! [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)))
% 4.82/1.76 | (72) ! [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)))
% 4.82/1.76 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2))
% 4.82/1.76 | (74) ! [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))
% 4.82/1.76 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 4.82/1.76 | (76) ! [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)))
% 4.82/1.76 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2))
% 4.82/1.76 | (78) ! [v0] : ! [v1] : ( ~ equally_directed_lines(v0, v1) | ~ unequally_directed_lines(v0, v1))
% 4.82/1.76 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2))
% 4.82/1.76 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | right_apart_point(v1, v2) | right_apart_point(v0, v2))
% 4.82/1.76 | (81) ! [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))
% 4.82/1.76 |
% 4.82/1.76 | Instantiating formula (31) with all_0_1_1, all_0_5_5 and discharging atoms left_apart_point(all_0_5_5, all_0_1_1), yields:
% 4.82/1.76 | (82) $false
% 4.82/1.76 |
% 4.82/1.76 |-The branch is then unsatisfiable
% 4.82/1.76 % SZS output end Proof for theBenchmark
% 4.82/1.76
% 4.82/1.76 1117ms
%------------------------------------------------------------------------------