TSTP Solution File: GEO242+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO242+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 03:49:07 EDT 2022
% Result : Theorem 2.81s 1.34s
% Output : Proof 4.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO242+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n018.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 00:02:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.47/0.57 ____ _
% 0.47/0.57 ___ / __ \_____(_)___ ________ __________
% 0.47/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.57
% 0.47/0.57 A Theorem Prover for First-Order Logic
% 0.47/0.57 (ePrincess v.1.0)
% 0.47/0.57
% 0.47/0.57 (c) Philipp Rümmer, 2009-2015
% 0.47/0.57 (c) Peter Backeman, 2014-2015
% 0.47/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.57 Bug reports to peter@backeman.se
% 0.47/0.57
% 0.47/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.57
% 0.47/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.47/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/0.96 Prover 0: Preprocessing ...
% 2.34/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.62/1.25 Prover 0: Constructing countermodel ...
% 2.81/1.33 Prover 0: proved (709ms)
% 2.81/1.34
% 2.81/1.34 No countermodel exists, formula is valid
% 2.81/1.34 % SZS status Theorem for theBenchmark
% 2.81/1.34
% 2.81/1.34 Generating proof ... Warning: ignoring some quantifiers
% 4.16/1.59 found it (size 4)
% 4.16/1.59
% 4.16/1.59 % SZS output start Proof for theBenchmark
% 4.16/1.59 Assumed formulas after preprocessing and simplification:
% 4.16/1.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (line_connecting(v0, v1) = v3 & reverse_line(v3) = v4 & reverse_line(v2) = v5 & left_convergent_lines(v2, v4) & distinct_points(v0, v1) & ~ left_apart_point(v1, v5) & ~ apart_point_and_line(v0, v2) & ! [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] : ( ~ (line_connecting(v7, v8) = v10) | ~ (reverse_line(v6) = v9) | ~ distinct_points(v7, v8) | before_on_line(v6, v7, v8) | unequally_directed_lines(v6, v10) | left_apart_point(v8, v9) | left_apart_point(v8, v6) | left_apart_point(v7, v9) | left_apart_point(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v7, v8) = v10) | ~ (reverse_line(v6) = v9) | ~ before_on_line(v6, v7, v8) | ~ unequally_directed_lines(v6, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v7, v8) = v10) | ~ (reverse_line(v6) = v9) | ~ before_on_line(v6, v7, v8) | ~ left_apart_point(v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v7, v8) = v10) | ~ (reverse_line(v6) = v9) | ~ before_on_line(v6, v7, v8) | ~ left_apart_point(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v7, v8) = v10) | ~ (reverse_line(v6) = v9) | ~ before_on_line(v6, v7, v8) | ~ left_apart_point(v7, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v7, v8) = v10) | ~ (reverse_line(v6) = v9) | ~ before_on_line(v6, v7, v8) | ~ left_apart_point(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v7, v8) = v10) | ~ (reverse_line(v6) = v9) | ~ before_on_line(v6, v7, v8) | distinct_points(v7, 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(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) | ~ divides_points(v8, v6, v7) | left_apart_point(v7, v9) | left_apart_point(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ divides_points(v8, v6, v7) | left_apart_point(v7, v9) | left_apart_point(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ divides_points(v8, v6, v7) | left_apart_point(v7, v8) | left_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ divides_points(v8, v6, v7) | left_apart_point(v6, v9) | left_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ unequally_directed_lines(v7, v8) | ~ left_apart_point(v6, v7) | distinct_lines(v7, v8) | left_apart_point(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ left_apart_point(v7, v9) | ~ left_apart_point(v6, v8) | divides_points(v8, v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ left_apart_point(v7, v8) | ~ left_apart_point(v6, v9) | divides_points(v8, v6, v7)) & ! [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) | ~ unequally_directed_lines(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ~ apart_point_and_line(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ~ point(v7) | ~ line(v6) | 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) | ~ unequally_directed_lines(v6, v7) | ~ apart_point_and_line(v8, v7) | ? [v9] : (reverse_line(v7) = v9 & ~ unequally_directed_lines(v6, v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ unequally_directed_lines(v6, v7) | ~ apart_point_and_line(v8, v6) | ? [v9] : (reverse_line(v7) = v9 & ~ unequally_directed_lines(v6, v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v7, v6) = v8) | ? [v9] : ? [v10] : (line_connecting(v6, v7) = v9 & reverse_line(v8) = v10 & ~ unequally_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) | ? [v9] : ? [v10] : (line_connecting(v7, v6) = v9 & reverse_line(v9) = v10 & ~ unequally_directed_lines(v8, v10))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ left_convergent_lines(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ line(v7) | ~ line(v6) | unequally_directed_lines(v6, v8) | unequally_directed_lines(v6, v7)) & ! [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_lines(v6, v7) | convergent_lines(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ convergent_lines(v6, v7) | unequally_directed_lines(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ convergent_lines(v6, v7) | unequally_directed_lines(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ left_apart_point(v6, v8) | apart_point_and_line(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ left_apart_point(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ left_apart_point(v6, v7) | apart_point_and_line(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ apart_point_and_line(v6, v7) | left_apart_point(v6, v8) | left_apart_point(v6, v7)) & ? [v6] : ! [v7] : ! [v8] : ( ~ left_convergent_lines(v7, v8) | left_convergent_lines(v7, v6) | unequally_directed_lines(v8, v6)) & ? [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] : ( ~ unequally_directed_lines(v7, v8) | unequally_directed_lines(v8, v6) | unequally_directed_lines(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ left_apart_point(v7, v8) | distinct_points(v7, v6) | left_apart_point(v6, v8)) & ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ line(v6) | line(v7)) & ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ distinct_lines(v6, v7)) & ! [v6] : ! [v7] : ~ left_convergent_lines(v6, v7) & ! [v6] : ! [v7] : ~ left_apart_point(v6, v7) & ! [v6] : ~ distinct_lines(v6, v6) & ! [v6] : ~ distinct_points(v6, v6) & ! [v6] : ~ unequally_directed_lines(v6, v6))
% 4.16/1.65 | 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:
% 4.16/1.65 | (1) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & reverse_line(all_0_2_2) = all_0_1_1 & reverse_line(all_0_3_3) = all_0_0_0 & left_convergent_lines(all_0_3_3, all_0_1_1) & distinct_points(all_0_5_5, all_0_4_4) & ~ left_apart_point(all_0_4_4, all_0_0_0) & ~ apart_point_and_line(all_0_5_5, all_0_3_3) & ! [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)
% 4.55/1.68 |
% 4.55/1.68 | Applying alpha-rule on (1) yields:
% 4.55/1.68 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3))
% 4.55/1.68 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.55/1.68 | (4) ! [v0] : ~ unequally_directed_lines(v0, v0)
% 4.55/1.68 | (5) ! [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))
% 4.55/1.68 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2))
% 4.55/1.68 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v2) | left_apart_point(v0, v1))
% 4.55/1.68 | (8) ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0))
% 4.55/1.68 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & ~ unequally_directed_lines(v2, v4)))
% 4.55/1.68 | (10) ! [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)))
% 4.55/1.68 | (11) ! [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))
% 4.55/1.68 | (12) ! [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))
% 4.55/1.68 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2))
% 4.55/1.68 | (14) ! [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))
% 4.55/1.69 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2))
% 4.55/1.69 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2))
% 4.55/1.69 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v1, v2))
% 4.55/1.69 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ line(v1) | ~ line(v0) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1))
% 4.55/1.69 | (19) ! [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))
% 4.55/1.69 | (20) ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1)
% 4.55/1.69 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3))
% 4.55/1.69 | (22) ! [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))
% 4.55/1.69 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2))
% 4.55/1.69 | (24) ! [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))
% 4.55/1.69 | (25) ~ apart_point_and_line(all_0_5_5, all_0_3_3)
% 4.55/1.69 | (26) ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0))
% 4.55/1.69 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2))
% 4.55/1.69 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v2))
% 4.55/1.69 | (29) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 4.55/1.69 | (30) ! [v0] : ~ distinct_lines(v0, v0)
% 4.55/1.69 | (31) left_convergent_lines(all_0_3_3, all_0_1_1)
% 4.55/1.69 | (32) ! [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))
% 4.55/1.69 | (33) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1))
% 4.55/1.69 | (34) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1))
% 4.55/1.69 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1) | convergent_lines(v0, v1))
% 4.55/1.69 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 4.55/1.69 | (37) ! [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)))
% 4.55/1.69 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v1, v2) | ~ left_apart_point(v0, v3) | divides_points(v2, v0, v1))
% 4.55/1.70 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v0, v3))
% 4.55/1.70 | (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, v2))
% 4.55/1.70 | (41) ! [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))
% 4.55/1.70 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 4.55/1.70 | (43) ! [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))
% 4.55/1.70 | (44) ~ left_apart_point(all_0_4_4, all_0_0_0)
% 4.55/1.70 | (45) ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2))
% 4.55/1.70 | (46) ! [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))
% 4.55/1.70 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2))
% 4.55/1.70 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ point(v1) | ~ line(v0) | line(v2))
% 4.55/1.70 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3))
% 4.55/1.70 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2))
% 4.55/1.70 | (51) ! [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)))
% 4.55/1.70 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | apart_point_and_line(v0, v1))
% 4.55/1.70 | (53) ! [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))
% 4.55/1.70 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v0, v3) | left_apart_point(v0, v2))
% 4.55/1.70 | (55) distinct_points(all_0_5_5, all_0_4_4)
% 4.55/1.70 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v1, v3) | ~ left_apart_point(v0, v2) | divides_points(v2, v0, v1))
% 4.55/1.70 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2))
% 4.55/1.70 | (58) ! [v0] : ! [v1] : ~ left_apart_point(v0, v1)
% 4.55/1.70 | (59) ! [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))
% 4.55/1.70 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 4.55/1.70 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 4.55/1.70 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ unequally_directed_lines(v2, v1))
% 4.55/1.70 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2))
% 4.55/1.70 | (64) reverse_line(all_0_2_2) = all_0_1_1
% 4.55/1.70 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & ~ unequally_directed_lines(v3, v4)))
% 4.55/1.70 | (66) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 4.55/1.70 | (67) ! [v0] : ~ distinct_points(v0, v0)
% 4.55/1.70 | (68) reverse_line(all_0_3_3) = all_0_0_0
% 4.55/1.71 | (69) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 4.55/1.71 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1))
% 4.55/1.71 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.55/1.71 |
% 4.55/1.71 | Instantiating formula (20) with all_0_1_1, all_0_3_3 and discharging atoms left_convergent_lines(all_0_3_3, all_0_1_1), yields:
% 4.55/1.71 | (72) $false
% 4.55/1.71 |
% 4.55/1.71 |-The branch is then unsatisfiable
% 4.55/1.71 % SZS output end Proof for theBenchmark
% 4.55/1.71
% 4.55/1.71 1125ms
%------------------------------------------------------------------------------