TSTP Solution File: GEO237+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% 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 03:49:04 EDT 2022
% Result : Theorem 3.16s 1.36s
% Output : Proof 4.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 14:01:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.57 ____ _
% 0.55/0.57 ___ / __ \_____(_)___ ________ __________
% 0.55/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.57
% 0.55/0.57 A Theorem Prover for First-Order Logic
% 0.55/0.57 (ePrincess v.1.0)
% 0.55/0.57
% 0.55/0.57 (c) Philipp Rümmer, 2009-2015
% 0.55/0.57 (c) Peter Backeman, 2014-2015
% 0.55/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.57 Bug reports to peter@backeman.se
% 0.55/0.57
% 0.55/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.57
% 0.55/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.60/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/0.92 Prover 0: Preprocessing ...
% 2.56/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.69/1.20 Prover 0: Constructing countermodel ...
% 3.16/1.36 Prover 0: proved (737ms)
% 3.16/1.36
% 3.16/1.36 No countermodel exists, formula is valid
% 3.16/1.36 % SZS status Theorem for theBenchmark
% 3.16/1.36
% 3.16/1.36 Generating proof ... Warning: ignoring some quantifiers
% 4.22/1.62 found it (size 8)
% 4.22/1.62
% 4.22/1.62 % SZS output start Proof for theBenchmark
% 4.22/1.62 Assumed formulas after preprocessing and simplification:
% 4.22/1.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (divides_points(v3, v0, v1) & apart_point_and_line(v2, v3) & ~ divides_points(v3, v1, v2) & ~ divides_points(v3, v0, v2) & ! [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))
% 4.63/1.68 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 4.63/1.68 | (1) divides_points(all_0_0_0, all_0_3_3, all_0_2_2) & apart_point_and_line(all_0_1_1, all_0_0_0) & ~ divides_points(all_0_0_0, all_0_2_2, all_0_1_1) & ~ divides_points(all_0_0_0, all_0_3_3, all_0_1_1) & ! [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)
% 4.88/1.70 |
% 4.88/1.70 | Applying alpha-rule on (1) yields:
% 4.88/1.70 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 4.88/1.71 | (3) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 4.88/1.71 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2))
% 4.88/1.71 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | right_apart_point(v1, v2))
% 4.88/1.71 | (6) ! [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)))
% 4.88/1.71 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v2))
% 4.88/1.71 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2))
% 4.88/1.71 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_opposite_lines(v0, v1) | unequally_directed_lines(v0, v2))
% 4.88/1.71 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | unequally_directed_opposite_lines(v0, v1))
% 4.88/1.71 | (11) ! [v0] : ! [v1] : ( ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v1) | right_apart_point(v0, v1))
% 4.88/1.71 | (12) ! [v0] : ! [v1] : ( ~ equally_directed_opposite_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1))
% 4.88/1.71 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | equally_directed_lines(v0, v3))
% 4.88/1.71 | (14) ? [v0] : ? [v1] : (equally_directed_opposite_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1))
% 4.88/1.71 | (15) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1))
% 4.88/1.71 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | ~ right_apart_point(v0, v2) | divides_points(v2, v0, v1))
% 4.88/1.71 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3))
% 4.88/1.71 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 4.88/1.71 | (19) ! [v0] : ~ distinct_lines(v0, v0)
% 4.88/1.71 | (20) divides_points(all_0_0_0, all_0_3_3, all_0_2_2)
% 4.88/1.71 | (21) ! [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))
% 4.88/1.71 | (22) ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0))
% 4.88/1.71 | (23) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.88/1.71 | (24) ! [v0] : ! [v1] : ( ~ right_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.88/1.71 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1))
% 4.88/1.71 | (26) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1))
% 4.88/1.71 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3))
% 4.88/1.71 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2))
% 4.88/1.71 | (29) ! [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))
% 4.88/1.72 | (30) ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1)
% 4.88/1.72 | (31) ~ divides_points(all_0_0_0, all_0_3_3, all_0_1_1)
% 4.88/1.72 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v2, v0))
% 4.88/1.72 | (33) ? [v0] : ? [v1] : (equally_directed_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.88/1.72 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v0, v2) | ~ right_apart_point(v1, v2) | divides_points(v2, v0, v1))
% 4.88/1.72 | (35) ! [v0] : ! [v1] : ( ~ equally_directed_lines(v0, v1) | ~ unequally_directed_lines(v0, v1))
% 4.88/1.72 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v4))
% 4.88/1.72 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2))
% 4.88/1.72 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2))
% 4.88/1.72 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2))
% 4.88/1.72 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | right_apart_point(v1, v2) | right_apart_point(v0, v2))
% 4.88/1.72 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2))
% 4.88/1.72 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v1, v0))
% 4.88/1.72 | (43) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1))
% 4.88/1.72 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2))
% 4.88/1.72 | (45) ! [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))
% 4.88/1.72 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 4.88/1.72 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 4.88/1.72 | (48) ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0))
% 4.88/1.72 | (49) ? [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1))
% 4.88/1.72 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3))
% 4.88/1.72 | (51) ! [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))
% 4.88/1.72 | (52) ! [v0] : ~ distinct_points(v0, v0)
% 4.88/1.72 | (53) ! [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))
% 4.88/1.73 | (54) ~ divides_points(all_0_0_0, all_0_2_2, all_0_1_1)
% 4.88/1.73 | (55) ! [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)))
% 4.88/1.73 | (56) ! [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)))
% 4.88/1.73 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_apart_point(v0, v1) | left_apart_point(v0, v2))
% 4.88/1.73 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | right_apart_point(v0, v1))
% 4.88/1.73 | (59) apart_point_and_line(all_0_1_1, all_0_0_0)
% 4.88/1.73 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2))
% 4.88/1.73 | (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)))
% 4.88/1.73 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v0, v2) | right_apart_point(v0, v2))
% 4.88/1.73 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2))
% 4.88/1.73 | (64) ? [v0] : equally_directed_lines(v0, v0)
% 4.88/1.73 | (65) ! [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))
% 4.88/1.73 | (66) ! [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))
% 4.88/1.73 | (67) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 4.88/1.73 | (68) ! [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)))
% 4.88/1.73 | (69) ! [v0] : ! [v1] : ~ left_apart_point(v0, v1)
% 4.88/1.73 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2))
% 4.88/1.73 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_convergent_lines(v0, v1) | left_convergent_lines(v0, v2))
% 4.88/1.73 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2) | right_convergent_lines(v0, v1))
% 4.88/1.73 | (73) ! [v0] : ! [v1] : ( ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.88/1.74 | (74) ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2))
% 4.88/1.74 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1))
% 4.88/1.74 | (76) ! [v0] : ! [v1] : ( ~ unequally_directed_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1) | convergent_lines(v0, v1))
% 4.88/1.74 |
% 4.88/1.74 | Instantiating formula (37) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms divides_points(all_0_0_0, all_0_3_3, all_0_2_2), yields:
% 4.88/1.74 | (77) left_apart_point(all_0_2_2, all_0_0_0) | left_apart_point(all_0_3_3, all_0_0_0)
% 4.88/1.74 |
% 4.88/1.74 +-Applying beta-rule and splitting (77), into two cases.
% 4.88/1.74 |-Branch one:
% 4.88/1.74 | (78) left_apart_point(all_0_2_2, all_0_0_0)
% 4.88/1.74 |
% 4.88/1.74 | Instantiating formula (69) with all_0_0_0, all_0_2_2 and discharging atoms left_apart_point(all_0_2_2, all_0_0_0), yields:
% 4.88/1.74 | (79) $false
% 4.88/1.74 |
% 4.88/1.74 |-The branch is then unsatisfiable
% 4.88/1.74 |-Branch two:
% 4.88/1.74 | (80) ~ left_apart_point(all_0_2_2, all_0_0_0)
% 4.88/1.74 | (81) left_apart_point(all_0_3_3, all_0_0_0)
% 4.88/1.74 |
% 4.88/1.74 | Instantiating formula (69) with all_0_0_0, all_0_3_3 and discharging atoms left_apart_point(all_0_3_3, all_0_0_0), yields:
% 4.88/1.74 | (79) $false
% 4.88/1.74 |
% 4.88/1.74 |-The branch is then unsatisfiable
% 4.88/1.74 % SZS output end Proof for theBenchmark
% 4.88/1.74
% 4.88/1.74 1156ms
%------------------------------------------------------------------------------