TSTP Solution File: GEO264+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO264+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 03:49:20 EDT 2022
% Result : Theorem 2.85s 1.35s
% Output : Proof 4.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO264+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 11:15:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.58 ____ _
% 0.57/0.58 ___ / __ \_____(_)___ ________ __________
% 0.57/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.58
% 0.57/0.58 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/0.97 Prover 0: Preprocessing ...
% 2.57/1.23 Prover 0: Warning: ignoring some quantifiers
% 2.57/1.26 Prover 0: Constructing countermodel ...
% 2.85/1.35 Prover 0: proved (715ms)
% 2.85/1.35
% 2.85/1.35 No countermodel exists, formula is valid
% 2.85/1.35 % SZS status Theorem for theBenchmark
% 2.85/1.35
% 2.85/1.35 Generating proof ... Warning: ignoring some quantifiers
% 3.81/1.61 found it (size 4)
% 3.81/1.61
% 3.81/1.61 % SZS output start Proof for theBenchmark
% 3.81/1.61 Assumed formulas after preprocessing and simplification:
% 3.81/1.61 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (line_connecting(v2, v0) = v7 & line_connecting(v1, v2) = v5 & line_connecting(v0, v1) = v4 & reverse_line(v7) = v8 & reverse_line(v5) = v6 & left_apart_point(v3, v8) & left_apart_point(v3, v6) & left_apart_point(v2, v4) & ~ left_apart_point(v3, v4) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (reverse_line(v12) = v14) | ~ (reverse_line(v11) = v13) | ~ distinct_lines(v11, v12) | ~ distinct_points(v9, v10) | left_apart_point(v10, v14) | left_apart_point(v10, v13) | left_apart_point(v10, v12) | left_apart_point(v10, v11) | left_apart_point(v9, v14) | left_apart_point(v9, v13) | left_apart_point(v9, v12) | left_apart_point(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (line_connecting(v10, v11) = v13) | ~ (reverse_line(v9) = v12) | ~ distinct_points(v10, v11) | before_on_line(v9, v10, v11) | unequally_directed_lines(v9, v13) | left_apart_point(v11, v12) | left_apart_point(v11, v9) | left_apart_point(v10, v12) | left_apart_point(v10, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (line_connecting(v10, v11) = v13) | ~ (reverse_line(v9) = v12) | ~ before_on_line(v9, v10, v11) | ~ unequally_directed_lines(v9, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (line_connecting(v10, v11) = v13) | ~ (reverse_line(v9) = v12) | ~ before_on_line(v9, v10, v11) | ~ left_apart_point(v11, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (line_connecting(v10, v11) = v13) | ~ (reverse_line(v9) = v12) | ~ before_on_line(v9, v10, v11) | ~ left_apart_point(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (line_connecting(v10, v11) = v13) | ~ (reverse_line(v9) = v12) | ~ before_on_line(v9, v10, v11) | ~ left_apart_point(v10, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (line_connecting(v10, v11) = v13) | ~ (reverse_line(v9) = v12) | ~ before_on_line(v9, v10, v11) | ~ left_apart_point(v10, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (line_connecting(v10, v11) = v13) | ~ (reverse_line(v9) = v12) | ~ before_on_line(v9, v10, v11) | distinct_points(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (reverse_line(v11) = v13) | ~ (reverse_line(v10) = v12) | ~ unequally_directed_lines(v9, v12) | ~ unequally_directed_lines(v9, v10) | unequally_directed_lines(v10, v13) | unequally_directed_lines(v9, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (reverse_line(v11) = v13) | ~ (reverse_line(v10) = v12) | ~ unequally_directed_lines(v9, v12) | ~ unequally_directed_lines(v9, v10) | unequally_directed_lines(v10, v13) | unequally_directed_lines(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (reverse_line(v11) = v13) | ~ (reverse_line(v10) = v12) | ~ unequally_directed_lines(v9, v12) | ~ unequally_directed_lines(v9, v10) | unequally_directed_lines(v10, v11) | unequally_directed_lines(v9, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (reverse_line(v11) = v13) | ~ (reverse_line(v10) = v12) | ~ unequally_directed_lines(v9, v12) | ~ unequally_directed_lines(v9, v10) | unequally_directed_lines(v10, v11) | unequally_directed_lines(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (parallel_through_point(v12, v11) = v10) | ~ (parallel_through_point(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (intersection_point(v12, v11) = v10) | ~ (intersection_point(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (line_connecting(v12, v11) = v10) | ~ (line_connecting(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v9, v10) = v12) | ~ distinct_points(v9, v10) | ~ left_apart_point(v9, v11) | left_convergent_lines(v12, v11) | left_apart_point(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (reverse_line(v11) = v12) | ~ divides_points(v11, v9, v10) | left_apart_point(v10, v12) | left_apart_point(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (reverse_line(v11) = v12) | ~ divides_points(v11, v9, v10) | left_apart_point(v10, v12) | left_apart_point(v9, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (reverse_line(v11) = v12) | ~ divides_points(v11, v9, v10) | left_apart_point(v10, v11) | left_apart_point(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (reverse_line(v11) = v12) | ~ divides_points(v11, v9, v10) | left_apart_point(v9, v12) | left_apart_point(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (reverse_line(v11) = v12) | ~ unequally_directed_lines(v10, v11) | ~ left_apart_point(v9, v10) | distinct_lines(v10, v11) | left_apart_point(v9, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (reverse_line(v11) = v12) | ~ left_apart_point(v10, v12) | ~ left_apart_point(v9, v11) | divides_points(v11, v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (reverse_line(v11) = v12) | ~ left_apart_point(v10, v11) | ~ left_apart_point(v9, v12) | divides_points(v11, v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ between_on_line(v9, v10, v11, v12) | before_on_line(v9, v12, v11) | before_on_line(v9, v11, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ between_on_line(v9, v10, v11, v12) | before_on_line(v9, v12, v11) | before_on_line(v9, v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ between_on_line(v9, v10, v11, v12) | before_on_line(v9, v11, v12) | before_on_line(v9, v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ between_on_line(v9, v10, v11, v12) | before_on_line(v9, v11, v10) | before_on_line(v9, v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ before_on_line(v9, v12, v11) | ~ before_on_line(v9, v11, v10) | between_on_line(v9, v10, v11, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ before_on_line(v9, v11, v12) | ~ before_on_line(v9, v10, v11) | between_on_line(v9, v10, v11, v12)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (reverse_line(v11) = v10) | ~ (reverse_line(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (parallel_through_point(v10, v9) = v11) | ~ unequally_directed_lines(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (parallel_through_point(v10, v9) = v11) | ~ apart_point_and_line(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (parallel_through_point(v9, v10) = v11) | ~ point(v10) | ~ line(v9) | line(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection_point(v9, v10) = v11) | ~ line(v10) | ~ line(v9) | ~ unequally_directed_lines(v9, v10) | point(v11) | ? [v12] : (reverse_line(v10) = v12 & ~ unequally_directed_lines(v9, v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection_point(v9, v10) = v11) | ~ unequally_directed_lines(v9, v10) | ~ apart_point_and_line(v11, v10) | ? [v12] : (reverse_line(v10) = v12 & ~ unequally_directed_lines(v9, v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection_point(v9, v10) = v11) | ~ unequally_directed_lines(v9, v10) | ~ apart_point_and_line(v11, v9) | ? [v12] : (reverse_line(v10) = v12 & ~ unequally_directed_lines(v9, v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v10, v9) = v11) | ? [v12] : ? [v13] : (line_connecting(v9, v10) = v12 & reverse_line(v11) = v13 & ~ unequally_directed_lines(v12, v13))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v9, v10) = v11) | ~ point(v10) | ~ point(v9) | ~ distinct_points(v9, v10) | line(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v9, v10) = v11) | ~ distinct_points(v9, v10) | ~ apart_point_and_line(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v9, v10) = v11) | ~ distinct_points(v9, v10) | ~ apart_point_and_line(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v9, v10) = v11) | ? [v12] : ? [v13] : (line_connecting(v10, v9) = v12 & reverse_line(v12) = v13 & ~ unequally_directed_lines(v11, v13))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ left_convergent_lines(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ line(v10) | ~ line(v9) | unequally_directed_lines(v9, v11) | unequally_directed_lines(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ unequally_directed_lines(v9, v11) | ~ unequally_directed_lines(v9, v10) | left_convergent_lines(v9, v11) | left_convergent_lines(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ unequally_directed_lines(v9, v11) | ~ unequally_directed_lines(v9, v10) | convergent_lines(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ convergent_lines(v9, v10) | unequally_directed_lines(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ convergent_lines(v9, v10) | unequally_directed_lines(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ left_apart_point(v9, v11) | apart_point_and_line(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ left_apart_point(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ left_apart_point(v9, v10) | apart_point_and_line(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v10) = v11) | ~ apart_point_and_line(v9, v10) | left_apart_point(v9, v11) | left_apart_point(v9, v10)) & ? [v9] : ! [v10] : ! [v11] : ( ~ left_convergent_lines(v10, v11) | left_convergent_lines(v10, v9) | unequally_directed_lines(v11, v9)) & ? [v9] : ! [v10] : ! [v11] : ( ~ distinct_lines(v10, v11) | distinct_lines(v11, v9) | distinct_lines(v10, v9)) & ? [v9] : ! [v10] : ! [v11] : ( ~ distinct_points(v10, v11) | distinct_points(v11, v9) | distinct_points(v10, v9)) & ? [v9] : ! [v10] : ! [v11] : ( ~ unequally_directed_lines(v10, v11) | unequally_directed_lines(v11, v9) | unequally_directed_lines(v10, v9)) & ? [v9] : ! [v10] : ! [v11] : ( ~ left_apart_point(v10, v11) | distinct_points(v10, v9) | left_apart_point(v9, v11)) & ! [v9] : ! [v10] : ( ~ (reverse_line(v9) = v10) | ~ line(v9) | line(v10)) & ! [v9] : ! [v10] : ( ~ (reverse_line(v9) = v10) | ~ distinct_lines(v9, v10)) & ! [v9] : ! [v10] : ~ left_convergent_lines(v9, v10) & ! [v9] : ! [v10] : ~ left_apart_point(v9, v10) & ! [v9] : ~ distinct_lines(v9, v9) & ! [v9] : ~ distinct_points(v9, v9) & ! [v9] : ~ unequally_directed_lines(v9, v9))
% 4.21/1.67 | 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, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 4.21/1.67 | (1) line_connecting(all_0_6_6, all_0_8_8) = all_0_1_1 & line_connecting(all_0_7_7, all_0_6_6) = all_0_3_3 & line_connecting(all_0_8_8, all_0_7_7) = all_0_4_4 & reverse_line(all_0_1_1) = all_0_0_0 & reverse_line(all_0_3_3) = all_0_2_2 & left_apart_point(all_0_5_5, all_0_0_0) & left_apart_point(all_0_5_5, all_0_2_2) & left_apart_point(all_0_6_6, all_0_4_4) & ~ left_apart_point(all_0_5_5, all_0_4_4) & ! [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)
% 4.21/1.70 |
% 4.21/1.70 | Applying alpha-rule on (1) yields:
% 4.21/1.70 | (2) ! [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))
% 4.21/1.70 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3))
% 4.21/1.70 | (4) reverse_line(all_0_1_1) = all_0_0_0
% 4.21/1.70 | (5) ! [v0] : ~ unequally_directed_lines(v0, v0)
% 4.21/1.70 | (6) ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0))
% 4.21/1.70 | (7) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1))
% 4.21/1.70 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2))
% 4.21/1.70 | (9) ! [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))
% 4.58/1.70 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ line(v1) | ~ line(v0) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1))
% 4.58/1.70 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2))
% 4.58/1.70 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2))
% 4.58/1.70 | (13) ! [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)))
% 4.58/1.70 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v1, v2))
% 4.58/1.70 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | apart_point_and_line(v0, v1))
% 4.58/1.70 | (16) ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1)
% 4.58/1.70 | (17) line_connecting(all_0_6_6, all_0_8_8) = all_0_1_1
% 4.58/1.70 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3))
% 4.58/1.70 | (19) ! [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))
% 4.58/1.70 | (20) line_connecting(all_0_7_7, all_0_6_6) = all_0_3_3
% 4.58/1.70 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ distinct_points(v0, v1) | ~ left_apart_point(v0, v2) | left_convergent_lines(v3, v2) | left_apart_point(v1, v2))
% 4.58/1.70 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ point(v1) | ~ line(v0) | line(v2))
% 4.58/1.70 | (23) ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0))
% 4.58/1.70 | (24) left_apart_point(all_0_5_5, all_0_2_2)
% 4.58/1.70 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v1, v2) | ~ left_apart_point(v0, v3) | divides_points(v2, v0, v1))
% 4.58/1.71 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v0, v3) | left_apart_point(v0, v2))
% 4.58/1.71 | (27) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 4.58/1.71 | (28) ! [v0] : ~ distinct_lines(v0, v0)
% 4.58/1.71 | (29) ! [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)))
% 4.58/1.71 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ unequally_directed_lines(v2, v1))
% 4.58/1.71 | (31) left_apart_point(all_0_6_6, all_0_4_4)
% 4.58/1.71 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | ~ left_apart_point(v2, v3))
% 4.58/1.71 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2))
% 4.58/1.71 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.58/1.71 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & ~ unequally_directed_lines(v3, v4)))
% 4.58/1.71 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v1, v3) | ~ left_apart_point(v0, v2) | divides_points(v2, v0, v1))
% 4.58/1.71 | (37) ! [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))
% 4.58/1.71 | (38) ! [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))
% 4.58/1.71 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v2) | left_apart_point(v0, v1))
% 4.58/1.71 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 4.58/1.71 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v4) | ~ (reverse_line(v0) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2))
% 4.58/1.71 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 4.58/1.71 | (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, v3))
% 4.58/1.71 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v0, v3))
% 4.58/1.71 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2))
% 4.58/1.71 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & ~ unequally_directed_lines(v2, v4)))
% 4.58/1.72 | (47) ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2))
% 4.58/1.72 | (48) ~ left_apart_point(all_0_5_5, all_0_4_4)
% 4.58/1.72 | (49) ! [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))
% 4.58/1.72 | (50) ! [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))
% 4.58/1.72 | (51) ! [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))
% 4.58/1.72 | (52) line_connecting(all_0_8_8, all_0_7_7) = all_0_4_4
% 4.58/1.72 | (53) left_apart_point(all_0_5_5, all_0_0_0)
% 4.58/1.72 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3))
% 4.58/1.72 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2))
% 4.58/1.72 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1) | convergent_lines(v0, v1))
% 4.58/1.72 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2))
% 4.58/1.72 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2))
% 4.58/1.72 | (59) ! [v0] : ! [v1] : ~ left_apart_point(v0, v1)
% 4.58/1.72 | (60) ! [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))
% 4.58/1.72 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 4.58/1.72 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 4.58/1.72 | (63) ! [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))
% 4.58/1.72 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v2))
% 4.58/1.72 | (65) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 4.58/1.72 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2))
% 4.58/1.72 | (67) ! [v0] : ~ distinct_points(v0, v0)
% 4.58/1.72 | (68) reverse_line(all_0_3_3) = all_0_2_2
% 4.58/1.72 | (69) ! [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))
% 4.58/1.72 | (70) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1))
% 4.58/1.72 | (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)))
% 4.58/1.72 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.58/1.72 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1))
% 4.58/1.72 |
% 4.58/1.73 | Instantiating formula (59) with all_0_4_4, all_0_6_6 and discharging atoms left_apart_point(all_0_6_6, all_0_4_4), yields:
% 4.58/1.73 | (74) $false
% 4.58/1.73 |
% 4.58/1.73 |-The branch is then unsatisfiable
% 4.58/1.73 % SZS output end Proof for theBenchmark
% 4.58/1.73
% 4.58/1.73 1131ms
%------------------------------------------------------------------------------