TSTP Solution File: GEO265+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 14.18s 4.06s
% Output : Proof 15.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 17 22:15:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.59
% 0.58/0.59 A Theorem Prover for First-Order Logic
% 0.58/0.59 (ePrincess v.1.0)
% 0.58/0.59
% 0.58/0.59 (c) Philipp Rümmer, 2009-2015
% 0.58/0.59 (c) Peter Backeman, 2014-2015
% 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59 Bug reports to peter@backeman.se
% 0.58/0.59
% 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59
% 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.96 Prover 0: Preprocessing ...
% 2.49/1.26 Prover 0: Warning: ignoring some quantifiers
% 2.49/1.31 Prover 0: Constructing countermodel ...
% 13.10/3.87 Prover 0: gave up
% 13.10/3.87 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 13.59/3.91 Prover 1: Preprocessing ...
% 14.18/4.04 Prover 1: Constructing countermodel ...
% 14.18/4.06 Prover 1: proved (189ms)
% 14.18/4.06
% 14.18/4.06 No countermodel exists, formula is valid
% 14.18/4.06 % SZS status Theorem for theBenchmark
% 14.18/4.06
% 14.18/4.06 Generating proof ... found it (size 18)
% 15.45/4.30
% 15.45/4.30 % SZS output start Proof for theBenchmark
% 15.45/4.30 Assumed formulas after preprocessing and simplification:
% 15.45/4.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & equally_directed_opposite_lines(v0, v1) = v3 & equally_directed_lines(v0, v2) = 0 & reverse_line(v1) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v4, v10) = v11) | ~ (left_apart_point(v4, v8) = v9) | ~ (reverse_line(v7) = v10) | ~ (reverse_line(v6) = v8) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (distinct_lines(v6, v7) = v12 & left_apart_point(v5, v10) = v18 & left_apart_point(v5, v8) = v17 & left_apart_point(v5, v7) = v16 & left_apart_point(v5, v6) = v14 & left_apart_point(v4, v7) = v15 & left_apart_point(v4, v6) = v13 & ( ~ (v12 = 0) | v18 = 0 | v17 = 0 | v16 = 0 | v15 = 0 | v14 = 0 | v13 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ~ (left_apart_point(v4, v8) = v9) | ~ (reverse_line(v6) = v8) | ? [v10] : ? [v11] : (left_apart_point(v4, v5) = v10 & unequally_directed_lines(v5, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (line_connecting(v5, v4) = v7) | ~ (line_connecting(v4, v5) = v6) | ~ (equally_directed_lines(v6, v8) = v9) | ~ (reverse_line(v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v4, v5) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = v4 | ~ (between_on_line(v9, v8, v7, v6) = v5) | ~ (between_on_line(v9, v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v8) | ~ (reverse_line(v5) = v7) | ~ (unequally_directed_lines(v4, v8) = v9) | ~ (unequally_directed_lines(v4, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (unequally_directed_lines(v5, v8) = v13 & unequally_directed_lines(v5, v6) = v12 & unequally_directed_lines(v4, v6) = v11 & unequally_directed_lines(v4, v5) = v10 & ( ~ (v10 = 0) | (v13 = 0 & v12 = 0) | (v11 = 0 & v9 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (between_on_line(v4, v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (before_on_line(v4, v7, v6) = v11 & before_on_line(v4, v6, v7) = v10 & before_on_line(v4, v6, v5) = v12 & before_on_line(v4, v5, v6) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0)) & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (line_connecting(v4, v5) = v7) | ~ (left_convergent_lines(v7, v6) = v8) | ? [v9] : ? [v10] : ? [v11] : (distinct_points(v4, v5) = v9 & left_apart_point(v5, v6) = v11 & left_apart_point(v4, v6) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (before_on_line(v8, v7, v6) = v5) | ~ (before_on_line(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (divides_points(v8, v7, v6) = v5) | ~ (divides_points(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v7) | ~ (equally_directed_lines(v4, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (before_on_line(v4, v5, v6) = v9 & distinct_points(v5, v6) = v10 & incident_point_and_line(v6, v4) = v12 & incident_point_and_line(v5, v4) = v11 & ( ~ (v9 = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & v8 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (parallel_through_point(v5, v4) = v6) | ~ (equally_directed_lines(v6, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v4, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v4, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v4, v5) = v7) | ~ (left_apart_point(v4, v6) = 0) | left_apart_point(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (divides_points(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (left_apart_point(v5, v6) = v11 & left_apart_point(v4, v6) = v8 & right_apart_point(v5, v6) = v9 & right_apart_point(v4, v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)) & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v4, v6) = v7) | ~ (left_convergent_lines(v4, v5) = 0) | unequally_directed_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v4, v6) = v7) | ~ (reverse_line(v5) = v6) | ? [v8] : ? [v9] : ? [v10] : (left_convergent_lines(v4, v5) = v10 & unequally_directed_lines(v4, v6) = v9 & unequally_directed_lines(v4, v5) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v4, v6) = v7) | ~ (reverse_line(v5) = v6) | ? [v8] : ( ~ (v8 = 0) & right_convergent_lines(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_apart_point(v4, v6) = v7) | ~ (reverse_line(v5) = v6) | ? [v8] : ( ~ (v8 = 0) & right_apart_point(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = v7) | unequally_directed_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & unequally_directed_opposite_lines(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_lines(v4, v6) = v7) | ~ (unequally_directed_lines(v4, v5) = 0) | unequally_directed_lines(v5, v6) = 0) & ! [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 | ~ (distinct_lines(v7, v6) = v5) | ~ (distinct_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (line_connecting(v7, v6) = v5) | ~ (line_connecting(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_points(v7, v6) = v5) | ~ (distinct_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (incident_point_and_line(v7, v6) = v5) | ~ (incident_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (convergent_lines(v7, v6) = v5) | ~ (convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (apart_point_and_line(v7, v6) = v5) | ~ (apart_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equally_directed_opposite_lines(v7, v6) = v5) | ~ (equally_directed_opposite_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equally_directed_lines(v7, v6) = v5) | ~ (equally_directed_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (left_convergent_lines(v7, v6) = v5) | ~ (left_convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (right_convergent_lines(v7, v6) = v5) | ~ (right_convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (left_apart_point(v7, v6) = v5) | ~ (left_apart_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (right_apart_point(v7, v6) = v5) | ~ (right_apart_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unequally_directed_lines(v7, v6) = v5) | ~ (unequally_directed_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unequally_directed_opposite_lines(v7, v6) = v5) | ~ (unequally_directed_opposite_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v4, v5) = v6) | ~ (apart_point_and_line(v6, v4) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (apart_point_and_line(v6, v5) = v11 & reverse_line(v5) = v9 & unequally_directed_lines(v4, v9) = v10 & unequally_directed_lines(v4, v5) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0) | ( ~ (v11 = 0) & ~ (v7 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (between_on_line(v4, v5, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (before_on_line(v4, v7, v6) = v10 & before_on_line(v4, v6, v7) = v9 & before_on_line(v4, v6, v5) = v11 & before_on_line(v4, v5, v6) = v8 & ((v11 = 0 & v10 = 0) | (v9 = 0 & v8 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ (equally_directed_lines(v4, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (before_on_line(v4, v5, v6) = v11 & distinct_points(v5, v6) = v8 & incident_point_and_line(v6, v4) = v10 & incident_point_and_line(v5, v4) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | v11 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v6) | ~ (apart_point_and_line(v4, v6) = v7) | ? [v8] : ? [v9] : (distinct_points(v4, v5) = v8 & apart_point_and_line(v5, v6) = v9 & ( ~ (v8 = 0) | ( ~ (v9 = 0) & ~ (v7 = 0))))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v4, v5) = v6) | ? [v7] : ? [v8] : (unequally_directed_lines(v4, v5) = v7 & unequally_directed_opposite_lines(v4, v5) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & left_apart_point(v4, v5) = v7 & right_apart_point(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equally_directed_opposite_lines(v4, v5) = v6) | unequally_directed_opposite_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equally_directed_lines(v4, v5) = v6) | unequally_directed_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (point(v6) = v5) | ~ (point(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (line(v6) = v5) | ~ (line(v6) = v4)) & ! [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) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (point(v5) = v7 & line(v6) = v9 & line(v4) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (divides_points(v6, v4, v5) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (left_apart_point(v5, v6) = v10 & left_apart_point(v4, v6) = v7 & right_apart_point(v5, v6) = v8 & right_apart_point(v4, v6) = v9 & ((v10 = 0 & v9 = 0) | (v8 = 0 & v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_convergent_lines(v4, v6) = 0) | ~ (reverse_line(v5) = v6) | right_convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_convergent_lines(v4, v6) = 0) | ~ (reverse_line(v5) = v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_apart_point(v4, v6) = 0) | ~ (reverse_line(v5) = v6) | right_apart_point(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_apart_point(v4, v6) = 0) | ~ (reverse_line(v5) = v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = 0) | unequally_directed_opposite_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (intersection_point(v4, v5) = v10 & point(v10) = v11 & line(v5) = v8 & line(v4) = v7 & unequally_directed_lines(v4, v5) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v11 = 0))) & ! [v4] : ! [v5] : (v5 = 0 | ~ (equally_directed_lines(v4, v4) = v5)) & ! [v4] : ! [v5] : ( ~ (point(v5) = 0) | ~ (point(v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (line(v7) = v8 & line_connecting(v4, v5) = v7 & distinct_points(v4, v5) = v6 & ( ~ (v6 = 0) | v8 = 0))) & ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | ~ (reverse_line(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | (unequally_directed_lines(v4, v5) = 0 & unequally_directed_opposite_lines(v4, v5) = 0)) & ! [v4] : ! [v5] : ( ~ (apart_point_and_line(v4, v5) = 0) | ? [v6] : ? [v7] : (left_apart_point(v4, v5) = v6 & right_apart_point(v4, v5) = v7 & (v7 = 0 | v6 = 0))) & ! [v4] : ! [v5] : ( ~ (equally_directed_opposite_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & unequally_directed_opposite_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (equally_directed_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & unequally_directed_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ~ (left_convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ~ (left_apart_point(v4, v5) = 0) & ! [v4] : ( ~ (line(v4) = 0) | ? [v5] : (line(v5) = 0 & reverse_line(v4) = v5)) & ! [v4] : ~ (distinct_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_points(v4, v4) = 0))
% 15.61/4.36 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 15.61/4.36 | (1) ~ (all_0_0_0 = 0) & equally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_0_0_0 & equally_directed_lines(all_0_3_3, all_0_1_1) = 0 & reverse_line(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v8 & left_apart_point(v1, v6) = v14 & left_apart_point(v1, v4) = v13 & left_apart_point(v1, v3) = v12 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v3) = v11 & left_apart_point(v0, v2) = v9 & ( ~ (v8 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : ? [v7] : (left_apart_point(v0, v1) = v6 & unequally_directed_lines(v1, v2) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (line_connecting(v1, v0) = v3) | ~ (line_connecting(v0, v1) = v2) | ~ (equally_directed_lines(v2, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v6] : ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (unequally_directed_lines(v1, v4) = v9 & unequally_directed_lines(v1, v2) = v8 & unequally_directed_lines(v0, v2) = v7 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v2, v3) = v6 & before_on_line(v0, v2, v1) = v8 & before_on_line(v0, v1, v2) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (distinct_points(v0, v1) = v5 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v1, v2) = v5 & distinct_points(v1, v2) = v6 & incident_point_and_line(v2, v0) = v8 & incident_point_and_line(v1, v0) = v7 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (parallel_through_point(v1, v0) = v2) | ~ (equally_directed_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v4 & right_apart_point(v1, v2) = v5 & right_apart_point(v0, v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ? [v5] : ? [v6] : (left_convergent_lines(v0, v1) = v6 & unequally_directed_lines(v0, v2) = v5 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) & ! [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 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | ( ~ (v7 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (before_on_line(v0, v3, v2) = v6 & before_on_line(v0, v2, v3) = v5 & before_on_line(v0, v2, v1) = v7 & before_on_line(v0, v1, v2) = v4 & ((v7 = 0 & v6 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (before_on_line(v0, v1, v2) = v7 & distinct_points(v1, v2) = v4 & incident_point_and_line(v2, v0) = v6 & incident_point_and_line(v1, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = v3) | ? [v4] : ? [v5] : (distinct_points(v0, v1) = v4 & apart_point_and_line(v1, v2) = v5 & ( ~ (v4 = 0) | ( ~ (v5 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (unequally_directed_lines(v0, v1) = v3 & unequally_directed_opposite_lines(v0, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [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) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & line(v2) = v5 & line(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (left_apart_point(v1, v2) = v6 & left_apart_point(v0, v2) = v3 & right_apart_point(v1, v2) = v4 & right_apart_point(v0, v2) = v5 & ((v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v4 & line(v0) = v3 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ~ (reverse_line(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ? [v3] : (left_apart_point(v0, v1) = v2 & right_apart_point(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0) & ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1)) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 15.61/4.37 |
% 15.61/4.37 | Applying alpha-rule on (1) yields:
% 15.61/4.37 | (2) equally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_0_0_0
% 15.61/4.37 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0)
% 15.61/4.37 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0)
% 15.61/4.37 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v1, v2) = v5 & distinct_points(v1, v2) = v6 & incident_point_and_line(v2, v0) = v8 & incident_point_and_line(v1, v0) = v7 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v4 = 0))))
% 15.61/4.37 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 15.61/4.38 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (unequally_directed_lines(v1, v4) = v9 & unequally_directed_lines(v1, v2) = v8 & unequally_directed_lines(v0, v2) = v7 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v5 = 0))))
% 15.61/4.38 | (8) ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))
% 15.61/4.38 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0))
% 15.61/4.38 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0))
% 15.61/4.38 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0))
% 15.61/4.38 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0))
% 15.61/4.38 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = v3) | ? [v4] : ? [v5] : (distinct_points(v0, v1) = v4 & apart_point_and_line(v1, v2) = v5 & ( ~ (v4 = 0) | ( ~ (v5 = 0) & ~ (v3 = 0)))))
% 15.61/4.38 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0)
% 15.61/4.38 | (15) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 15.61/4.38 | (16) ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))
% 15.61/4.38 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (parallel_through_point(v1, v0) = v2) | ~ (equally_directed_lines(v2, v1) = v3))
% 15.61/4.38 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0))
% 15.61/4.38 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & line(v2) = v5 & line(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 15.61/4.38 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0))
% 15.61/4.38 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0)
% 15.61/4.38 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0))
% 15.61/4.38 | (23) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0)
% 15.61/4.38 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 15.61/4.38 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (distinct_points(v0, v1) = v5 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))
% 15.61/4.38 | (26) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 15.61/4.38 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 15.61/4.38 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (line_connecting(v1, v0) = v3) | ~ (line_connecting(v0, v1) = v2) | ~ (equally_directed_lines(v2, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v6] : ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))
% 15.61/4.38 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 15.61/4.38 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0)
% 15.61/4.38 | (31) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0)
% 15.61/4.38 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : ? [v7] : (left_apart_point(v0, v1) = v6 & unequally_directed_lines(v1, v2) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 15.61/4.38 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 15.61/4.38 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (unequally_directed_lines(v0, v1) = v3 & unequally_directed_opposite_lines(v0, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 15.61/4.38 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | ( ~ (v7 = 0) & ~ (v3 = 0)))))
% 15.61/4.38 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (left_apart_point(v1, v2) = v6 & left_apart_point(v0, v2) = v3 & right_apart_point(v1, v2) = v4 & right_apart_point(v0, v2) = v5 & ((v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 15.61/4.38 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0))
% 15.61/4.38 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (before_on_line(v0, v3, v2) = v6 & before_on_line(v0, v2, v3) = v5 & before_on_line(v0, v2, v1) = v7 & before_on_line(v0, v1, v2) = v4 & ((v7 = 0 & v6 = 0) | (v5 = 0 & v4 = 0))))
% 15.61/4.39 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 15.61/4.39 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 15.61/4.39 | (41) ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1))
% 15.61/4.39 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v8 & left_apart_point(v1, v6) = v14 & left_apart_point(v1, v4) = v13 & left_apart_point(v1, v3) = v12 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v3) = v11 & left_apart_point(v0, v2) = v9 & ( ~ (v8 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))
% 15.61/4.39 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0)
% 15.61/4.39 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4))
% 15.61/4.39 | (45) equally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 15.61/4.39 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 15.61/4.39 | (47) ~ (all_0_0_0 = 0)
% 15.61/4.39 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v4 & line(v0) = v3 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0)))
% 15.61/4.39 | (49) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0))
% 15.61/4.39 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 15.61/4.39 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 15.61/4.39 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 15.61/4.39 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0))
% 15.61/4.39 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 15.61/4.39 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0))
% 15.61/4.39 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v2, v3) = v6 & before_on_line(v0, v2, v1) = v8 & before_on_line(v0, v1, v2) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 15.61/4.39 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 15.61/4.39 | (58) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ? [v3] : (left_apart_point(v0, v1) = v2 & right_apart_point(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 15.61/4.39 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 15.61/4.39 | (60) reverse_line(all_0_2_2) = all_0_1_1
% 15.61/4.39 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4))
% 15.61/4.39 | (62) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ~ (reverse_line(v0) = v1))
% 15.61/4.39 | (63) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 15.61/4.39 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 15.61/4.39 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0)
% 15.61/4.39 | (66) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1))
% 15.61/4.39 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0))
% 15.61/4.39 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (before_on_line(v0, v1, v2) = v7 & distinct_points(v1, v2) = v4 & incident_point_and_line(v2, v0) = v6 & incident_point_and_line(v1, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0)))
% 15.61/4.39 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 15.61/4.39 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v4 & right_apart_point(v1, v2) = v5 & right_apart_point(v0, v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 15.61/4.39 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ? [v5] : ? [v6] : (left_convergent_lines(v0, v1) = v6 & unequally_directed_lines(v0, v2) = v5 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)))
% 15.61/4.39 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 15.61/4.39 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 15.61/4.39 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4))
% 15.61/4.39 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4))
% 15.61/4.39 |
% 15.61/4.39 | Instantiating formula (43) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms equally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 15.61/4.39 | (76) all_0_0_0 = 0 | unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = 0
% 15.61/4.39 |
% 15.61/4.39 | Instantiating formula (8) with all_0_1_1, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 15.61/4.39 | (77) ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_1_1) = v0)
% 15.61/4.39 |
% 15.61/4.39 | Instantiating (77) with all_8_0_4 yields:
% 15.61/4.39 | (78) ~ (all_8_0_4 = 0) & unequally_directed_lines(all_0_3_3, all_0_1_1) = all_8_0_4
% 15.61/4.39 |
% 15.61/4.39 | Applying alpha-rule on (78) yields:
% 15.61/4.39 | (79) ~ (all_8_0_4 = 0)
% 15.61/4.39 | (80) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_8_0_4
% 15.61/4.39 |
% 15.61/4.39 +-Applying beta-rule and splitting (76), into two cases.
% 15.61/4.39 |-Branch one:
% 15.61/4.39 | (81) unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = 0
% 15.61/4.39 |
% 15.61/4.39 | Instantiating formula (74) with all_8_0_4, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms reverse_line(all_0_2_2) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = all_8_0_4, yields:
% 15.61/4.40 | (82) all_8_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = v0)
% 15.61/4.40 |
% 15.61/4.40 +-Applying beta-rule and splitting (82), into two cases.
% 15.61/4.40 |-Branch one:
% 15.61/4.40 | (83) all_8_0_4 = 0
% 15.61/4.40 |
% 15.61/4.40 | Equations (83) can reduce 79 to:
% 15.61/4.40 | (84) $false
% 15.61/4.40 |
% 15.61/4.40 |-The branch is then unsatisfiable
% 15.61/4.40 |-Branch two:
% 15.61/4.40 | (79) ~ (all_8_0_4 = 0)
% 15.61/4.40 | (86) ? [v0] : ( ~ (v0 = 0) & unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = v0)
% 15.61/4.40 |
% 15.61/4.40 | Instantiating (86) with all_25_0_5 yields:
% 15.61/4.40 | (87) ~ (all_25_0_5 = 0) & unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_25_0_5
% 15.61/4.40 |
% 15.61/4.40 | Applying alpha-rule on (87) yields:
% 15.61/4.40 | (88) ~ (all_25_0_5 = 0)
% 15.61/4.40 | (89) unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_25_0_5
% 15.61/4.40 |
% 15.61/4.40 | Instantiating formula (10) with all_0_3_3, all_0_2_2, all_25_0_5, 0 and discharging atoms unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_25_0_5, unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 15.61/4.40 | (90) all_25_0_5 = 0
% 15.61/4.40 |
% 15.61/4.40 | Equations (90) can reduce 88 to:
% 15.61/4.40 | (84) $false
% 15.61/4.40 |
% 15.61/4.40 |-The branch is then unsatisfiable
% 15.61/4.40 |-Branch two:
% 15.61/4.40 | (92) ~ (unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = 0)
% 15.61/4.40 | (93) all_0_0_0 = 0
% 15.61/4.40 |
% 15.61/4.40 | Equations (93) can reduce 47 to:
% 15.61/4.40 | (84) $false
% 15.61/4.40 |
% 15.61/4.40 |-The branch is then unsatisfiable
% 15.61/4.40 % SZS output end Proof for theBenchmark
% 15.61/4.40
% 15.61/4.40 3797ms
%------------------------------------------------------------------------------