TSTP Solution File: GEO212+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO212+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 03:48:47 EDT 2022
% Result : Theorem 6.74s 2.26s
% Output : Proof 15.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.19 % Problem : GEO212+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.20 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.41 % Computer : n019.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8042.1875MB
% 0.12/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 600
% 0.12/0.41 % DateTime : Sat Jun 18 01:48:24 EDT 2022
% 0.12/0.41 % CPUTime :
% 0.52/0.66 ____ _
% 0.52/0.66 ___ / __ \_____(_)___ ________ __________
% 0.52/0.66 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.66 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.66 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.66
% 0.52/0.66 A Theorem Prover for First-Order Logic
% 0.52/0.66 (ePrincess v.1.0)
% 0.52/0.66
% 0.52/0.66 (c) Philipp Rümmer, 2009-2015
% 0.52/0.66 (c) Peter Backeman, 2014-2015
% 0.52/0.66 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.66 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.66 Bug reports to peter@backeman.se
% 0.52/0.66
% 0.52/0.66 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.66
% 0.52/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/1.03 Prover 0: Preprocessing ...
% 2.23/1.20 Prover 0: Warning: ignoring some quantifiers
% 2.33/1.22 Prover 0: Constructing countermodel ...
% 3.94/1.65 Prover 0: gave up
% 3.94/1.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.94/1.69 Prover 1: Preprocessing ...
% 4.74/1.79 Prover 1: Constructing countermodel ...
% 4.94/1.85 Prover 1: gave up
% 4.94/1.85 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.94/1.88 Prover 2: Preprocessing ...
% 5.73/2.02 Prover 2: Warning: ignoring some quantifiers
% 5.73/2.03 Prover 2: Constructing countermodel ...
% 6.74/2.26 Prover 2: proved (413ms)
% 6.74/2.26
% 6.74/2.26 No countermodel exists, formula is valid
% 6.74/2.26 % SZS status Theorem for theBenchmark
% 6.74/2.26
% 6.74/2.26 Generating proof ... Warning: ignoring some quantifiers
% 14.33/4.08 found it (size 279)
% 14.33/4.08
% 14.33/4.08 % SZS output start Proof for theBenchmark
% 14.33/4.08 Assumed formulas after preprocessing and simplification:
% 14.33/4.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v2) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v5, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v5, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v7, v6) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v5, v6) = v8) | ? [v10] : ((v10 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection_point(v5, v6) = v8) | ~ (distinct_points(v7, v8) = v9) | ? [v10] : ? [v11] : (( ~ (v11 = 0) & ~ (v10 = 0) & apart_point_and_line(v7, v6) = v11 & apart_point_and_line(v7, v5) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (unorthogonal_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v7, v6) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v5, v6) = 0) | (v9 = 0 & convergent_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v5, v7) = 0) | (v9 = 0 & convergent_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | apart_point_and_line(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_points(v5, v7) = v8) | apart_point_and_line(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (orthogonal_through_point(v8, v7) = v6) | ~ (orthogonal_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_through_point(v8, v7) = v6) | ~ (parallel_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v8) | ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & distinct_points(v7, v6) = 0 & distinct_points(v7, v5) = 0) | ( ~ (v9 = 0) & distinct_points(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v6, v8) = 0) | (v9 = 0 & apart_point_and_line(v6, v7) = 0) | (v9 = 0 & apart_point_and_line(v5, v8) = 0) | (v9 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v7, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | distinct_lines(v5, v6) = 0) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : orthogonal_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unorthogonal_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : parallel_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : line_connecting(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : apart_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_points(v6, v5) = v7)
% 14.98/4.14 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 14.98/4.14 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [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(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, 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] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [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] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_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 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 14.98/4.16 |
% 14.98/4.16 | Applying alpha-rule on (1) yields:
% 14.98/4.16 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 14.98/4.16 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 14.98/4.16 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 14.98/4.16 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 14.98/4.16 | (6) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 14.98/4.16 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 14.98/4.16 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 14.98/4.16 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 14.98/4.16 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 14.98/4.16 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 14.98/4.16 | (12) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 14.98/4.16 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 14.98/4.16 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 14.98/4.16 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 14.98/4.16 | (16) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 14.98/4.16 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0)))
% 14.98/4.16 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 14.98/4.16 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 14.98/4.16 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 14.98/4.16 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 14.98/4.17 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 14.98/4.17 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 14.98/4.17 | (24) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 14.98/4.17 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 14.98/4.17 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 14.98/4.17 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 14.98/4.17 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 14.98/4.17 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 14.98/4.17 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 14.98/4.17 | (31) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 14.98/4.17 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 14.98/4.17 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 14.98/4.17 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 14.98/4.17 | (35) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0
% 14.98/4.17 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 14.98/4.17 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4)))
% 14.98/4.17 | (38) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 14.98/4.17 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 14.98/4.17 | (40) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 14.98/4.17 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 14.98/4.17 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 14.98/4.17 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 14.98/4.17 | (44) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 14.98/4.17 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 14.98/4.17 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 14.98/4.17 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 14.98/4.17 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 14.98/4.17 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 14.98/4.17 | (50) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 14.98/4.17 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 14.98/4.17 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 14.98/4.18 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 14.98/4.18 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 14.98/4.18 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 14.98/4.18 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 14.98/4.18 | (57) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 14.98/4.18 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 14.98/4.18 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 14.98/4.18 | (60) ~ (all_0_0_0 = 0)
% 14.98/4.18 | (61) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 14.98/4.18 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 14.98/4.18 | (63) ~ (all_0_1_1 = 0)
% 14.98/4.18 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 14.98/4.18 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 14.98/4.18 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0)))
% 14.98/4.18 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 14.98/4.18 | (68) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 14.98/4.18 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 14.98/4.18 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 14.98/4.18 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 14.98/4.18 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 14.98/4.18 | (73) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 14.98/4.18 | (74) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 14.98/4.18 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 14.98/4.18 | (76) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 14.98/4.18 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 14.98/4.18 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 14.98/4.18 | (79) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 14.98/4.18 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 14.98/4.18 |
% 14.98/4.19 | Instantiating formula (58) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 14.98/4.19 | (81) all_0_0_0 = 0 | convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (56) with 0, 0, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 14.98/4.19 | (82) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (54) with 0, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 14.98/4.19 | (83) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (3) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 14.98/4.19 | (84) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (33) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 14.98/4.19 | (85) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (49) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 14.98/4.19 | (86) ? [v0] : ((v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (47) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 14.98/4.19 | (87) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (21) with all_0_1_1, all_0_0_0, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 14.98/4.19 | (88) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0))
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (42) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 14.98/4.19 | (89) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 14.98/4.19 |
% 14.98/4.19 | Instantiating formula (57) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 14.98/4.19 | (90) all_0_1_1 = 0 | unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.19 |
% 14.98/4.19 | Instantiating (89) with all_26_0_32, all_26_1_33 yields:
% 14.98/4.19 | (91) (all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_26_1_33 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_26_1_33 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33)
% 14.98/4.19 |
% 14.98/4.19 | Instantiating (88) with all_27_0_34 yields:
% 14.98/4.19 | (92) (all_27_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_27_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_27_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34) | ( ~ (all_27_0_34 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_27_0_34)
% 14.98/4.19 |
% 14.98/4.19 | Instantiating (87) with all_28_0_35 yields:
% 14.98/4.19 | (93) (all_28_0_35 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_28_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_28_0_35 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35) | ( ~ (all_28_0_35 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_28_0_35)
% 14.98/4.19 |
% 14.98/4.19 | Instantiating (86) with all_29_0_36 yields:
% 14.98/4.19 | (94) (all_29_0_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_29_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36) | ( ~ (all_29_0_36 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_29_0_36)
% 14.98/4.19 |
% 14.98/4.19 | Instantiating (83) with all_30_0_37, all_30_1_38 yields:
% 14.98/4.19 | (95) (all_30_0_37 = 0 & all_30_1_38 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_30_1_38 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_30_1_38 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_30_1_38)
% 14.98/4.19 |
% 14.98/4.19 | Instantiating (82) with all_31_0_39 yields:
% 14.98/4.19 | (96) (all_31_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_31_0_39 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39) | ( ~ (all_31_0_39 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_31_0_39)
% 14.98/4.19 |
% 14.98/4.19 | Instantiating (84) with all_33_0_41, all_33_1_42 yields:
% 14.98/4.19 | (97) (all_33_0_41 = 0 & all_33_1_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_33_1_42 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_33_1_42 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42)
% 14.98/4.19 |
% 14.98/4.19 +-Applying beta-rule and splitting (81), into two cases.
% 14.98/4.19 |-Branch one:
% 14.98/4.19 | (98) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.19 |
% 14.98/4.19 +-Applying beta-rule and splitting (90), into two cases.
% 14.98/4.19 |-Branch one:
% 14.98/4.19 | (99) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.19 |
% 14.98/4.19 +-Applying beta-rule and splitting (97), into two cases.
% 14.98/4.19 |-Branch one:
% 14.98/4.19 | (100) (all_33_0_41 = 0 & all_33_1_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_33_1_42 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 14.98/4.19 |
% 14.98/4.20 +-Applying beta-rule and splitting (100), into two cases.
% 14.98/4.20 |-Branch one:
% 14.98/4.20 | (101) all_33_0_41 = 0 & all_33_1_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (101) yields:
% 14.98/4.20 | (102) all_33_0_41 = 0
% 14.98/4.20 | (103) all_33_1_42 = 0
% 14.98/4.20 | (99) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.20 | (105) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 +-Applying beta-rule and splitting (85), into two cases.
% 14.98/4.20 |-Branch one:
% 14.98/4.20 | (106) all_0_1_1 = 0
% 14.98/4.20 |
% 14.98/4.20 | Equations (106) can reduce 63 to:
% 14.98/4.20 | (107) $false
% 14.98/4.20 |
% 14.98/4.20 |-The branch is then unsatisfiable
% 14.98/4.20 |-Branch two:
% 14.98/4.20 | (63) ~ (all_0_1_1 = 0)
% 14.98/4.20 | (109) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 14.98/4.20 |
% 14.98/4.20 | Instantiating formula (71) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 14.98/4.20 | (106) all_0_1_1 = 0
% 14.98/4.20 |
% 14.98/4.20 | Equations (106) can reduce 63 to:
% 14.98/4.20 | (107) $false
% 14.98/4.20 |
% 14.98/4.20 |-The branch is then unsatisfiable
% 14.98/4.20 |-Branch two:
% 14.98/4.20 | (112) all_33_1_42 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (112) yields:
% 14.98/4.20 | (103) all_33_1_42 = 0
% 14.98/4.20 | (114) all_0_0_0 = 0
% 14.98/4.20 | (98) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Equations (114) can reduce 60 to:
% 14.98/4.20 | (107) $false
% 14.98/4.20 |
% 14.98/4.20 |-The branch is then unsatisfiable
% 14.98/4.20 |-Branch two:
% 14.98/4.20 | (117) ~ (all_33_1_42 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (117) yields:
% 14.98/4.20 | (118) ~ (all_33_1_42 = 0)
% 14.98/4.20 | (119) convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42
% 14.98/4.20 |
% 14.98/4.20 +-Applying beta-rule and splitting (85), into two cases.
% 14.98/4.20 |-Branch one:
% 14.98/4.20 | (106) all_0_1_1 = 0
% 14.98/4.20 |
% 14.98/4.20 | Equations (106) can reduce 63 to:
% 14.98/4.20 | (107) $false
% 14.98/4.20 |
% 14.98/4.20 |-The branch is then unsatisfiable
% 14.98/4.20 |-Branch two:
% 14.98/4.20 | (63) ~ (all_0_1_1 = 0)
% 14.98/4.20 | (109) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 14.98/4.20 |
% 14.98/4.20 | Instantiating (109) with all_47_0_44 yields:
% 14.98/4.20 | (124) ~ (all_47_0_44 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (124) yields:
% 14.98/4.20 | (125) ~ (all_47_0_44 = 0)
% 14.98/4.20 | (126) convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44
% 14.98/4.20 |
% 14.98/4.20 +-Applying beta-rule and splitting (91), into two cases.
% 14.98/4.20 |-Branch one:
% 14.98/4.20 | (127) (all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_26_1_33 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 14.98/4.20 |
% 14.98/4.20 +-Applying beta-rule and splitting (127), into two cases.
% 14.98/4.20 |-Branch one:
% 14.98/4.20 | (128) all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (128) yields:
% 14.98/4.20 | (129) all_26_0_32 = 0
% 14.98/4.20 | (130) all_26_1_33 = 0
% 14.98/4.20 | (131) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.20 | (98) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Instantiating formula (30) with all_0_3_3, all_0_2_2, 0, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 14.98/4.20 | (114) all_0_0_0 = 0
% 14.98/4.20 |
% 14.98/4.20 | Equations (114) can reduce 60 to:
% 14.98/4.20 | (107) $false
% 14.98/4.20 |
% 14.98/4.20 |-The branch is then unsatisfiable
% 14.98/4.20 |-Branch two:
% 14.98/4.20 | (135) all_26_1_33 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (135) yields:
% 14.98/4.20 | (130) all_26_1_33 = 0
% 14.98/4.20 | (106) all_0_1_1 = 0
% 14.98/4.20 | (99) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Equations (106) can reduce 63 to:
% 14.98/4.20 | (107) $false
% 14.98/4.20 |
% 14.98/4.20 |-The branch is then unsatisfiable
% 14.98/4.20 |-Branch two:
% 14.98/4.20 | (140) ~ (all_26_1_33 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (140) yields:
% 14.98/4.20 | (141) ~ (all_26_1_33 = 0)
% 14.98/4.20 | (142) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 14.98/4.20 |
% 14.98/4.20 +-Applying beta-rule and splitting (93), into two cases.
% 14.98/4.20 |-Branch one:
% 14.98/4.20 | (143) (all_28_0_35 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_28_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_28_0_35 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35)
% 14.98/4.20 |
% 14.98/4.20 +-Applying beta-rule and splitting (143), into two cases.
% 14.98/4.20 |-Branch one:
% 14.98/4.20 | (144) (all_28_0_35 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_28_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 14.98/4.20 |
% 14.98/4.20 +-Applying beta-rule and splitting (144), into two cases.
% 14.98/4.20 |-Branch one:
% 14.98/4.20 | (145) all_28_0_35 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (145) yields:
% 14.98/4.20 | (146) all_28_0_35 = 0
% 14.98/4.20 | (114) all_0_0_0 = 0
% 14.98/4.20 | (98) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Equations (114) can reduce 60 to:
% 14.98/4.20 | (107) $false
% 14.98/4.20 |
% 14.98/4.20 |-The branch is then unsatisfiable
% 14.98/4.20 |-Branch two:
% 14.98/4.20 | (150) all_28_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (150) yields:
% 14.98/4.20 | (146) all_28_0_35 = 0
% 14.98/4.20 | (106) all_0_1_1 = 0
% 14.98/4.20 | (99) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.20 |
% 14.98/4.20 | Equations (106) can reduce 63 to:
% 14.98/4.20 | (107) $false
% 14.98/4.20 |
% 14.98/4.20 |-The branch is then unsatisfiable
% 14.98/4.20 |-Branch two:
% 14.98/4.20 | (155) ~ (all_28_0_35 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35
% 14.98/4.20 |
% 14.98/4.20 | Applying alpha-rule on (155) yields:
% 14.98/4.20 | (156) ~ (all_28_0_35 = 0)
% 14.98/4.20 | (157) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35
% 14.98/4.20 |
% 14.98/4.20 | Instantiating formula (30) with all_0_4_4, all_0_3_3, all_28_0_35, 0 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 14.98/4.21 | (146) all_28_0_35 = 0
% 14.98/4.21 |
% 14.98/4.21 | Equations (146) can reduce 156 to:
% 14.98/4.21 | (107) $false
% 14.98/4.21 |
% 14.98/4.21 |-The branch is then unsatisfiable
% 14.98/4.21 |-Branch two:
% 14.98/4.21 | (160) ~ (all_28_0_35 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_28_0_35
% 14.98/4.21 |
% 14.98/4.21 | Applying alpha-rule on (160) yields:
% 14.98/4.21 | (156) ~ (all_28_0_35 = 0)
% 14.98/4.21 | (162) convergent_lines(all_0_4_4, all_0_3_3) = all_28_0_35
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (71) with all_0_4_4, all_0_3_3, all_28_0_35, all_33_1_42 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42, convergent_lines(all_0_4_4, all_0_3_3) = all_28_0_35, yields:
% 14.98/4.21 | (163) all_33_1_42 = all_28_0_35
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (71) with all_0_4_4, all_0_3_3, all_26_1_33, all_33_1_42 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 14.98/4.21 | (164) all_33_1_42 = all_26_1_33
% 14.98/4.21 |
% 14.98/4.21 | Combining equations (163,164) yields a new equation:
% 14.98/4.21 | (165) all_28_0_35 = all_26_1_33
% 14.98/4.21 |
% 14.98/4.21 | Simplifying 165 yields:
% 14.98/4.21 | (166) all_28_0_35 = all_26_1_33
% 14.98/4.21 |
% 14.98/4.21 | Equations (166) can reduce 156 to:
% 14.98/4.21 | (141) ~ (all_26_1_33 = 0)
% 14.98/4.21 |
% 14.98/4.21 | From (166) and (162) follows:
% 14.98/4.21 | (142) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (56) with 0, 0, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 14.98/4.21 | (169) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (47) with 0, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 14.98/4.21 | (170) ? [v0] : ((v0 = 0 & all_0_1_1 = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (49) with all_26_1_33, all_26_1_33, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 14.98/4.21 | (171) ? [v0] : ((v0 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (47) with 0, all_26_1_33, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 14.98/4.21 | (172) ? [v0] : ((v0 = 0 & all_26_1_33 = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (42) with all_26_1_33, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 14.98/4.21 | (173) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & all_26_1_33 = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (49) with all_47_0_44, all_47_0_44, all_0_4_4, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 14.98/4.21 | (174) ? [v0] : ((v0 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (42) with all_47_0_44, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 14.98/4.21 | (175) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 14.98/4.21 |
% 14.98/4.21 | Instantiating formula (57) with all_47_0_44, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 14.98/4.21 | (176) all_47_0_44 = 0 | unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 14.98/4.21 |
% 14.98/4.21 | Instantiating (171) with all_67_0_45 yields:
% 14.98/4.21 | (177) (all_67_0_45 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_67_0_45 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_45) | ( ~ (all_67_0_45 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_45)
% 14.98/4.21 |
% 14.98/4.21 | Instantiating (175) with all_75_0_57, all_75_1_58 yields:
% 14.98/4.21 | (178) (all_75_0_57 = 0 & all_75_1_58 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_75_1_58 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_75_1_58 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_75_1_58)
% 14.98/4.21 |
% 14.98/4.21 | Instantiating (170) with all_77_0_60 yields:
% 14.98/4.21 | (179) (all_77_0_60 = 0 & all_0_1_1 = 0) | (all_77_0_60 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_77_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_77_0_60) | ( ~ (all_77_0_60 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_77_0_60)
% 14.98/4.21 |
% 14.98/4.21 | Instantiating (174) with all_79_0_63 yields:
% 14.98/4.21 | (180) (all_79_0_63 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_79_0_63 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_79_0_63) | ( ~ (all_79_0_63 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_79_0_63)
% 14.98/4.21 |
% 14.98/4.21 | Instantiating (173) with all_81_0_66, all_81_1_67 yields:
% 14.98/4.21 | (181) (all_81_0_66 = 0 & all_81_1_67 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_81_1_67 = 0 & all_26_1_33 = 0) | ( ~ (all_81_1_67 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_81_1_67)
% 14.98/4.21 |
% 14.98/4.21 | Instantiating (172) with all_82_0_68 yields:
% 14.98/4.21 | (182) (all_82_0_68 = 0 & all_26_1_33 = 0) | (all_82_0_68 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_82_0_68 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_82_0_68) | ( ~ (all_82_0_68 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_82_0_68)
% 14.98/4.21 |
% 14.98/4.21 | Instantiating (169) with all_83_0_69 yields:
% 14.98/4.21 | (183) (all_83_0_69 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_83_0_69 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_83_0_69) | ( ~ (all_83_0_69 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_83_0_69)
% 14.98/4.21 |
% 14.98/4.21 +-Applying beta-rule and splitting (176), into two cases.
% 14.98/4.21 |-Branch one:
% 14.98/4.21 | (184) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 14.98/4.22 |
% 14.98/4.22 +-Applying beta-rule and splitting (96), into two cases.
% 14.98/4.22 |-Branch one:
% 14.98/4.22 | (185) (all_31_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_31_0_39 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39)
% 14.98/4.22 |
% 14.98/4.22 +-Applying beta-rule and splitting (185), into two cases.
% 14.98/4.22 |-Branch one:
% 14.98/4.22 | (186) all_31_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (186) yields:
% 14.98/4.22 | (187) all_31_0_39 = 0
% 14.98/4.22 | (188) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 14.98/4.22 |
% 14.98/4.22 | Instantiating formula (71) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 14.98/4.22 | (130) all_26_1_33 = 0
% 14.98/4.22 |
% 14.98/4.22 | Equations (130) can reduce 141 to:
% 14.98/4.22 | (107) $false
% 14.98/4.22 |
% 14.98/4.22 |-The branch is then unsatisfiable
% 14.98/4.22 |-Branch two:
% 14.98/4.22 | (191) ~ (all_31_0_39 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (191) yields:
% 14.98/4.22 | (192) ~ (all_31_0_39 = 0)
% 14.98/4.22 | (193) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39
% 14.98/4.22 |
% 14.98/4.22 | Instantiating formula (30) with all_0_4_4, all_0_4_4, 0, all_31_0_39 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 14.98/4.22 | (187) all_31_0_39 = 0
% 14.98/4.22 |
% 14.98/4.22 | Equations (187) can reduce 192 to:
% 14.98/4.22 | (107) $false
% 14.98/4.22 |
% 14.98/4.22 |-The branch is then unsatisfiable
% 14.98/4.22 |-Branch two:
% 14.98/4.22 | (196) ~ (all_31_0_39 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_31_0_39
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (196) yields:
% 14.98/4.22 | (192) ~ (all_31_0_39 = 0)
% 14.98/4.22 | (198) convergent_lines(all_0_4_4, all_0_4_4) = all_31_0_39
% 14.98/4.22 |
% 14.98/4.22 +-Applying beta-rule and splitting (94), into two cases.
% 14.98/4.22 |-Branch one:
% 14.98/4.22 | (199) (all_29_0_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_29_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36)
% 14.98/4.22 |
% 14.98/4.22 +-Applying beta-rule and splitting (199), into two cases.
% 14.98/4.22 |-Branch one:
% 14.98/4.22 | (200) all_29_0_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (200) yields:
% 14.98/4.22 | (201) all_29_0_36 = 0
% 14.98/4.22 | (106) all_0_1_1 = 0
% 14.98/4.22 | (99) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 14.98/4.22 |
% 14.98/4.22 | Equations (106) can reduce 63 to:
% 14.98/4.22 | (107) $false
% 14.98/4.22 |
% 14.98/4.22 |-The branch is then unsatisfiable
% 14.98/4.22 |-Branch two:
% 14.98/4.22 | (205) ~ (all_29_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (205) yields:
% 14.98/4.22 | (206) ~ (all_29_0_36 = 0)
% 14.98/4.22 | (207) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36
% 14.98/4.22 |
% 14.98/4.22 | Instantiating formula (30) with all_0_4_4, all_0_4_4, 0, all_29_0_36 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 14.98/4.22 | (201) all_29_0_36 = 0
% 14.98/4.22 |
% 14.98/4.22 | Equations (201) can reduce 206 to:
% 14.98/4.22 | (107) $false
% 14.98/4.22 |
% 14.98/4.22 |-The branch is then unsatisfiable
% 14.98/4.22 |-Branch two:
% 14.98/4.22 | (210) ~ (all_29_0_36 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_29_0_36
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (210) yields:
% 14.98/4.22 | (206) ~ (all_29_0_36 = 0)
% 14.98/4.22 | (212) convergent_lines(all_0_4_4, all_0_4_4) = all_29_0_36
% 14.98/4.22 |
% 14.98/4.22 +-Applying beta-rule and splitting (177), into two cases.
% 14.98/4.22 |-Branch one:
% 14.98/4.22 | (213) (all_67_0_45 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_67_0_45 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_45)
% 14.98/4.22 |
% 14.98/4.22 +-Applying beta-rule and splitting (213), into two cases.
% 14.98/4.22 |-Branch one:
% 14.98/4.22 | (214) all_67_0_45 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (214) yields:
% 14.98/4.22 | (215) all_67_0_45 = 0
% 14.98/4.22 | (130) all_26_1_33 = 0
% 14.98/4.22 | (24) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 14.98/4.22 |
% 14.98/4.22 | Equations (130) can reduce 141 to:
% 14.98/4.22 | (107) $false
% 14.98/4.22 |
% 14.98/4.22 |-The branch is then unsatisfiable
% 14.98/4.22 |-Branch two:
% 14.98/4.22 | (219) ~ (all_67_0_45 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_45
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (219) yields:
% 14.98/4.22 | (220) ~ (all_67_0_45 = 0)
% 14.98/4.22 | (221) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_45
% 14.98/4.22 |
% 14.98/4.22 | Instantiating formula (30) with all_0_4_4, all_0_4_4, 0, all_67_0_45 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_45, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 14.98/4.22 | (215) all_67_0_45 = 0
% 14.98/4.22 |
% 14.98/4.22 | Equations (215) can reduce 220 to:
% 14.98/4.22 | (107) $false
% 14.98/4.22 |
% 14.98/4.22 |-The branch is then unsatisfiable
% 14.98/4.22 |-Branch two:
% 14.98/4.22 | (224) ~ (all_67_0_45 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_45
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (224) yields:
% 14.98/4.22 | (220) ~ (all_67_0_45 = 0)
% 14.98/4.22 | (226) convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_45
% 14.98/4.22 |
% 14.98/4.22 +-Applying beta-rule and splitting (180), into two cases.
% 14.98/4.22 |-Branch one:
% 14.98/4.22 | (227) (all_79_0_63 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_79_0_63 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_79_0_63)
% 14.98/4.22 |
% 14.98/4.22 +-Applying beta-rule and splitting (227), into two cases.
% 14.98/4.22 |-Branch one:
% 14.98/4.22 | (228) all_79_0_63 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (228) yields:
% 14.98/4.22 | (229) all_79_0_63 = 0
% 14.98/4.22 | (230) all_47_0_44 = 0
% 14.98/4.22 | (184) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 14.98/4.22 |
% 14.98/4.22 | Equations (230) can reduce 125 to:
% 14.98/4.22 | (107) $false
% 14.98/4.22 |
% 14.98/4.22 |-The branch is then unsatisfiable
% 14.98/4.22 |-Branch two:
% 14.98/4.22 | (233) ~ (all_79_0_63 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_79_0_63
% 14.98/4.22 |
% 14.98/4.22 | Applying alpha-rule on (233) yields:
% 14.98/4.22 | (234) ~ (all_79_0_63 = 0)
% 14.98/4.22 | (235) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_79_0_63
% 14.98/4.22 |
% 14.98/4.22 | Instantiating formula (30) with all_0_4_4, all_0_4_4, 0, all_79_0_63 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_79_0_63, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 15.44/4.23 | (229) all_79_0_63 = 0
% 15.44/4.23 |
% 15.44/4.23 | Equations (229) can reduce 234 to:
% 15.44/4.23 | (107) $false
% 15.44/4.23 |
% 15.44/4.23 |-The branch is then unsatisfiable
% 15.44/4.23 |-Branch two:
% 15.44/4.23 | (238) ~ (all_79_0_63 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_79_0_63
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (238) yields:
% 15.44/4.23 | (234) ~ (all_79_0_63 = 0)
% 15.44/4.23 | (240) convergent_lines(all_0_4_4, all_0_4_4) = all_79_0_63
% 15.44/4.23 |
% 15.44/4.23 +-Applying beta-rule and splitting (182), into two cases.
% 15.44/4.23 |-Branch one:
% 15.44/4.23 | (241) (all_82_0_68 = 0 & all_26_1_33 = 0) | (all_82_0_68 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_82_0_68 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_82_0_68)
% 15.44/4.23 |
% 15.44/4.23 +-Applying beta-rule and splitting (241), into two cases.
% 15.44/4.23 |-Branch one:
% 15.44/4.23 | (242) (all_82_0_68 = 0 & all_26_1_33 = 0) | (all_82_0_68 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 15.44/4.23 |
% 15.44/4.23 +-Applying beta-rule and splitting (242), into two cases.
% 15.44/4.23 |-Branch one:
% 15.44/4.23 | (243) all_82_0_68 = 0 & all_26_1_33 = 0
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (243) yields:
% 15.44/4.23 | (244) all_82_0_68 = 0
% 15.44/4.23 | (130) all_26_1_33 = 0
% 15.44/4.23 |
% 15.44/4.23 | Equations (130) can reduce 141 to:
% 15.44/4.23 | (107) $false
% 15.44/4.23 |
% 15.44/4.23 |-The branch is then unsatisfiable
% 15.44/4.23 |-Branch two:
% 15.44/4.23 | (247) all_82_0_68 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (247) yields:
% 15.44/4.23 | (244) all_82_0_68 = 0
% 15.44/4.23 | (188) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 15.44/4.23 |
% 15.44/4.23 | Instantiating formula (71) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 15.44/4.23 | (130) all_26_1_33 = 0
% 15.44/4.23 |
% 15.44/4.23 | Equations (130) can reduce 141 to:
% 15.44/4.23 | (107) $false
% 15.44/4.23 |
% 15.44/4.23 |-The branch is then unsatisfiable
% 15.44/4.23 |-Branch two:
% 15.44/4.23 | (252) ~ (all_82_0_68 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_82_0_68
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (252) yields:
% 15.44/4.23 | (253) ~ (all_82_0_68 = 0)
% 15.44/4.23 | (254) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_82_0_68
% 15.44/4.23 |
% 15.44/4.23 | Instantiating formula (30) with all_0_4_4, all_0_4_4, 0, all_82_0_68 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_82_0_68, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 15.44/4.23 | (244) all_82_0_68 = 0
% 15.44/4.23 |
% 15.44/4.23 | Equations (244) can reduce 253 to:
% 15.44/4.23 | (107) $false
% 15.44/4.23 |
% 15.44/4.23 |-The branch is then unsatisfiable
% 15.44/4.23 |-Branch two:
% 15.44/4.23 | (257) ~ (all_82_0_68 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_82_0_68
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (257) yields:
% 15.44/4.23 | (253) ~ (all_82_0_68 = 0)
% 15.44/4.23 | (259) convergent_lines(all_0_4_4, all_0_4_4) = all_82_0_68
% 15.44/4.23 |
% 15.44/4.23 +-Applying beta-rule and splitting (179), into two cases.
% 15.44/4.23 |-Branch one:
% 15.44/4.23 | (260) (all_77_0_60 = 0 & all_0_1_1 = 0) | (all_77_0_60 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_77_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_77_0_60)
% 15.44/4.23 |
% 15.44/4.23 +-Applying beta-rule and splitting (260), into two cases.
% 15.44/4.23 |-Branch one:
% 15.44/4.23 | (261) (all_77_0_60 = 0 & all_0_1_1 = 0) | (all_77_0_60 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0)
% 15.44/4.23 |
% 15.44/4.23 +-Applying beta-rule and splitting (261), into two cases.
% 15.44/4.23 |-Branch one:
% 15.44/4.23 | (262) all_77_0_60 = 0 & all_0_1_1 = 0
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (262) yields:
% 15.44/4.23 | (263) all_77_0_60 = 0
% 15.44/4.23 | (106) all_0_1_1 = 0
% 15.44/4.23 |
% 15.44/4.23 | Equations (106) can reduce 63 to:
% 15.44/4.23 | (107) $false
% 15.44/4.23 |
% 15.44/4.23 |-The branch is then unsatisfiable
% 15.44/4.23 |-Branch two:
% 15.44/4.23 | (266) all_77_0_60 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (266) yields:
% 15.44/4.23 | (263) all_77_0_60 = 0
% 15.44/4.23 | (105) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 15.44/4.23 |
% 15.44/4.23 | Instantiating formula (71) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 15.44/4.23 | (106) all_0_1_1 = 0
% 15.44/4.23 |
% 15.44/4.23 | Equations (106) can reduce 63 to:
% 15.44/4.23 | (107) $false
% 15.44/4.23 |
% 15.44/4.23 |-The branch is then unsatisfiable
% 15.44/4.23 |-Branch two:
% 15.44/4.23 | (271) ~ (all_77_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_77_0_60
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (271) yields:
% 15.44/4.23 | (272) ~ (all_77_0_60 = 0)
% 15.44/4.23 | (273) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_77_0_60
% 15.44/4.23 |
% 15.44/4.23 | Instantiating formula (30) with all_0_4_4, all_0_4_4, 0, all_77_0_60 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_77_0_60, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 15.44/4.23 | (263) all_77_0_60 = 0
% 15.44/4.23 |
% 15.44/4.23 | Equations (263) can reduce 272 to:
% 15.44/4.23 | (107) $false
% 15.44/4.23 |
% 15.44/4.23 |-The branch is then unsatisfiable
% 15.44/4.23 |-Branch two:
% 15.44/4.23 | (276) ~ (all_77_0_60 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_77_0_60
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (276) yields:
% 15.44/4.23 | (272) ~ (all_77_0_60 = 0)
% 15.44/4.23 | (278) convergent_lines(all_0_4_4, all_0_4_4) = all_77_0_60
% 15.44/4.23 |
% 15.44/4.23 +-Applying beta-rule and splitting (183), into two cases.
% 15.44/4.23 |-Branch one:
% 15.44/4.23 | (279) (all_83_0_69 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_83_0_69 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_83_0_69)
% 15.44/4.23 |
% 15.44/4.23 +-Applying beta-rule and splitting (279), into two cases.
% 15.44/4.23 |-Branch one:
% 15.44/4.23 | (280) all_83_0_69 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (280) yields:
% 15.44/4.23 | (281) all_83_0_69 = 0
% 15.44/4.23 | (105) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 15.44/4.23 |
% 15.44/4.23 | Instantiating formula (71) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 15.44/4.23 | (106) all_0_1_1 = 0
% 15.44/4.23 |
% 15.44/4.23 | Equations (106) can reduce 63 to:
% 15.44/4.23 | (107) $false
% 15.44/4.23 |
% 15.44/4.23 |-The branch is then unsatisfiable
% 15.44/4.23 |-Branch two:
% 15.44/4.23 | (285) ~ (all_83_0_69 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_83_0_69
% 15.44/4.23 |
% 15.44/4.23 | Applying alpha-rule on (285) yields:
% 15.44/4.23 | (286) ~ (all_83_0_69 = 0)
% 15.44/4.23 | (287) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_83_0_69
% 15.44/4.23 |
% 15.44/4.23 | Instantiating formula (30) with all_0_4_4, all_0_4_4, 0, all_83_0_69 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_83_0_69, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 15.44/4.24 | (281) all_83_0_69 = 0
% 15.44/4.24 |
% 15.44/4.24 | Equations (281) can reduce 286 to:
% 15.44/4.24 | (107) $false
% 15.44/4.24 |
% 15.44/4.24 |-The branch is then unsatisfiable
% 15.44/4.24 |-Branch two:
% 15.44/4.24 | (290) ~ (all_83_0_69 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_83_0_69
% 15.44/4.24 |
% 15.44/4.24 | Applying alpha-rule on (290) yields:
% 15.44/4.24 | (286) ~ (all_83_0_69 = 0)
% 15.44/4.24 | (292) convergent_lines(all_0_4_4, all_0_4_4) = all_83_0_69
% 15.44/4.24 |
% 15.44/4.24 | Instantiating formula (71) with all_0_4_4, all_0_4_4, all_82_0_68, all_47_0_44 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_82_0_68, convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 15.44/4.24 | (293) all_82_0_68 = all_47_0_44
% 15.44/4.24 |
% 15.44/4.24 | Instantiating formula (71) with all_0_4_4, all_0_4_4, all_79_0_63, all_83_0_69 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_83_0_69, convergent_lines(all_0_4_4, all_0_4_4) = all_79_0_63, yields:
% 15.44/4.24 | (294) all_83_0_69 = all_79_0_63
% 15.44/4.24 |
% 15.44/4.24 | Instantiating formula (71) with all_0_4_4, all_0_4_4, all_79_0_63, all_82_0_68 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_82_0_68, convergent_lines(all_0_4_4, all_0_4_4) = all_79_0_63, yields:
% 15.44/4.24 | (295) all_82_0_68 = all_79_0_63
% 15.44/4.24 |
% 15.44/4.24 | Instantiating formula (71) with all_0_4_4, all_0_4_4, all_77_0_60, all_82_0_68 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_82_0_68, convergent_lines(all_0_4_4, all_0_4_4) = all_77_0_60, yields:
% 15.44/4.24 | (296) all_82_0_68 = all_77_0_60
% 15.44/4.24 |
% 15.44/4.24 | Instantiating formula (71) with all_0_4_4, all_0_4_4, all_67_0_45, all_47_0_44 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_45, convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 15.44/4.24 | (297) all_67_0_45 = all_47_0_44
% 15.44/4.24 |
% 15.44/4.24 | Instantiating formula (71) with all_0_4_4, all_0_4_4, all_31_0_39, all_67_0_45 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_45, convergent_lines(all_0_4_4, all_0_4_4) = all_31_0_39, yields:
% 15.44/4.24 | (298) all_67_0_45 = all_31_0_39
% 15.44/4.24 |
% 15.44/4.24 | Instantiating formula (71) with all_0_4_4, all_0_4_4, all_29_0_36, all_83_0_69 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_83_0_69, convergent_lines(all_0_4_4, all_0_4_4) = all_29_0_36, yields:
% 15.44/4.24 | (299) all_83_0_69 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Combining equations (294,299) yields a new equation:
% 15.44/4.24 | (300) all_79_0_63 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Simplifying 300 yields:
% 15.44/4.24 | (301) all_79_0_63 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Combining equations (295,296) yields a new equation:
% 15.44/4.24 | (302) all_79_0_63 = all_77_0_60
% 15.44/4.24 |
% 15.44/4.24 | Simplifying 302 yields:
% 15.44/4.24 | (303) all_79_0_63 = all_77_0_60
% 15.44/4.24 |
% 15.44/4.24 | Combining equations (293,296) yields a new equation:
% 15.44/4.24 | (304) all_77_0_60 = all_47_0_44
% 15.44/4.24 |
% 15.44/4.24 | Combining equations (303,301) yields a new equation:
% 15.44/4.24 | (305) all_77_0_60 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Simplifying 305 yields:
% 15.44/4.24 | (306) all_77_0_60 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Combining equations (304,306) yields a new equation:
% 15.44/4.24 | (307) all_47_0_44 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Simplifying 307 yields:
% 15.44/4.24 | (308) all_47_0_44 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Combining equations (297,298) yields a new equation:
% 15.44/4.24 | (309) all_47_0_44 = all_31_0_39
% 15.44/4.24 |
% 15.44/4.24 | Simplifying 309 yields:
% 15.44/4.24 | (310) all_47_0_44 = all_31_0_39
% 15.44/4.24 |
% 15.44/4.24 | Combining equations (310,308) yields a new equation:
% 15.44/4.24 | (311) all_31_0_39 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Simplifying 311 yields:
% 15.44/4.24 | (312) all_31_0_39 = all_29_0_36
% 15.44/4.24 |
% 15.44/4.24 | Equations (312) can reduce 192 to:
% 15.44/4.24 | (206) ~ (all_29_0_36 = 0)
% 15.44/4.24 |
% 15.44/4.24 | Instantiating formula (54) with 0, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 15.44/4.24 | (314) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 15.44/4.24 |
% 15.44/4.24 | Instantiating (314) with all_127_0_73, all_127_1_74 yields:
% 15.44/4.24 | (315) (all_127_0_73 = 0 & all_127_1_74 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_127_1_74 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_127_1_74 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_127_1_74)
% 15.44/4.24 |
% 15.44/4.24 +-Applying beta-rule and splitting (92), into two cases.
% 15.44/4.24 |-Branch one:
% 15.44/4.24 | (316) (all_27_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_27_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_27_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34)
% 15.44/4.24 |
% 15.44/4.24 +-Applying beta-rule and splitting (316), into two cases.
% 15.44/4.24 |-Branch one:
% 15.44/4.24 | (317) (all_27_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_27_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 15.44/4.24 |
% 15.44/4.24 +-Applying beta-rule and splitting (317), into two cases.
% 15.44/4.24 |-Branch one:
% 15.44/4.24 | (318) all_27_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 15.44/4.24 |
% 15.44/4.24 | Applying alpha-rule on (318) yields:
% 15.44/4.24 | (319) all_27_0_34 = 0
% 15.44/4.24 | (114) all_0_0_0 = 0
% 15.44/4.24 | (98) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 15.44/4.24 |
% 15.44/4.24 | Equations (114) can reduce 60 to:
% 15.44/4.24 | (107) $false
% 15.44/4.24 |
% 15.44/4.24 |-The branch is then unsatisfiable
% 15.44/4.24 |-Branch two:
% 15.44/4.24 | (323) all_27_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 15.44/4.24 |
% 15.44/4.24 | Applying alpha-rule on (323) yields:
% 15.44/4.24 | (319) all_27_0_34 = 0
% 15.44/4.24 | (106) all_0_1_1 = 0
% 15.44/4.24 | (99) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 15.44/4.24 |
% 15.44/4.24 | Equations (106) can reduce 63 to:
% 15.44/4.24 | (107) $false
% 15.44/4.24 |
% 15.44/4.24 |-The branch is then unsatisfiable
% 15.44/4.24 |-Branch two:
% 15.44/4.24 | (328) ~ (all_27_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34
% 15.44/4.24 |
% 15.44/4.24 | Applying alpha-rule on (328) yields:
% 15.44/4.24 | (329) ~ (all_27_0_34 = 0)
% 15.44/4.24 | (330) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34
% 15.44/4.24 |
% 15.44/4.24 +-Applying beta-rule and splitting (315), into two cases.
% 15.44/4.24 |-Branch one:
% 15.44/4.24 | (331) (all_127_0_73 = 0 & all_127_1_74 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_127_1_74 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0)
% 15.44/4.24 |
% 15.44/4.24 +-Applying beta-rule and splitting (331), into two cases.
% 15.44/4.24 |-Branch one:
% 15.44/4.24 | (332) all_127_0_73 = 0 & all_127_1_74 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0
% 15.44/4.24 |
% 15.44/4.24 | Applying alpha-rule on (332) yields:
% 15.44/4.24 | (333) all_127_0_73 = 0
% 15.44/4.25 | (334) all_127_1_74 = 0
% 15.44/4.25 | (335) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 15.44/4.25 | (336) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (30) with all_0_3_3, all_0_4_4, 0, all_27_0_34 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 15.44/4.25 | (319) all_27_0_34 = 0
% 15.44/4.25 |
% 15.44/4.25 | Equations (319) can reduce 329 to:
% 15.44/4.25 | (107) $false
% 15.44/4.25 |
% 15.44/4.25 |-The branch is then unsatisfiable
% 15.44/4.25 |-Branch two:
% 15.44/4.25 | (339) all_127_1_74 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (339) yields:
% 15.44/4.25 | (334) all_127_1_74 = 0
% 15.44/4.25 | (341) convergent_lines(all_0_4_4, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (73) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 15.44/4.25 | (342) $false
% 15.44/4.25 |
% 15.44/4.25 |-The branch is then unsatisfiable
% 15.44/4.25 |-Branch two:
% 15.44/4.25 | (343) ~ (all_127_1_74 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_127_1_74
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (343) yields:
% 15.44/4.25 | (344) ~ (all_127_1_74 = 0)
% 15.44/4.25 | (345) convergent_lines(all_0_4_4, all_0_3_3) = all_127_1_74
% 15.44/4.25 |
% 15.44/4.25 +-Applying beta-rule and splitting (178), into two cases.
% 15.44/4.25 |-Branch one:
% 15.44/4.25 | (346) (all_75_0_57 = 0 & all_75_1_58 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_75_1_58 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0)
% 15.44/4.25 |
% 15.44/4.25 +-Applying beta-rule and splitting (346), into two cases.
% 15.44/4.25 |-Branch one:
% 15.44/4.25 | (347) all_75_0_57 = 0 & all_75_1_58 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (347) yields:
% 15.44/4.25 | (348) all_75_0_57 = 0
% 15.44/4.25 | (349) all_75_1_58 = 0
% 15.44/4.25 | (335) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 15.44/4.25 | (336) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (30) with all_0_3_3, all_0_4_4, 0, all_27_0_34 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 15.44/4.25 | (319) all_27_0_34 = 0
% 15.44/4.25 |
% 15.44/4.25 | Equations (319) can reduce 329 to:
% 15.44/4.25 | (107) $false
% 15.44/4.25 |
% 15.44/4.25 |-The branch is then unsatisfiable
% 15.44/4.25 |-Branch two:
% 15.44/4.25 | (354) all_75_1_58 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (354) yields:
% 15.44/4.25 | (349) all_75_1_58 = 0
% 15.44/4.25 | (230) all_47_0_44 = 0
% 15.44/4.25 | (184) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 | Combining equations (308,230) yields a new equation:
% 15.44/4.25 | (358) all_29_0_36 = 0
% 15.44/4.25 |
% 15.44/4.25 | Simplifying 358 yields:
% 15.44/4.25 | (201) all_29_0_36 = 0
% 15.44/4.25 |
% 15.44/4.25 | Equations (201) can reduce 206 to:
% 15.44/4.25 | (107) $false
% 15.44/4.25 |
% 15.44/4.25 |-The branch is then unsatisfiable
% 15.44/4.25 |-Branch two:
% 15.44/4.25 | (361) ~ (all_75_1_58 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_75_1_58
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (361) yields:
% 15.44/4.25 | (362) ~ (all_75_1_58 = 0)
% 15.44/4.25 | (363) convergent_lines(all_0_4_4, all_0_3_3) = all_75_1_58
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (71) with all_0_4_4, all_0_3_3, all_127_1_74, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_127_1_74, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 15.44/4.25 | (364) all_127_1_74 = all_26_1_33
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (71) with all_0_4_4, all_0_3_3, all_75_1_58, all_127_1_74 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_127_1_74, convergent_lines(all_0_4_4, all_0_3_3) = all_75_1_58, yields:
% 15.44/4.25 | (365) all_127_1_74 = all_75_1_58
% 15.44/4.25 |
% 15.44/4.25 | Combining equations (364,365) yields a new equation:
% 15.44/4.25 | (366) all_75_1_58 = all_26_1_33
% 15.44/4.25 |
% 15.44/4.25 | Equations (366) can reduce 362 to:
% 15.44/4.25 | (141) ~ (all_26_1_33 = 0)
% 15.44/4.25 |
% 15.44/4.25 | From (366) and (363) follows:
% 15.44/4.25 | (142) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (58) with all_27_0_34, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34, yields:
% 15.44/4.25 | (369) all_27_0_34 = 0 | convergent_lines(all_0_3_3, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 +-Applying beta-rule and splitting (95), into two cases.
% 15.44/4.25 |-Branch one:
% 15.44/4.25 | (370) (all_30_0_37 = 0 & all_30_1_38 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_30_1_38 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 15.44/4.25 |
% 15.44/4.25 +-Applying beta-rule and splitting (370), into two cases.
% 15.44/4.25 |-Branch one:
% 15.44/4.25 | (371) all_30_0_37 = 0 & all_30_1_38 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (371) yields:
% 15.44/4.25 | (372) all_30_0_37 = 0
% 15.44/4.25 | (373) all_30_1_38 = 0
% 15.44/4.25 | (374) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 15.44/4.25 | (375) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (73) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 15.44/4.25 | (342) $false
% 15.44/4.25 |
% 15.44/4.25 |-The branch is then unsatisfiable
% 15.44/4.25 |-Branch two:
% 15.44/4.25 | (377) all_30_1_38 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (377) yields:
% 15.44/4.25 | (373) all_30_1_38 = 0
% 15.44/4.25 | (188) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (71) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 15.44/4.25 | (130) all_26_1_33 = 0
% 15.44/4.25 |
% 15.44/4.25 | Equations (130) can reduce 141 to:
% 15.44/4.25 | (107) $false
% 15.44/4.25 |
% 15.44/4.25 |-The branch is then unsatisfiable
% 15.44/4.25 |-Branch two:
% 15.44/4.25 | (382) ~ (all_30_1_38 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_30_1_38
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (382) yields:
% 15.44/4.25 | (383) ~ (all_30_1_38 = 0)
% 15.44/4.25 | (384) convergent_lines(all_0_4_4, all_0_3_3) = all_30_1_38
% 15.44/4.25 |
% 15.44/4.25 +-Applying beta-rule and splitting (369), into two cases.
% 15.44/4.25 |-Branch one:
% 15.44/4.25 | (336) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (71) with all_0_4_4, all_0_3_3, all_30_1_38, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_30_1_38, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 15.44/4.25 | (386) all_30_1_38 = all_26_1_33
% 15.44/4.25 |
% 15.44/4.25 | Equations (386) can reduce 383 to:
% 15.44/4.25 | (141) ~ (all_26_1_33 = 0)
% 15.44/4.25 |
% 15.44/4.25 | From (386) and (384) follows:
% 15.44/4.25 | (142) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 15.44/4.25 |
% 15.44/4.25 +-Applying beta-rule and splitting (181), into two cases.
% 15.44/4.25 |-Branch one:
% 15.44/4.25 | (389) (all_81_0_66 = 0 & all_81_1_67 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_81_1_67 = 0 & all_26_1_33 = 0)
% 15.44/4.25 |
% 15.44/4.25 +-Applying beta-rule and splitting (389), into two cases.
% 15.44/4.25 |-Branch one:
% 15.44/4.25 | (390) all_81_0_66 = 0 & all_81_1_67 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (390) yields:
% 15.44/4.25 | (391) all_81_0_66 = 0
% 15.44/4.25 | (392) all_81_1_67 = 0
% 15.44/4.25 | (374) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 15.44/4.25 | (375) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (73) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 15.44/4.25 | (342) $false
% 15.44/4.25 |
% 15.44/4.25 |-The branch is then unsatisfiable
% 15.44/4.25 |-Branch two:
% 15.44/4.25 | (396) all_81_1_67 = 0 & all_26_1_33 = 0
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (396) yields:
% 15.44/4.25 | (392) all_81_1_67 = 0
% 15.44/4.25 | (130) all_26_1_33 = 0
% 15.44/4.25 |
% 15.44/4.25 | Equations (130) can reduce 141 to:
% 15.44/4.25 | (107) $false
% 15.44/4.25 |
% 15.44/4.25 |-The branch is then unsatisfiable
% 15.44/4.25 |-Branch two:
% 15.44/4.25 | (400) ~ (all_81_1_67 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_81_1_67
% 15.44/4.25 |
% 15.44/4.25 | Applying alpha-rule on (400) yields:
% 15.44/4.25 | (401) ~ (all_81_1_67 = 0)
% 15.44/4.25 | (402) convergent_lines(all_0_4_4, all_0_3_3) = all_81_1_67
% 15.44/4.25 |
% 15.44/4.25 | Instantiating formula (71) with all_0_4_4, all_0_3_3, all_81_1_67, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_81_1_67, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 15.44/4.25 | (403) all_81_1_67 = all_26_1_33
% 15.44/4.25 |
% 15.44/4.25 | Equations (403) can reduce 401 to:
% 15.44/4.25 | (141) ~ (all_26_1_33 = 0)
% 15.44/4.25 |
% 15.44/4.25 | From (403) and (402) follows:
% 15.44/4.26 | (142) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 15.44/4.26 |
% 15.44/4.26 | Instantiating formula (41) with all_26_1_33, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 15.44/4.26 | (406) all_26_1_33 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0
% 15.44/4.26 |
% 15.44/4.26 +-Applying beta-rule and splitting (406), into two cases.
% 15.44/4.26 |-Branch one:
% 15.44/4.26 | (375) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 15.44/4.26 |
% 15.44/4.26 | Instantiating formula (73) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 15.44/4.26 | (342) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 |-Branch two:
% 15.44/4.26 | (409) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0)
% 15.44/4.26 | (130) all_26_1_33 = 0
% 15.44/4.26 |
% 15.44/4.26 | Equations (130) can reduce 141 to:
% 15.44/4.26 | (107) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 |-Branch two:
% 15.44/4.26 | (412) ~ (convergent_lines(all_0_3_3, all_0_4_4) = 0)
% 15.44/4.26 | (319) all_27_0_34 = 0
% 15.44/4.26 |
% 15.44/4.26 | Equations (319) can reduce 329 to:
% 15.44/4.26 | (107) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 |-Branch two:
% 15.44/4.26 | (415) ~ (all_27_0_34 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_27_0_34
% 15.44/4.26 |
% 15.44/4.26 | Applying alpha-rule on (415) yields:
% 15.44/4.26 | (329) ~ (all_27_0_34 = 0)
% 15.44/4.26 | (417) convergent_lines(all_0_3_3, all_0_4_4) = all_27_0_34
% 15.44/4.26 |
% 15.44/4.26 | Instantiating formula (45) with all_27_0_34, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_3_3, all_0_4_4) = all_27_0_34, yields:
% 15.44/4.26 | (418) all_27_0_34 = 0 | convergent_lines(all_0_2_2, all_0_4_4) = 0
% 15.44/4.26 |
% 15.44/4.26 +-Applying beta-rule and splitting (418), into two cases.
% 15.44/4.26 |-Branch one:
% 15.44/4.26 | (419) convergent_lines(all_0_2_2, all_0_4_4) = 0
% 15.44/4.26 |
% 15.44/4.26 | Instantiating formula (41) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 15.44/4.26 | (420) all_0_1_1 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 15.44/4.26 |
% 15.44/4.26 +-Applying beta-rule and splitting (420), into two cases.
% 15.44/4.26 |-Branch one:
% 15.44/4.26 | (421) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 15.44/4.26 |
% 15.44/4.26 | Instantiating formula (73) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 15.44/4.26 | (342) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 |-Branch two:
% 15.44/4.26 | (423) ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 15.44/4.26 | (106) all_0_1_1 = 0
% 15.44/4.26 |
% 15.44/4.26 | Equations (106) can reduce 63 to:
% 15.44/4.26 | (107) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 |-Branch two:
% 15.44/4.26 | (426) ~ (convergent_lines(all_0_2_2, all_0_4_4) = 0)
% 15.44/4.26 | (319) all_27_0_34 = 0
% 15.44/4.26 |
% 15.44/4.26 | Equations (319) can reduce 329 to:
% 15.44/4.26 | (107) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 |-Branch two:
% 15.44/4.26 | (429) ~ (unorthogonal_lines(all_0_4_4, all_0_4_4) = 0)
% 15.44/4.26 | (230) all_47_0_44 = 0
% 15.44/4.26 |
% 15.44/4.26 | Equations (230) can reduce 125 to:
% 15.44/4.26 | (107) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 |-Branch two:
% 15.44/4.26 | (432) ~ (unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 15.44/4.26 | (106) all_0_1_1 = 0
% 15.44/4.26 |
% 15.44/4.26 | Equations (106) can reduce 63 to:
% 15.44/4.26 | (107) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 |-Branch two:
% 15.44/4.26 | (435) ~ (convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 15.44/4.26 | (114) all_0_0_0 = 0
% 15.44/4.26 |
% 15.44/4.26 | Equations (114) can reduce 60 to:
% 15.44/4.26 | (107) $false
% 15.44/4.26 |
% 15.44/4.26 |-The branch is then unsatisfiable
% 15.44/4.26 % SZS output end Proof for theBenchmark
% 15.44/4.26
% 15.44/4.26 3586ms
%------------------------------------------------------------------------------