TSTP Solution File: GEO217+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO217+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 03:48:50 EDT 2022
% Result : Theorem 6.61s 2.21s
% Output : Proof 35.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO217+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jun 17 19:04:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.60/0.57 ____ _
% 0.60/0.57 ___ / __ \_____(_)___ ________ __________
% 0.60/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.57
% 0.60/0.57 A Theorem Prover for First-Order Logic
% 0.60/0.57 (ePrincess v.1.0)
% 0.60/0.57
% 0.60/0.57 (c) Philipp Rümmer, 2009-2015
% 0.60/0.57 (c) Peter Backeman, 2014-2015
% 0.60/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.57 Bug reports to peter@backeman.se
% 0.60/0.57
% 0.60/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.57
% 0.60/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.95 Prover 0: Preprocessing ...
% 2.10/1.10 Prover 0: Warning: ignoring some quantifiers
% 2.10/1.12 Prover 0: Constructing countermodel ...
% 4.26/1.65 Prover 0: gave up
% 4.26/1.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.26/1.67 Prover 1: Preprocessing ...
% 4.52/1.76 Prover 1: Constructing countermodel ...
% 4.93/1.78 Prover 1: gave up
% 4.93/1.79 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.00/1.81 Prover 2: Preprocessing ...
% 5.58/1.95 Prover 2: Warning: ignoring some quantifiers
% 5.58/1.96 Prover 2: Constructing countermodel ...
% 6.61/2.21 Prover 2: proved (426ms)
% 6.61/2.21
% 6.61/2.21 No countermodel exists, formula is valid
% 6.61/2.21 % SZS status Theorem for theBenchmark
% 6.61/2.21
% 6.61/2.21 Generating proof ... Warning: ignoring some quantifiers
% 34.32/13.47 found it (size 262)
% 34.32/13.47
% 34.32/13.47 % SZS output start Proof for theBenchmark
% 34.32/13.47 Assumed formulas after preprocessing and simplification:
% 34.32/13.47 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & convergent_lines(v1, v2) = 0 & convergent_lines(v0, v2) = v4 & convergent_lines(v0, v1) = v3 & ! [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 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10)) & ! [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) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = 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 | ~ (convergent_lines(v5, v7) = v9) | ~ (distinct_lines(v6, 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] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (convergent_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v5, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v5, v7) = v9) | ~ (convergent_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = 0) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = 0) | unorthogonal_lines(v5, v7) = 0) & ! [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, 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 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | convergent_lines(v5, 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 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(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) = 0) | ~ (unorthogonal_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = 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] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v6) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v5) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v6, v7) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : unorthogonal_lines(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)
% 34.48/13.54 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 34.48/13.54 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0 & convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & ! [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 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [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) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = 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 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, 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] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [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, 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 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, 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 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(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) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = 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] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(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
% 34.68/13.57 |
% 34.68/13.57 | Applying alpha-rule on (1) yields:
% 34.68/13.57 | (2) ~ (all_0_1_1 = 0)
% 34.68/13.57 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 34.68/13.57 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 34.68/13.57 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 34.68/13.57 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 34.68/13.57 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 34.68/13.57 | (8) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 34.68/13.57 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 34.68/13.57 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 34.68/13.57 | (11) convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1
% 34.68/13.57 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 34.68/13.57 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 34.68/13.57 | (14) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 34.68/13.57 | (15) ! [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)))
% 34.68/13.57 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 34.68/13.57 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 34.68/13.57 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 34.68/13.58 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 34.68/13.58 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 34.68/13.58 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 34.68/13.58 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 34.68/13.58 | (23) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 34.68/13.58 | (24) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 34.68/13.58 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 34.68/13.58 | (26) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 34.68/13.58 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 34.68/13.58 | (28) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 34.68/13.58 | (29) ! [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)))
% 34.68/13.58 | (30) ! [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))
% 34.68/13.58 | (31) ~ (all_0_0_0 = 0)
% 34.68/13.58 | (32) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 34.68/13.58 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 34.68/13.58 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 34.68/13.58 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 34.68/13.58 | (36) ! [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)
% 34.68/13.58 | (37) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 34.68/13.58 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 34.68/13.58 | (39) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 34.68/13.58 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 34.68/13.58 | (41) ! [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)))
% 34.68/13.58 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 34.68/13.59 | (43) ! [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)))
% 34.68/13.59 | (44) convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0
% 34.68/13.59 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 34.68/13.59 | (46) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 34.68/13.59 | (47) ! [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)
% 34.68/13.59 | (48) ! [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)))
% 34.68/13.59 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 34.68/13.59 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 34.68/13.59 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 34.68/13.59 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 34.68/13.59 | (53) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 34.68/13.59 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 34.68/13.59 | (55) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 34.68/13.59 | (56) ! [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)))
% 34.68/13.59 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 34.68/13.59 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 34.68/13.59 | (59) ! [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))
% 34.68/13.59 | (60) ! [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))
% 34.68/13.59 | (61) ! [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)
% 34.68/13.59 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 34.68/13.59 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 34.68/13.59 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 34.68/13.59 | (65) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 34.68/13.60 | (66) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 34.68/13.60 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 34.68/13.60 | (68) ! [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))
% 34.68/13.60 | (69) ! [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)))
% 34.68/13.60 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 34.68/13.60 | (71) ! [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))
% 34.68/13.60 | (72) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 34.68/13.60 | (73) ! [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)
% 34.68/13.60 |
% 34.68/13.60 | Instantiating formula (12) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 34.68/13.60 | (74) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0))
% 34.68/13.60 |
% 34.68/13.60 | Instantiating formula (30) with all_0_0_0, all_0_0_0, 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_0_0, yields:
% 34.68/13.60 | (75) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 34.68/13.60 |
% 34.68/13.60 | Instantiating formula (35) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 34.68/13.60 | (76) ? [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_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0))
% 34.68/13.60 |
% 34.68/13.60 | Instantiating formula (42) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 34.68/13.60 | (77) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 34.68/13.60 |
% 34.68/13.60 | Instantiating formula (42) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 34.68/13.60 | (78) ? [v0] : ((v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0))
% 34.68/13.60 |
% 34.68/13.60 | Instantiating formula (62) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 34.68/13.60 | (79) all_0_1_1 = 0 | unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.60 |
% 34.68/13.60 | Instantiating (78) with all_22_0_26 yields:
% 34.68/13.60 | (80) (all_22_0_26 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_22_0_26) | ( ~ (all_22_0_26 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_22_0_26)
% 34.68/13.60 |
% 34.68/13.60 | Instantiating (74) with all_24_0_28, all_24_1_29 yields:
% 34.68/13.60 | (81) (all_24_0_28 = 0 & all_24_1_29 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_24_1_29 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_24_1_29 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_1_29)
% 34.68/13.60 |
% 34.68/13.60 | Instantiating (77) with all_30_0_35 yields:
% 34.68/13.60 | (82) (all_30_0_35 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_30_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_30_0_35 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_30_0_35) | ( ~ (all_30_0_35 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_30_0_35)
% 34.68/13.60 |
% 34.68/13.60 | Instantiating (76) with all_32_0_37, all_32_1_38 yields:
% 34.68/13.60 | (83) (all_32_0_37 = 0 & all_32_1_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_32_1_38 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_32_1_38 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_32_1_38)
% 34.68/13.60 |
% 34.68/13.60 +-Applying beta-rule and splitting (83), into two cases.
% 34.68/13.60 |-Branch one:
% 34.68/13.60 | (84) (all_32_0_37 = 0 & all_32_1_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_32_1_38 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0)
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (84), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (85) all_32_0_37 = 0 & all_32_1_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 34.68/13.61 |
% 34.68/13.61 | Applying alpha-rule on (85) yields:
% 34.68/13.61 | (86) all_32_0_37 = 0
% 34.68/13.61 | (87) all_32_1_38 = 0
% 34.68/13.61 | (88) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 34.68/13.61 | (89) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (75), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (90) all_0_0_0 = 0
% 34.68/13.61 |
% 34.68/13.61 | Equations (90) can reduce 31 to:
% 34.68/13.61 | (91) $false
% 34.68/13.61 |
% 34.68/13.61 |-The branch is then unsatisfiable
% 34.68/13.61 |-Branch two:
% 34.68/13.61 | (31) ~ (all_0_0_0 = 0)
% 34.68/13.61 | (93) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 34.68/13.61 |
% 34.68/13.61 | Instantiating formula (6) with all_0_4_4, all_0_2_2, 0, all_0_0_0 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 34.68/13.61 | (90) all_0_0_0 = 0
% 34.68/13.61 |
% 34.68/13.61 | Equations (90) can reduce 31 to:
% 34.68/13.61 | (91) $false
% 34.68/13.61 |
% 34.68/13.61 |-The branch is then unsatisfiable
% 34.68/13.61 |-Branch two:
% 34.68/13.61 | (96) all_32_1_38 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.61 |
% 34.68/13.61 | Applying alpha-rule on (96) yields:
% 34.68/13.61 | (87) all_32_1_38 = 0
% 34.68/13.61 | (98) all_0_1_1 = 0
% 34.68/13.61 | (99) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.61 |
% 34.68/13.61 | Equations (98) can reduce 2 to:
% 34.68/13.61 | (91) $false
% 34.68/13.61 |
% 34.68/13.61 |-The branch is then unsatisfiable
% 34.68/13.61 |-Branch two:
% 34.68/13.61 | (101) ~ (all_32_1_38 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_32_1_38
% 34.68/13.61 |
% 34.68/13.61 | Applying alpha-rule on (101) yields:
% 34.68/13.61 | (102) ~ (all_32_1_38 = 0)
% 34.68/13.61 | (103) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_32_1_38
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (75), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (90) all_0_0_0 = 0
% 34.68/13.61 |
% 34.68/13.61 | Equations (90) can reduce 31 to:
% 34.68/13.61 | (91) $false
% 34.68/13.61 |
% 34.68/13.61 |-The branch is then unsatisfiable
% 34.68/13.61 |-Branch two:
% 34.68/13.61 | (31) ~ (all_0_0_0 = 0)
% 34.68/13.61 | (93) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 34.68/13.61 |
% 34.68/13.61 | Instantiating (93) with all_45_0_42 yields:
% 34.68/13.61 | (108) ~ (all_45_0_42 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_45_0_42
% 34.68/13.61 |
% 34.68/13.61 | Applying alpha-rule on (108) yields:
% 34.68/13.61 | (109) ~ (all_45_0_42 = 0)
% 34.68/13.61 | (110) convergent_lines(all_0_4_4, all_0_4_4) = all_45_0_42
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (79), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (99) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (81), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (112) (all_24_0_28 = 0 & all_24_1_29 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_24_1_29 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (112), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (113) all_24_0_28 = 0 & all_24_1_29 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.61 |
% 34.68/13.61 | Applying alpha-rule on (113) yields:
% 34.68/13.61 | (114) all_24_0_28 = 0
% 34.68/13.61 | (115) all_24_1_29 = 0
% 34.68/13.61 | (99) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.61 | (117) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.61 |
% 34.68/13.61 | Instantiating formula (6) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 34.68/13.61 | (98) all_0_1_1 = 0
% 34.68/13.61 |
% 34.68/13.61 | Equations (98) can reduce 2 to:
% 34.68/13.61 | (91) $false
% 34.68/13.61 |
% 34.68/13.61 |-The branch is then unsatisfiable
% 34.68/13.61 |-Branch two:
% 34.68/13.61 | (120) all_24_1_29 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 34.68/13.61 |
% 34.68/13.61 | Applying alpha-rule on (120) yields:
% 34.68/13.61 | (115) all_24_1_29 = 0
% 34.68/13.61 | (90) all_0_0_0 = 0
% 34.68/13.61 | (88) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 34.68/13.61 |
% 34.68/13.61 | Equations (90) can reduce 31 to:
% 34.68/13.61 | (91) $false
% 34.68/13.61 |
% 34.68/13.61 |-The branch is then unsatisfiable
% 34.68/13.61 |-Branch two:
% 34.68/13.61 | (125) ~ (all_24_1_29 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_1_29
% 34.68/13.61 |
% 34.68/13.61 | Applying alpha-rule on (125) yields:
% 34.68/13.61 | (126) ~ (all_24_1_29 = 0)
% 34.68/13.61 | (127) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_1_29
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (82), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (128) (all_30_0_35 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_30_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_30_0_35 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_30_0_35)
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (128), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (129) (all_30_0_35 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_30_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0)
% 34.68/13.61 |
% 34.68/13.61 +-Applying beta-rule and splitting (129), into two cases.
% 34.68/13.61 |-Branch one:
% 34.68/13.61 | (130) all_30_0_35 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 34.68/13.61 |
% 34.68/13.61 | Applying alpha-rule on (130) yields:
% 34.68/13.61 | (131) all_30_0_35 = 0
% 34.68/13.62 | (90) all_0_0_0 = 0
% 34.68/13.62 | (88) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 34.68/13.62 |
% 34.68/13.62 | Equations (90) can reduce 31 to:
% 34.68/13.62 | (91) $false
% 34.68/13.62 |
% 34.68/13.62 |-The branch is then unsatisfiable
% 34.68/13.62 |-Branch two:
% 34.68/13.62 | (135) all_30_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.62 |
% 34.68/13.62 | Applying alpha-rule on (135) yields:
% 34.68/13.62 | (131) all_30_0_35 = 0
% 34.68/13.62 | (98) all_0_1_1 = 0
% 34.68/13.62 | (99) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.62 |
% 34.68/13.62 | Equations (98) can reduce 2 to:
% 34.68/13.62 | (91) $false
% 34.68/13.62 |
% 34.68/13.62 |-The branch is then unsatisfiable
% 34.68/13.62 |-Branch two:
% 34.68/13.62 | (140) ~ (all_30_0_35 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_30_0_35
% 34.68/13.62 |
% 34.68/13.62 | Applying alpha-rule on (140) yields:
% 34.68/13.62 | (141) ~ (all_30_0_35 = 0)
% 34.68/13.62 | (142) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_30_0_35
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (40) with all_0_3_3, all_0_2_2, all_30_0_35, all_32_1_38 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_32_1_38, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_30_0_35, yields:
% 34.68/13.62 | (143) all_32_1_38 = all_30_0_35
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (40) with all_0_3_3, all_0_2_2, all_24_1_29, all_32_1_38 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_32_1_38, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_1_29, yields:
% 34.68/13.62 | (144) all_32_1_38 = all_24_1_29
% 34.68/13.62 |
% 34.68/13.62 | Combining equations (143,144) yields a new equation:
% 34.68/13.62 | (145) all_30_0_35 = all_24_1_29
% 34.68/13.62 |
% 34.68/13.62 | Simplifying 145 yields:
% 34.68/13.62 | (146) all_30_0_35 = all_24_1_29
% 34.68/13.62 |
% 34.68/13.62 | Equations (146) can reduce 141 to:
% 34.68/13.62 | (126) ~ (all_24_1_29 = 0)
% 34.68/13.62 |
% 34.68/13.62 | From (146) and (142) follows:
% 34.68/13.62 | (127) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_1_29
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (3) with all_24_1_29, all_24_1_29, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_1_29, yields:
% 34.68/13.62 | (149) all_24_1_29 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (58) with all_24_1_29, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_1_29, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 34.68/13.62 | (150) all_24_1_29 = 0 | unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (4) with 0, 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:
% 34.68/13.62 | (151) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0))
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (45) with 0, all_0_1_1, 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_0_1_1, yields:
% 34.68/13.62 | (152) ? [v0] : ((v0 = 0 & all_0_1_1 = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0))
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (42) with all_45_0_42, all_45_0_42, 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_45_0_42, yields:
% 34.68/13.62 | (153) ? [v0] : ((v0 = 0 & all_45_0_42 = 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))
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (9) with all_45_0_42, 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, convergent_lines(all_0_4_4, all_0_4_4) = all_45_0_42, yields:
% 34.68/13.62 | (154) ? [v0] : ((v0 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 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))
% 34.68/13.62 |
% 34.68/13.62 | Instantiating formula (62) with all_45_0_42, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_45_0_42, yields:
% 34.68/13.62 | (155) all_45_0_42 = 0 | unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 34.68/13.62 |
% 34.68/13.62 | Instantiating (154) with all_68_0_43 yields:
% 34.68/13.62 | (156) (all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_68_0_43 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43) | ( ~ (all_68_0_43 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43)
% 34.68/13.62 |
% 34.68/13.62 | Instantiating (153) with all_78_0_54 yields:
% 34.68/13.62 | (157) (all_78_0_54 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_78_0_54 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_78_0_54) | ( ~ (all_78_0_54 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_78_0_54)
% 34.68/13.62 |
% 34.68/13.62 | Instantiating (152) with all_79_0_55 yields:
% 34.68/13.62 | (158) (all_79_0_55 = 0 & all_0_1_1 = 0) | (all_79_0_55 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_79_0_55 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_79_0_55) | ( ~ (all_79_0_55 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_79_0_55)
% 34.68/13.62 |
% 34.68/13.62 | Instantiating (151) with all_81_0_57 yields:
% 34.68/13.62 | (159) (all_81_0_57 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_81_0_57 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_81_0_57) | ( ~ (all_81_0_57 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_81_0_57)
% 34.68/13.62 |
% 34.68/13.62 +-Applying beta-rule and splitting (80), into two cases.
% 34.68/13.62 |-Branch one:
% 34.68/13.63 | (160) (all_22_0_26 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_22_0_26)
% 34.68/13.63 |
% 34.68/13.63 +-Applying beta-rule and splitting (160), into two cases.
% 34.68/13.63 |-Branch one:
% 34.68/13.63 | (161) all_22_0_26 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.63 |
% 34.68/13.63 | Applying alpha-rule on (161) yields:
% 34.68/13.63 | (162) all_22_0_26 = 0
% 34.68/13.63 | (98) all_0_1_1 = 0
% 34.68/13.63 | (99) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.63 |
% 34.68/13.63 | Equations (98) can reduce 2 to:
% 34.68/13.63 | (91) $false
% 34.68/13.63 |
% 34.68/13.63 |-The branch is then unsatisfiable
% 34.68/13.63 |-Branch two:
% 34.68/13.63 | (166) ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_22_0_26
% 34.68/13.63 |
% 34.68/13.63 | Applying alpha-rule on (166) yields:
% 34.68/13.63 | (167) ~ (all_22_0_26 = 0)
% 34.68/13.63 | (168) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_22_0_26
% 34.68/13.63 |
% 34.68/13.63 +-Applying beta-rule and splitting (150), into two cases.
% 34.68/13.63 |-Branch one:
% 34.68/13.63 | (169) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 34.68/13.63 |
% 34.68/13.63 | Instantiating formula (40) with all_0_3_3, all_0_3_3, 0, all_22_0_26 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_22_0_26, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 34.68/13.63 | (162) all_22_0_26 = 0
% 34.68/13.63 |
% 34.68/13.63 | Equations (162) can reduce 167 to:
% 34.68/13.63 | (91) $false
% 34.68/13.63 |
% 34.68/13.63 |-The branch is then unsatisfiable
% 34.68/13.63 |-Branch two:
% 34.68/13.63 | (172) ~ (unorthogonal_lines(all_0_3_3, all_0_3_3) = 0)
% 34.68/13.63 | (115) all_24_1_29 = 0
% 34.68/13.63 |
% 34.68/13.63 | Equations (115) can reduce 126 to:
% 34.68/13.63 | (91) $false
% 34.68/13.63 |
% 34.68/13.63 |-The branch is then unsatisfiable
% 34.68/13.63 |-Branch two:
% 34.68/13.63 | (175) ~ (all_22_0_26 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_22_0_26
% 34.68/13.63 |
% 34.68/13.63 | Applying alpha-rule on (175) yields:
% 34.68/13.63 | (167) ~ (all_22_0_26 = 0)
% 34.68/13.63 | (177) convergent_lines(all_0_3_3, all_0_3_3) = all_22_0_26
% 34.68/13.63 |
% 34.68/13.63 +-Applying beta-rule and splitting (155), into two cases.
% 34.68/13.63 |-Branch one:
% 34.68/13.63 | (178) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 34.68/13.63 |
% 34.68/13.63 +-Applying beta-rule and splitting (150), into two cases.
% 34.68/13.63 |-Branch one:
% 34.68/13.63 | (169) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 34.68/13.63 |
% 34.68/13.63 +-Applying beta-rule and splitting (157), into two cases.
% 34.68/13.63 |-Branch one:
% 34.68/13.63 | (180) (all_78_0_54 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_78_0_54 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_78_0_54)
% 34.68/13.63 |
% 34.68/13.63 +-Applying beta-rule and splitting (180), into two cases.
% 34.68/13.63 |-Branch one:
% 34.68/13.63 | (181) all_78_0_54 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 34.68/13.63 |
% 34.68/13.63 | Applying alpha-rule on (181) yields:
% 34.68/13.63 | (182) all_78_0_54 = 0
% 34.68/13.63 | (183) all_45_0_42 = 0
% 34.68/13.63 | (178) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 34.68/13.63 |
% 34.68/13.63 | Equations (183) can reduce 109 to:
% 34.68/13.63 | (91) $false
% 34.68/13.63 |
% 34.68/13.63 |-The branch is then unsatisfiable
% 34.68/13.63 |-Branch two:
% 34.68/13.63 | (186) ~ (all_78_0_54 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_78_0_54
% 34.68/13.63 |
% 34.68/13.63 | Applying alpha-rule on (186) yields:
% 34.68/13.63 | (187) ~ (all_78_0_54 = 0)
% 34.68/13.63 | (188) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_78_0_54
% 34.68/13.63 |
% 34.68/13.63 | Instantiating formula (40) with all_0_4_4, all_0_4_4, 0, all_78_0_54 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_78_0_54, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 34.68/13.63 | (182) all_78_0_54 = 0
% 34.68/13.63 |
% 34.68/13.63 | Equations (182) can reduce 187 to:
% 34.68/13.63 | (91) $false
% 34.68/13.63 |
% 34.68/13.63 |-The branch is then unsatisfiable
% 34.68/13.63 |-Branch two:
% 34.68/13.63 | (191) ~ (all_78_0_54 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_78_0_54
% 34.68/13.63 |
% 34.68/13.63 | Applying alpha-rule on (191) yields:
% 34.68/13.63 | (187) ~ (all_78_0_54 = 0)
% 34.68/13.63 | (193) convergent_lines(all_0_4_4, all_0_4_4) = all_78_0_54
% 34.68/13.63 |
% 34.68/13.63 +-Applying beta-rule and splitting (159), into two cases.
% 34.68/13.63 |-Branch one:
% 34.68/13.63 | (194) (all_81_0_57 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_81_0_57 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_81_0_57)
% 34.68/13.63 |
% 34.68/13.63 +-Applying beta-rule and splitting (194), into two cases.
% 34.68/13.63 |-Branch one:
% 34.68/13.63 | (195) all_81_0_57 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.63 |
% 34.68/13.63 | Applying alpha-rule on (195) yields:
% 34.68/13.63 | (196) all_81_0_57 = 0
% 34.68/13.63 | (117) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 34.68/13.64 |
% 34.68/13.64 | Instantiating formula (6) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 34.68/13.64 | (98) all_0_1_1 = 0
% 34.68/13.64 |
% 34.68/13.64 | Equations (98) can reduce 2 to:
% 34.68/13.64 | (91) $false
% 34.68/13.64 |
% 34.68/13.64 |-The branch is then unsatisfiable
% 34.68/13.64 |-Branch two:
% 34.68/13.64 | (200) ~ (all_81_0_57 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_81_0_57
% 34.68/13.64 |
% 34.68/13.64 | Applying alpha-rule on (200) yields:
% 34.68/13.64 | (201) ~ (all_81_0_57 = 0)
% 34.68/13.64 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_81_0_57
% 34.68/13.64 |
% 34.68/13.64 | Instantiating formula (40) with all_0_3_3, all_0_3_3, 0, all_81_0_57 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_81_0_57, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 34.68/13.64 | (196) all_81_0_57 = 0
% 34.68/13.64 |
% 34.68/13.64 | Equations (196) can reduce 201 to:
% 34.68/13.64 | (91) $false
% 34.68/13.64 |
% 34.68/13.64 |-The branch is then unsatisfiable
% 34.68/13.64 |-Branch two:
% 34.68/13.64 | (205) ~ (all_81_0_57 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_81_0_57
% 34.68/13.64 |
% 34.68/13.64 | Applying alpha-rule on (205) yields:
% 34.68/13.64 | (201) ~ (all_81_0_57 = 0)
% 34.68/13.64 | (207) convergent_lines(all_0_3_3, all_0_3_3) = all_81_0_57
% 34.68/13.64 |
% 34.68/13.64 +-Applying beta-rule and splitting (149), into two cases.
% 34.68/13.64 |-Branch one:
% 34.68/13.64 | (115) all_24_1_29 = 0
% 34.68/13.64 |
% 34.68/13.64 | Equations (115) can reduce 126 to:
% 34.68/13.64 | (91) $false
% 34.68/13.64 |
% 34.68/13.64 |-The branch is then unsatisfiable
% 34.68/13.64 |-Branch two:
% 34.68/13.64 | (126) ~ (all_24_1_29 = 0)
% 34.68/13.64 | (211) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 35.13/13.64 |
% 35.13/13.64 | Instantiating (211) with all_121_0_133 yields:
% 35.13/13.64 | (212) ~ (all_121_0_133 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = all_121_0_133
% 35.13/13.64 |
% 35.13/13.64 | Applying alpha-rule on (212) yields:
% 35.13/13.64 | (213) ~ (all_121_0_133 = 0)
% 35.13/13.64 | (214) convergent_lines(all_0_2_2, all_0_2_2) = all_121_0_133
% 35.13/13.64 |
% 35.13/13.64 +-Applying beta-rule and splitting (158), into two cases.
% 35.13/13.64 |-Branch one:
% 35.13/13.64 | (215) (all_79_0_55 = 0 & all_0_1_1 = 0) | (all_79_0_55 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_79_0_55 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_79_0_55)
% 35.13/13.64 |
% 35.13/13.64 +-Applying beta-rule and splitting (215), into two cases.
% 35.13/13.64 |-Branch one:
% 35.13/13.64 | (216) (all_79_0_55 = 0 & all_0_1_1 = 0) | (all_79_0_55 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 35.13/13.64 |
% 35.13/13.64 +-Applying beta-rule and splitting (216), into two cases.
% 35.13/13.64 |-Branch one:
% 35.13/13.64 | (217) all_79_0_55 = 0 & all_0_1_1 = 0
% 35.13/13.64 |
% 35.13/13.64 | Applying alpha-rule on (217) yields:
% 35.13/13.64 | (218) all_79_0_55 = 0
% 35.13/13.64 | (98) all_0_1_1 = 0
% 35.13/13.64 |
% 35.13/13.64 | Equations (98) can reduce 2 to:
% 35.13/13.64 | (91) $false
% 35.13/13.64 |
% 35.13/13.64 |-The branch is then unsatisfiable
% 35.13/13.64 |-Branch two:
% 35.13/13.64 | (221) all_79_0_55 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 35.13/13.64 |
% 35.13/13.64 | Applying alpha-rule on (221) yields:
% 35.13/13.64 | (218) all_79_0_55 = 0
% 35.13/13.64 | (117) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 35.13/13.64 |
% 35.13/13.64 | Instantiating formula (6) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 35.13/13.64 | (98) all_0_1_1 = 0
% 35.13/13.64 |
% 35.13/13.64 | Equations (98) can reduce 2 to:
% 35.13/13.64 | (91) $false
% 35.13/13.64 |
% 35.13/13.64 |-The branch is then unsatisfiable
% 35.13/13.64 |-Branch two:
% 35.13/13.64 | (226) ~ (all_79_0_55 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_79_0_55
% 35.13/13.64 |
% 35.13/13.64 | Applying alpha-rule on (226) yields:
% 35.13/13.64 | (227) ~ (all_79_0_55 = 0)
% 35.13/13.64 | (228) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_79_0_55
% 35.13/13.64 |
% 35.13/13.64 | Instantiating formula (40) with all_0_3_3, all_0_3_3, 0, all_79_0_55 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_79_0_55, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 35.13/13.64 | (218) all_79_0_55 = 0
% 35.13/13.64 |
% 35.13/13.64 | Equations (218) can reduce 227 to:
% 35.13/13.64 | (91) $false
% 35.13/13.64 |
% 35.13/13.64 |-The branch is then unsatisfiable
% 35.13/13.64 |-Branch two:
% 35.13/13.64 | (231) ~ (all_79_0_55 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_79_0_55
% 35.13/13.64 |
% 35.13/13.64 | Applying alpha-rule on (231) yields:
% 35.13/13.64 | (227) ~ (all_79_0_55 = 0)
% 35.13/13.64 | (233) convergent_lines(all_0_3_3, all_0_3_3) = all_79_0_55
% 35.13/13.64 |
% 35.13/13.64 | Instantiating formula (6) with all_0_3_3, all_0_3_3, all_79_0_55, all_81_0_57 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_81_0_57, convergent_lines(all_0_3_3, all_0_3_3) = all_79_0_55, yields:
% 35.13/13.64 | (234) all_81_0_57 = all_79_0_55
% 35.13/13.64 |
% 35.13/13.64 | Instantiating formula (6) with all_0_3_3, all_0_3_3, all_22_0_26, all_81_0_57 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_81_0_57, convergent_lines(all_0_3_3, all_0_3_3) = all_22_0_26, yields:
% 35.13/13.64 | (235) all_81_0_57 = all_22_0_26
% 35.13/13.64 |
% 35.13/13.64 | Instantiating formula (6) with all_0_4_4, all_0_4_4, all_78_0_54, all_45_0_42 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_78_0_54, convergent_lines(all_0_4_4, all_0_4_4) = all_45_0_42, yields:
% 35.13/13.64 | (236) all_78_0_54 = all_45_0_42
% 35.13/13.64 |
% 35.13/13.64 | Combining equations (234,235) yields a new equation:
% 35.13/13.64 | (237) all_79_0_55 = all_22_0_26
% 35.13/13.64 |
% 35.13/13.64 | Simplifying 237 yields:
% 35.13/13.64 | (238) all_79_0_55 = all_22_0_26
% 35.13/13.64 |
% 35.13/13.64 | Equations (238) can reduce 227 to:
% 35.13/13.64 | (167) ~ (all_22_0_26 = 0)
% 35.13/13.64 |
% 35.13/13.64 | Equations (236) can reduce 187 to:
% 35.13/13.64 | (109) ~ (all_45_0_42 = 0)
% 35.13/13.64 |
% 35.13/13.64 | From (238) and (233) follows:
% 35.13/13.64 | (177) convergent_lines(all_0_3_3, all_0_3_3) = all_22_0_26
% 35.13/13.64 |
% 35.13/13.64 | Instantiating formula (22) with 0, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 35.13/13.64 | (242) ? [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_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 35.13/13.64 |
% 35.13/13.64 | Instantiating formula (30) with all_0_0_0, all_121_0_133, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = all_121_0_133, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 35.13/13.65 | (243) all_121_0_133 = 0 | all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = v0)
% 35.13/13.65 |
% 35.13/13.65 | Instantiating formula (16) with all_22_0_26, all_0_3_3, 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_3_3) = all_22_0_26, yields:
% 35.13/13.65 | (244) all_22_0_26 = 0 | convergent_lines(all_0_2_2, all_0_3_3) = 0
% 35.13/13.65 |
% 35.13/13.65 | Instantiating formula (30) with all_0_1_1, all_22_0_26, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_22_0_26, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 35.13/13.65 | (245) all_22_0_26 = 0 | all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 35.13/13.65 |
% 35.13/13.65 | Instantiating formula (25) with all_22_0_26, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_3_3, all_0_3_3) = all_22_0_26, yields:
% 35.13/13.65 | (246) ? [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_22_0_26 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 35.13/13.65 |
% 35.13/13.65 | Instantiating (246) with all_152_0_139, all_152_1_140 yields:
% 35.13/13.65 | (247) (all_152_0_139 = 0 & all_152_1_140 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_152_1_140 = 0 & all_22_0_26 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_152_1_140 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_152_1_140)
% 35.13/13.65 |
% 35.13/13.65 | Instantiating (242) with all_158_0_147, all_158_1_148 yields:
% 35.13/13.65 | (248) (all_158_0_147 = 0 & all_158_1_148 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_158_1_148 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_158_1_148 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_158_1_148)
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (244), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (249) convergent_lines(all_0_2_2, all_0_3_3) = 0
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (245), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (162) all_22_0_26 = 0
% 35.13/13.65 |
% 35.13/13.65 | Equations (162) can reduce 167 to:
% 35.13/13.65 | (91) $false
% 35.13/13.65 |
% 35.13/13.65 |-The branch is then unsatisfiable
% 35.13/13.65 |-Branch two:
% 35.13/13.65 | (167) ~ (all_22_0_26 = 0)
% 35.13/13.65 | (253) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (243), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (254) all_121_0_133 = 0
% 35.13/13.65 |
% 35.13/13.65 | Equations (254) can reduce 213 to:
% 35.13/13.65 | (91) $false
% 35.13/13.65 |
% 35.13/13.65 |-The branch is then unsatisfiable
% 35.13/13.65 |-Branch two:
% 35.13/13.65 | (213) ~ (all_121_0_133 = 0)
% 35.13/13.65 | (257) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = v0)
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (253), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (98) all_0_1_1 = 0
% 35.13/13.65 |
% 35.13/13.65 | Equations (98) can reduce 2 to:
% 35.13/13.65 | (91) $false
% 35.13/13.65 |
% 35.13/13.65 |-The branch is then unsatisfiable
% 35.13/13.65 |-Branch two:
% 35.13/13.65 | (2) ~ (all_0_1_1 = 0)
% 35.13/13.65 | (261) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 35.13/13.65 |
% 35.13/13.65 | Instantiating (261) with all_248_0_634 yields:
% 35.13/13.65 | (262) ~ (all_248_0_634 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (262) yields:
% 35.13/13.65 | (263) ~ (all_248_0_634 = 0)
% 35.13/13.65 | (264) convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (247), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (265) (all_152_0_139 = 0 & all_152_1_140 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_152_1_140 = 0 & all_22_0_26 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0)
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (265), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (266) all_152_0_139 = 0 & all_152_1_140 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (266) yields:
% 35.13/13.65 | (267) all_152_0_139 = 0
% 35.13/13.65 | (268) all_152_1_140 = 0
% 35.13/13.65 | (269) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.65 | (270) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (156), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (271) (all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_68_0_43 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43)
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (271), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (272) (all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (272), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (273) all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (273) yields:
% 35.13/13.65 | (274) all_68_0_43 = 0
% 35.13/13.65 | (183) all_45_0_42 = 0
% 35.13/13.65 | (178) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 35.13/13.65 |
% 35.13/13.65 | Equations (183) can reduce 109 to:
% 35.13/13.65 | (91) $false
% 35.13/13.65 |
% 35.13/13.65 |-The branch is then unsatisfiable
% 35.13/13.65 |-Branch two:
% 35.13/13.65 | (278) all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (278) yields:
% 35.13/13.65 | (274) all_68_0_43 = 0
% 35.13/13.65 | (117) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 35.13/13.65 |
% 35.13/13.65 | Instantiating formula (6) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 35.13/13.65 | (98) all_0_1_1 = 0
% 35.13/13.65 |
% 35.13/13.65 | Equations (98) can reduce 2 to:
% 35.13/13.65 | (91) $false
% 35.13/13.65 |
% 35.13/13.65 |-The branch is then unsatisfiable
% 35.13/13.65 |-Branch two:
% 35.13/13.65 | (283) ~ (all_68_0_43 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (283) yields:
% 35.13/13.65 | (284) ~ (all_68_0_43 = 0)
% 35.13/13.65 | (285) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.65 |
% 35.13/13.65 | Instantiating formula (40) with all_0_3_3, all_0_4_4, 0, all_68_0_43 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 35.13/13.65 | (274) all_68_0_43 = 0
% 35.13/13.65 |
% 35.13/13.65 | Equations (274) can reduce 284 to:
% 35.13/13.65 | (91) $false
% 35.13/13.65 |
% 35.13/13.65 |-The branch is then unsatisfiable
% 35.13/13.65 |-Branch two:
% 35.13/13.65 | (288) ~ (all_68_0_43 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (288) yields:
% 35.13/13.65 | (284) ~ (all_68_0_43 = 0)
% 35.13/13.65 | (290) convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.65 |
% 35.13/13.65 | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_68_0_43, all_248_0_634 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634, convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43, yields:
% 35.13/13.65 | (291) all_248_0_634 = all_68_0_43
% 35.13/13.65 |
% 35.13/13.65 | Instantiating formula (6) with all_0_3_3, all_0_4_4, 0, all_248_0_634 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 35.13/13.65 | (292) all_248_0_634 = 0
% 35.13/13.65 |
% 35.13/13.65 | Combining equations (291,292) yields a new equation:
% 35.13/13.65 | (293) all_68_0_43 = 0
% 35.13/13.65 |
% 35.13/13.65 | Simplifying 293 yields:
% 35.13/13.65 | (274) all_68_0_43 = 0
% 35.13/13.65 |
% 35.13/13.65 | Equations (274) can reduce 284 to:
% 35.13/13.65 | (91) $false
% 35.13/13.65 |
% 35.13/13.65 |-The branch is then unsatisfiable
% 35.13/13.65 |-Branch two:
% 35.13/13.65 | (296) all_152_1_140 = 0 & all_22_0_26 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (296) yields:
% 35.13/13.65 | (268) all_152_1_140 = 0
% 35.13/13.65 | (162) all_22_0_26 = 0
% 35.13/13.65 | (169) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 35.13/13.65 |
% 35.13/13.65 | Equations (162) can reduce 167 to:
% 35.13/13.65 | (91) $false
% 35.13/13.65 |
% 35.13/13.65 |-The branch is then unsatisfiable
% 35.13/13.65 |-Branch two:
% 35.13/13.65 | (301) ~ (all_152_1_140 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_152_1_140
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (301) yields:
% 35.13/13.65 | (302) ~ (all_152_1_140 = 0)
% 35.13/13.65 | (303) convergent_lines(all_0_4_4, all_0_3_3) = all_152_1_140
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (248), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (304) (all_158_0_147 = 0 & all_158_1_148 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_158_1_148 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0)
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (304), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (305) all_158_0_147 = 0 & all_158_1_148 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.65 |
% 35.13/13.65 | Applying alpha-rule on (305) yields:
% 35.13/13.65 | (306) all_158_0_147 = 0
% 35.13/13.65 | (307) all_158_1_148 = 0
% 35.13/13.65 | (269) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.65 | (270) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.65 |
% 35.13/13.65 +-Applying beta-rule and splitting (156), into two cases.
% 35.13/13.65 |-Branch one:
% 35.13/13.65 | (271) (all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_68_0_43 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43)
% 35.13/13.66 |
% 35.13/13.66 +-Applying beta-rule and splitting (271), into two cases.
% 35.13/13.66 |-Branch one:
% 35.13/13.66 | (272) (all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 35.13/13.66 |
% 35.13/13.66 +-Applying beta-rule and splitting (272), into two cases.
% 35.13/13.66 |-Branch one:
% 35.13/13.66 | (273) all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (273) yields:
% 35.13/13.66 | (274) all_68_0_43 = 0
% 35.13/13.66 | (183) all_45_0_42 = 0
% 35.13/13.66 | (178) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (183) can reduce 109 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (278) all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (278) yields:
% 35.13/13.66 | (274) all_68_0_43 = 0
% 35.13/13.66 | (117) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_4_4, all_0_3_3, all_152_1_140, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_152_1_140, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 35.13/13.66 | (320) all_152_1_140 = all_0_1_1
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_4_4, all_0_3_3, 0, all_152_1_140 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_152_1_140, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 35.13/13.66 | (268) all_152_1_140 = 0
% 35.13/13.66 |
% 35.13/13.66 | Combining equations (320,268) yields a new equation:
% 35.13/13.66 | (322) all_0_1_1 = 0
% 35.13/13.66 |
% 35.13/13.66 | Simplifying 322 yields:
% 35.13/13.66 | (98) all_0_1_1 = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (98) can reduce 2 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (283) ~ (all_68_0_43 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (283) yields:
% 35.13/13.66 | (284) ~ (all_68_0_43 = 0)
% 35.13/13.66 | (285) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (40) with all_0_3_3, all_0_4_4, 0, all_68_0_43 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 35.13/13.66 | (274) all_68_0_43 = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (274) can reduce 284 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (288) ~ (all_68_0_43 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (288) yields:
% 35.13/13.66 | (284) ~ (all_68_0_43 = 0)
% 35.13/13.66 | (290) convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_68_0_43, all_248_0_634 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634, convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43, yields:
% 35.13/13.66 | (291) all_248_0_634 = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_3_3, all_0_4_4, 0, all_248_0_634 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 35.13/13.66 | (292) all_248_0_634 = 0
% 35.13/13.66 |
% 35.13/13.66 | Combining equations (291,292) yields a new equation:
% 35.13/13.66 | (293) all_68_0_43 = 0
% 35.13/13.66 |
% 35.13/13.66 | Simplifying 293 yields:
% 35.13/13.66 | (274) all_68_0_43 = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (274) can reduce 284 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (338) all_158_1_148 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (338) yields:
% 35.13/13.66 | (307) all_158_1_148 = 0
% 35.13/13.66 | (340) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (28) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 35.13/13.66 | (341) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (342) ~ (all_158_1_148 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_158_1_148
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (342) yields:
% 35.13/13.66 | (343) ~ (all_158_1_148 = 0)
% 35.13/13.66 | (344) convergent_lines(all_0_4_4, all_0_3_3) = all_158_1_148
% 35.13/13.66 |
% 35.13/13.66 +-Applying beta-rule and splitting (257), into two cases.
% 35.13/13.66 |-Branch one:
% 35.13/13.66 | (90) all_0_0_0 = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (90) can reduce 31 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (31) ~ (all_0_0_0 = 0)
% 35.13/13.66 | (348) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = v0)
% 35.13/13.66 |
% 35.13/13.66 | Instantiating (348) with all_274_0_650 yields:
% 35.13/13.66 | (349) ~ (all_274_0_650 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = all_274_0_650
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (349) yields:
% 35.13/13.66 | (350) ~ (all_274_0_650 = 0)
% 35.13/13.66 | (351) convergent_lines(all_0_2_2, all_0_4_4) = all_274_0_650
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_4_4, all_0_3_3, all_158_1_148, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_158_1_148, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 35.13/13.66 | (352) all_158_1_148 = all_0_1_1
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_4_4, all_0_3_3, all_152_1_140, all_158_1_148 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_158_1_148, convergent_lines(all_0_4_4, all_0_3_3) = all_152_1_140, yields:
% 35.13/13.66 | (353) all_158_1_148 = all_152_1_140
% 35.13/13.66 |
% 35.13/13.66 | Combining equations (353,352) yields a new equation:
% 35.13/13.66 | (354) all_152_1_140 = all_0_1_1
% 35.13/13.66 |
% 35.13/13.66 | Simplifying 354 yields:
% 35.13/13.66 | (320) all_152_1_140 = all_0_1_1
% 35.13/13.66 |
% 35.13/13.66 | Equations (320) can reduce 302 to:
% 35.13/13.66 | (2) ~ (all_0_1_1 = 0)
% 35.13/13.66 |
% 35.13/13.66 | From (320) and (303) follows:
% 35.13/13.66 | (11) convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (16) with all_274_0_650, all_0_4_4, all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = 0, convergent_lines(all_0_2_2, all_0_4_4) = all_274_0_650, yields:
% 35.13/13.66 | (358) all_274_0_650 = 0 | convergent_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (62) with all_248_0_634, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634, yields:
% 35.13/13.66 | (359) all_248_0_634 = 0 | unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.66 |
% 35.13/13.66 +-Applying beta-rule and splitting (358), into two cases.
% 35.13/13.66 |-Branch one:
% 35.13/13.66 | (270) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.66 |
% 35.13/13.66 +-Applying beta-rule and splitting (359), into two cases.
% 35.13/13.66 |-Branch one:
% 35.13/13.66 | (269) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 35.13/13.66 |
% 35.13/13.66 +-Applying beta-rule and splitting (156), into two cases.
% 35.13/13.66 |-Branch one:
% 35.13/13.66 | (271) (all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_68_0_43 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43)
% 35.13/13.66 |
% 35.13/13.66 +-Applying beta-rule and splitting (271), into two cases.
% 35.13/13.66 |-Branch one:
% 35.13/13.66 | (272) (all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 35.13/13.66 |
% 35.13/13.66 +-Applying beta-rule and splitting (272), into two cases.
% 35.13/13.66 |-Branch one:
% 35.13/13.66 | (273) all_68_0_43 = 0 & all_45_0_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (273) yields:
% 35.13/13.66 | (274) all_68_0_43 = 0
% 35.13/13.66 | (183) all_45_0_42 = 0
% 35.13/13.66 | (178) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (183) can reduce 109 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (278) all_68_0_43 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (278) yields:
% 35.13/13.66 | (274) all_68_0_43 = 0
% 35.13/13.66 | (117) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 35.13/13.66 | (98) all_0_1_1 = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (98) can reduce 2 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (283) ~ (all_68_0_43 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (283) yields:
% 35.13/13.66 | (284) ~ (all_68_0_43 = 0)
% 35.13/13.66 | (285) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (40) with all_0_3_3, all_0_4_4, 0, all_68_0_43 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_68_0_43, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 35.13/13.66 | (274) all_68_0_43 = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (274) can reduce 284 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (288) ~ (all_68_0_43 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Applying alpha-rule on (288) yields:
% 35.13/13.66 | (284) ~ (all_68_0_43 = 0)
% 35.13/13.66 | (290) convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_68_0_43, all_248_0_634 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634, convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_43, yields:
% 35.13/13.66 | (291) all_248_0_634 = all_68_0_43
% 35.13/13.66 |
% 35.13/13.66 | Instantiating formula (6) with all_0_3_3, all_0_4_4, 0, all_248_0_634 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_248_0_634, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 35.13/13.66 | (292) all_248_0_634 = 0
% 35.13/13.66 |
% 35.13/13.66 | Combining equations (291,292) yields a new equation:
% 35.13/13.66 | (293) all_68_0_43 = 0
% 35.13/13.66 |
% 35.13/13.66 | Simplifying 293 yields:
% 35.13/13.66 | (274) all_68_0_43 = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (274) can reduce 284 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (387) ~ (unorthogonal_lines(all_0_3_3, all_0_4_4) = 0)
% 35.13/13.66 | (292) all_248_0_634 = 0
% 35.13/13.66 |
% 35.13/13.66 | Equations (292) can reduce 263 to:
% 35.13/13.66 | (91) $false
% 35.13/13.66 |
% 35.13/13.66 |-The branch is then unsatisfiable
% 35.13/13.66 |-Branch two:
% 35.13/13.66 | (390) ~ (convergent_lines(all_0_3_3, all_0_4_4) = 0)
% 35.13/13.66 | (391) all_274_0_650 = 0
% 35.13/13.66 |
% 35.13/13.67 | Equations (391) can reduce 350 to:
% 35.13/13.67 | (91) $false
% 35.13/13.67 |
% 35.13/13.67 |-The branch is then unsatisfiable
% 35.13/13.67 |-Branch two:
% 35.13/13.67 | (393) ~ (convergent_lines(all_0_2_2, all_0_3_3) = 0)
% 35.13/13.67 | (162) all_22_0_26 = 0
% 35.13/13.67 |
% 35.13/13.67 | Equations (162) can reduce 167 to:
% 35.13/13.67 | (91) $false
% 35.13/13.67 |
% 35.13/13.67 |-The branch is then unsatisfiable
% 35.13/13.67 |-Branch two:
% 35.13/13.67 | (172) ~ (unorthogonal_lines(all_0_3_3, all_0_3_3) = 0)
% 35.13/13.67 | (115) all_24_1_29 = 0
% 35.13/13.67 |
% 35.13/13.67 | Equations (115) can reduce 126 to:
% 35.13/13.67 | (91) $false
% 35.13/13.67 |
% 35.13/13.67 |-The branch is then unsatisfiable
% 35.13/13.67 |-Branch two:
% 35.13/13.67 | (399) ~ (unorthogonal_lines(all_0_4_4, all_0_4_4) = 0)
% 35.13/13.67 | (183) all_45_0_42 = 0
% 35.13/13.67 |
% 35.13/13.67 | Equations (183) can reduce 109 to:
% 35.13/13.67 | (91) $false
% 35.13/13.67 |
% 35.13/13.67 |-The branch is then unsatisfiable
% 35.13/13.67 |-Branch two:
% 35.13/13.67 | (402) ~ (all_30_0_35 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_30_0_35
% 35.13/13.67 |
% 35.13/13.67 | Applying alpha-rule on (402) yields:
% 35.13/13.67 | (141) ~ (all_30_0_35 = 0)
% 35.13/13.67 | (404) convergent_lines(all_0_3_3, all_0_2_2) = all_30_0_35
% 35.13/13.67 |
% 35.13/13.67 | Instantiating formula (6) with all_0_3_3, all_0_2_2, all_30_0_35, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_30_0_35, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 35.13/13.67 | (131) all_30_0_35 = 0
% 35.13/13.67 |
% 35.13/13.67 | Equations (131) can reduce 141 to:
% 35.13/13.67 | (91) $false
% 35.13/13.67 |
% 35.13/13.67 |-The branch is then unsatisfiable
% 35.13/13.67 |-Branch two:
% 35.13/13.67 | (407) ~ (unorthogonal_lines(all_0_4_4, all_0_3_3) = 0)
% 35.13/13.67 | (98) all_0_1_1 = 0
% 35.13/13.67 |
% 35.13/13.67 | Equations (98) can reduce 2 to:
% 35.13/13.67 | (91) $false
% 35.13/13.67 |
% 35.13/13.67 |-The branch is then unsatisfiable
% 35.13/13.67 % SZS output end Proof for theBenchmark
% 35.13/13.67
% 35.13/13.67 13082ms
%------------------------------------------------------------------------------