TSTP Solution File: GEO195+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO195+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 03:48:32 EDT 2022
% Result : Theorem 47.91s 14.62s
% Output : Proof 64.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO195+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 04:51:02 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.57 ____ _
% 0.20/0.57 ___ / __ \_____(_)___ ________ __________
% 0.20/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.57
% 0.20/0.57 A Theorem Prover for First-Order Logic
% 0.20/0.57 (ePrincess v.1.0)
% 0.20/0.57
% 0.20/0.57 (c) Philipp Rümmer, 2009-2015
% 0.20/0.57 (c) Peter Backeman, 2014-2015
% 0.20/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.57 Bug reports to peter@backeman.se
% 0.20/0.57
% 0.20/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.57
% 0.59/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.82/0.95 Prover 0: Preprocessing ...
% 2.43/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.54/1.25 Prover 0: Constructing countermodel ...
% 19.11/5.91 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.40/5.97 Prover 1: Preprocessing ...
% 20.19/6.16 Prover 1: Constructing countermodel ...
% 20.45/6.22 Prover 1: gave up
% 20.45/6.22 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.45/6.25 Prover 2: Preprocessing ...
% 21.20/6.40 Prover 2: Warning: ignoring some quantifiers
% 21.20/6.41 Prover 2: Constructing countermodel ...
% 28.07/7.96 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.07/8.01 Prover 3: Preprocessing ...
% 28.07/8.04 Prover 3: Warning: ignoring some quantifiers
% 28.07/8.05 Prover 3: Constructing countermodel ...
% 39.07/12.32 Prover 3: gave up
% 39.07/12.32 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 39.07/12.34 Prover 4: Preprocessing ...
% 39.29/12.44 Prover 4: Warning: ignoring some quantifiers
% 39.29/12.44 Prover 4: Constructing countermodel ...
% 45.27/13.93 Prover 0: stopped
% 45.69/14.13 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 46.02/14.17 Prover 5: Preprocessing ...
% 46.25/14.25 Prover 5: Constructing countermodel ...
% 47.91/14.62 Prover 5: proved (488ms)
% 47.91/14.62 Prover 2: stopped
% 47.91/14.62 Prover 4: stopped
% 47.91/14.62
% 47.91/14.62 No countermodel exists, formula is valid
% 47.91/14.62 % SZS status Theorem for theBenchmark
% 47.91/14.62
% 47.91/14.62 Generating proof ... found it (size 482)
% 62.98/20.17
% 62.98/20.17 % SZS output start Proof for theBenchmark
% 62.98/20.17 Assumed formulas after preprocessing and simplification:
% 62.98/20.17 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [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] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [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] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [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) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ? [v6] : (convergent_lines(v1, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : (apart_point_and_line(v0, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [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(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [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, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v1) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 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 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & orthogonal_through_point(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & parallel_through_point(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (line(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (point(v3) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 & intersection_point(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) & ! [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] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & line_connecting(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) & ! [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] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v1, v0) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v2) = v5 & apart_point_and_line(v3, v2) = 0 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0)
% 63.47/20.26 | Applying alpha-rule on (0) yields:
% 63.47/20.26 | (1) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 63.47/20.26 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 63.47/20.26 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 63.47/20.26 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 63.47/20.26 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 63.47/20.26 | (6) ! [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)
% 63.47/20.26 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)))
% 63.47/20.27 | (8) ! [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))
% 63.47/20.27 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0)))
% 63.47/20.27 | (10) ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 63.47/20.27 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 63.47/20.27 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 63.47/20.27 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 63.47/20.27 | (14) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & parallel_through_point(v0, v1) = v2))
% 63.47/20.27 | (15) ! [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))
% 63.47/20.27 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0))))
% 63.47/20.27 | (17) ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 63.47/20.27 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 63.47/20.27 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 63.47/20.27 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 63.47/20.27 | (21) ! [v0] : ! [v1] : ( ~ (line(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (point(v3) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 63.47/20.27 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 63.47/20.27 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 63.47/20.27 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 63.47/20.27 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 63.47/20.27 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 63.47/20.27 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 63.47/20.27 | (28) ! [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)
% 63.47/20.27 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 63.47/20.27 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0))))
% 63.47/20.28 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 63.47/20.28 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 63.47/20.28 | (33) ! [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))
% 63.47/20.28 | (34) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 63.47/20.28 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 63.47/20.28 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)))
% 63.47/20.28 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 63.47/20.28 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 63.47/20.28 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 63.47/20.28 | (40) ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 63.47/20.28 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 63.47/20.28 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0))))
% 63.47/20.28 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 63.47/20.28 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 63.47/20.28 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 63.47/20.28 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 63.47/20.28 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 63.47/20.28 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 63.47/20.28 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 = 0 | v6 = 0)))
% 63.47/20.28 | (50) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 63.47/20.28 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0))))
% 63.47/20.28 | (52) ! [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] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 63.47/20.28 | (53) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & line_connecting(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0)))
% 63.47/20.29 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ? [v6] : (convergent_lines(v1, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 63.47/20.29 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 63.47/20.29 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 63.47/20.29 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0))))
% 63.47/20.29 | (58) ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 63.47/20.29 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 63.47/20.29 | (60) ! [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))
% 63.47/20.29 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 63.47/20.29 | (62) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 63.47/20.29 | (63) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 63.47/20.29 | (64) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 63.47/20.29 | (65) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 63.47/20.29 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 63.47/20.29 | (67) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v1, v0) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v2) = v5 & apart_point_and_line(v3, v2) = 0 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0)
% 63.47/20.29 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 63.47/20.29 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 63.47/20.29 | (70) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 63.47/20.29 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : (apart_point_and_line(v0, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 63.47/20.29 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 63.47/20.29 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v1) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0)))
% 63.47/20.29 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 63.47/20.29 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 63.47/20.29 | (76) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 63.47/20.29 | (77) ! [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)
% 63.47/20.29 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 63.47/20.29 | (79) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 63.47/20.29 | (80) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 63.47/20.29 | (81) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & orthogonal_through_point(v0, v1) = v2))
% 63.47/20.30 | (82) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 & intersection_point(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0)))
% 63.47/20.30 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 63.47/20.30 | (84) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 63.47/20.30 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 63.47/20.30 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0))))
% 63.47/20.30 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 63.47/20.30 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 63.47/20.30 | (89) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 63.47/20.30 | (90) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 63.47/20.30 | (91) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 63.47/20.30 | (92) ! [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))
% 63.47/20.30 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 63.47/20.30 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 63.47/20.30 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 63.47/20.30 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 63.47/20.30 | (97) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 63.47/20.30 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 63.47/20.30 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 63.47/20.30 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 63.47/20.30 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0)))
% 63.47/20.30 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 63.47/20.30 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 63.47/20.30 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 63.47/20.30 | (105) ! [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))
% 63.47/20.30 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0))))
% 63.47/20.31 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 63.47/20.31 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 63.47/20.31 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0))))
% 63.47/20.31 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 63.47/20.31 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 63.47/20.31 | (112) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 63.47/20.31 | (113) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 63.47/20.31 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 63.47/20.31 | (115) ! [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)
% 63.47/20.31 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 63.47/20.31 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 63.47/20.31 | (118) ! [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] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 63.47/20.31 | (119) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 63.47/20.31 | (120) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 63.47/20.31 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 63.47/20.31 | (122) ! [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))
% 63.47/20.31 | (123) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 63.47/20.31 | (124) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 63.47/20.31 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 63.47/20.31 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 63.47/20.31 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 63.47/20.31 |
% 63.47/20.31 | Instantiating (67) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 yields:
% 63.47/20.31 | (128) ~ (all_1_0_0 = 0) & intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1 & intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2 & apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0 & apart_point_and_line(all_1_2_2, all_1_3_3) = 0 & convergent_lines(all_1_3_3, all_1_4_4) = 0 & convergent_lines(all_1_5_5, all_1_3_3) = 0 & convergent_lines(all_1_5_5, all_1_4_4) = 0
% 63.47/20.31 |
% 63.47/20.31 | Applying alpha-rule on (128) yields:
% 63.47/20.31 | (129) apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0
% 63.47/20.31 | (130) intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2
% 63.47/20.31 | (131) intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1
% 63.47/20.31 | (132) convergent_lines(all_1_3_3, all_1_4_4) = 0
% 63.47/20.31 | (133) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 63.47/20.31 | (134) apart_point_and_line(all_1_2_2, all_1_3_3) = 0
% 63.47/20.31 | (135) ~ (all_1_0_0 = 0)
% 63.47/20.31 | (136) convergent_lines(all_1_5_5, all_1_3_3) = 0
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (65) with all_1_5_5 yields:
% 63.47/20.32 | (137) ~ (convergent_lines(all_1_5_5, all_1_5_5) = 0)
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (7) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1, yields:
% 63.47/20.32 | (138) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_1_1) = v3 & line(all_1_4_4) = v0 & line(all_1_5_5) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (107) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1, yields:
% 63.47/20.32 | (139) ? [v0] : ? [v1] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (2) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1, yields:
% 63.47/20.32 | (140) ? [v0] : ? [v1] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (7) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 63.47/20.32 | (141) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_2_2) = v3 & line(all_1_4_4) = v1 & line(all_1_5_5) = v0 & convergent_lines(all_1_5_5, all_1_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (107) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 63.47/20.32 | (142) ? [v0] : ? [v1] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (2) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 63.47/20.32 | (143) ? [v0] : ? [v1] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (54) with all_1_0_0, all_1_0_0, all_1_3_3, all_1_3_3, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, yields:
% 63.47/20.32 | (144) all_1_0_0 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_3_3, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (118) with all_1_0_0, all_1_0_0, all_1_3_3, all_1_3_3, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, yields:
% 63.47/20.32 | (145) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (6) with all_1_0_0, all_1_1_1, all_1_3_3, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_2_2, all_1_3_3) = 0, yields:
% 63.47/20.32 | (146) all_1_0_0 = 0 | distinct_points(all_1_2_2, all_1_1_1) = 0
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (27) with 0, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 63.47/20.32 | (147) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_4_4) = v1 & unorthogonal_lines(all_1_3_3, all_1_4_4) = v0 & unorthogonal_lines(all_1_4_4, all_1_4_4) = v3 & convergent_lines(all_1_4_4, all_1_4_4) = v2 & ( ~ (v0 = 0) | v1 = 0 | (v3 = 0 & v2 = 0)))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (93) with 0, 0, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 63.47/20.32 | (148) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_4_4) = v1 & unorthogonal_lines(all_1_3_3, all_1_4_4) = v0 & unorthogonal_lines(all_1_4_4, all_1_4_4) = v3 & convergent_lines(all_1_4_4, all_1_4_4) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0 | v0 = 0))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (82) with all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 63.47/20.32 | (149) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(v2) = v3 & line(all_1_3_3) = v0 & line(all_1_4_4) = v1 & intersection_point(all_1_3_3, all_1_4_4) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (1) with all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 63.47/20.32 | (150) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(v0, all_1_4_4) = v1)
% 63.47/20.32 |
% 63.47/20.32 | Instantiating formula (70) with all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 63.47/20.32 | (151) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(v0, all_1_3_3) = v1)
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (100) with 0, all_1_4_4, all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 63.47/20.33 | (152) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v0 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v2 & convergent_lines(all_1_5_5, all_1_4_4) = v1 & ( ~ (v3 = 0) | v0 = 0 | (v2 = 0 & v1 = 0)))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (16) with 0, all_1_3_3, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 63.47/20.33 | (153) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_5_5, all_1_3_3) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v2 & unorthogonal_lines(all_1_5_5, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v3 = 0) | v2 = 0 | (v1 = 0 & v0 = 0)))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (95) with 0, 0, all_1_3_3, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 63.47/20.33 | (154) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_5_5, all_1_3_3) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v2 & unorthogonal_lines(all_1_5_5, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (51) with 0, all_1_4_4, all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 63.47/20.33 | (155) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v0 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v2 & convergent_lines(all_1_5_5, all_1_4_4) = v1 & ( ~ (v0 = 0) | v3 = 0 | (v2 = 0 & v1 = 0)))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (82) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 63.47/20.33 | (156) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(v2) = v3 & line(all_1_3_3) = v1 & line(all_1_5_5) = v0 & intersection_point(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (1) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 63.47/20.33 | (157) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(v0, all_1_3_3) = v1)
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (70) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 63.47/20.33 | (158) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(v0, all_1_5_5) = v1)
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (27) with 0, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 63.47/20.33 | (159) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_4_4, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v1 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v0 & convergent_lines(all_1_4_4, all_1_4_4) = v2 & ( ~ (v0 = 0) | v1 = 0 | (v3 = 0 & v2 = 0)))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (16) with 0, all_1_4_4, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 63.47/20.33 | (160) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_5_5, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v2 & unorthogonal_lines(all_1_5_5, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v3 = 0) | v2 = 0 | (v1 = 0 & v0 = 0)))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (95) with 0, 0, all_1_4_4, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 63.47/20.33 | (161) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_5_5, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v2 & unorthogonal_lines(all_1_5_5, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (93) with 0, 0, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 63.47/20.33 | (162) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unorthogonal_lines(all_1_4_4, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v1 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v0 & convergent_lines(all_1_4_4, all_1_4_4) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0 | v0 = 0))
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (1) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 63.47/20.33 | (163) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(v0, all_1_4_4) = v1)
% 63.47/20.33 |
% 63.47/20.33 | Instantiating formula (70) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 63.47/20.33 | (164) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(v0, all_1_5_5) = v1)
% 63.47/20.33 |
% 63.47/20.33 | Instantiating (162) with all_24_0_19, all_24_1_20, all_24_2_21, all_24_3_22 yields:
% 63.47/20.33 | (165) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_24_0_19 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_24_2_21 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_24_3_22 & convergent_lines(all_1_4_4, all_1_4_4) = all_24_1_20 & ( ~ (all_24_0_19 = 0) | ~ (all_24_1_20 = 0) | all_24_2_21 = 0 | all_24_3_22 = 0)
% 63.47/20.33 |
% 63.47/20.33 | Applying alpha-rule on (165) yields:
% 63.47/20.33 | (166) convergent_lines(all_1_4_4, all_1_4_4) = all_24_1_20
% 63.47/20.33 | (167) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_24_0_19
% 63.47/20.33 | (168) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_24_3_22
% 63.47/20.33 | (169) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_24_2_21
% 63.47/20.33 | (170) ~ (all_24_0_19 = 0) | ~ (all_24_1_20 = 0) | all_24_2_21 = 0 | all_24_3_22 = 0
% 63.47/20.33 |
% 63.47/20.33 | Instantiating (164) with all_26_0_23, all_26_1_24 yields:
% 63.47/20.33 | (171) ~ (all_26_0_23 = 0) & intersection_point(all_1_5_5, all_1_4_4) = all_26_1_24 & apart_point_and_line(all_26_1_24, all_1_5_5) = all_26_0_23
% 63.47/20.33 |
% 63.47/20.33 | Applying alpha-rule on (171) yields:
% 63.47/20.33 | (172) ~ (all_26_0_23 = 0)
% 63.47/20.33 | (173) intersection_point(all_1_5_5, all_1_4_4) = all_26_1_24
% 63.47/20.33 | (174) apart_point_and_line(all_26_1_24, all_1_5_5) = all_26_0_23
% 63.47/20.33 |
% 63.47/20.33 | Instantiating (163) with all_28_0_25, all_28_1_26 yields:
% 63.47/20.33 | (175) ~ (all_28_0_25 = 0) & intersection_point(all_1_5_5, all_1_4_4) = all_28_1_26 & apart_point_and_line(all_28_1_26, all_1_4_4) = all_28_0_25
% 63.47/20.33 |
% 63.47/20.33 | Applying alpha-rule on (175) yields:
% 63.47/20.33 | (176) ~ (all_28_0_25 = 0)
% 63.47/20.33 | (177) intersection_point(all_1_5_5, all_1_4_4) = all_28_1_26
% 63.47/20.33 | (178) apart_point_and_line(all_28_1_26, all_1_4_4) = all_28_0_25
% 63.47/20.33 |
% 63.47/20.33 | Instantiating (161) with all_30_0_27, all_30_1_28, all_30_2_29, all_30_3_30 yields:
% 63.47/20.33 | (179) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_30_0_27 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_30_1_28 & unorthogonal_lines(all_1_5_5, all_1_5_5) = all_30_2_29 & convergent_lines(all_1_5_5, all_1_5_5) = all_30_3_30 & ( ~ (all_30_2_29 = 0) | ~ (all_30_3_30 = 0) | all_30_0_27 = 0 | all_30_1_28 = 0)
% 63.47/20.33 |
% 63.47/20.33 | Applying alpha-rule on (179) yields:
% 63.47/20.33 | (180) unorthogonal_lines(all_1_5_5, all_1_5_5) = all_30_2_29
% 63.47/20.33 | (181) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_30_1_28
% 63.47/20.33 | (182) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_30_0_27
% 63.47/20.33 | (183) convergent_lines(all_1_5_5, all_1_5_5) = all_30_3_30
% 63.80/20.33 | (184) ~ (all_30_2_29 = 0) | ~ (all_30_3_30 = 0) | all_30_0_27 = 0 | all_30_1_28 = 0
% 63.80/20.33 |
% 63.80/20.33 | Instantiating (159) with all_32_0_31, all_32_1_32, all_32_2_33, all_32_3_34 yields:
% 63.80/20.33 | (185) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_32_0_31 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_32_2_33 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_32_3_34 & convergent_lines(all_1_4_4, all_1_4_4) = all_32_1_32 & ( ~ (all_32_3_34 = 0) | all_32_2_33 = 0 | (all_32_0_31 = 0 & all_32_1_32 = 0))
% 63.80/20.33 |
% 63.80/20.33 | Applying alpha-rule on (185) yields:
% 63.80/20.33 | (186) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_32_3_34
% 63.80/20.33 | (187) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_32_0_31
% 63.80/20.33 | (188) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_32_2_33
% 63.80/20.34 | (189) convergent_lines(all_1_4_4, all_1_4_4) = all_32_1_32
% 63.80/20.34 | (190) ~ (all_32_3_34 = 0) | all_32_2_33 = 0 | (all_32_0_31 = 0 & all_32_1_32 = 0)
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (158) with all_44_0_52, all_44_1_53 yields:
% 63.80/20.34 | (191) ~ (all_44_0_52 = 0) & intersection_point(all_1_5_5, all_1_3_3) = all_44_1_53 & apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (191) yields:
% 63.80/20.34 | (192) ~ (all_44_0_52 = 0)
% 63.80/20.34 | (193) intersection_point(all_1_5_5, all_1_3_3) = all_44_1_53
% 63.80/20.34 | (194) apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (157) with all_46_0_54, all_46_1_55 yields:
% 63.80/20.34 | (195) ~ (all_46_0_54 = 0) & intersection_point(all_1_5_5, all_1_3_3) = all_46_1_55 & apart_point_and_line(all_46_1_55, all_1_3_3) = all_46_0_54
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (195) yields:
% 63.80/20.34 | (196) ~ (all_46_0_54 = 0)
% 63.80/20.34 | (197) intersection_point(all_1_5_5, all_1_3_3) = all_46_1_55
% 63.80/20.34 | (198) apart_point_and_line(all_46_1_55, all_1_3_3) = all_46_0_54
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (147) with all_48_0_56, all_48_1_57, all_48_2_58, all_48_3_59 yields:
% 63.80/20.34 | (199) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_48_2_58 & unorthogonal_lines(all_1_3_3, all_1_4_4) = all_48_3_59 & unorthogonal_lines(all_1_4_4, all_1_4_4) = all_48_0_56 & convergent_lines(all_1_4_4, all_1_4_4) = all_48_1_57 & ( ~ (all_48_3_59 = 0) | all_48_2_58 = 0 | (all_48_0_56 = 0 & all_48_1_57 = 0))
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (199) yields:
% 63.80/20.34 | (200) ~ (all_48_3_59 = 0) | all_48_2_58 = 0 | (all_48_0_56 = 0 & all_48_1_57 = 0)
% 63.80/20.34 | (201) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_48_0_56
% 63.80/20.34 | (202) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_48_3_59
% 63.80/20.34 | (203) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_48_2_58
% 63.80/20.34 | (204) convergent_lines(all_1_4_4, all_1_4_4) = all_48_1_57
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (156) with all_52_0_61, all_52_1_62, all_52_2_63, all_52_3_64 yields:
% 63.80/20.34 | (205) point(all_52_1_62) = all_52_0_61 & line(all_1_3_3) = all_52_2_63 & line(all_1_5_5) = all_52_3_64 & intersection_point(all_1_5_5, all_1_3_3) = all_52_1_62 & ( ~ (all_52_2_63 = 0) | ~ (all_52_3_64 = 0) | all_52_0_61 = 0)
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (205) yields:
% 63.80/20.34 | (206) intersection_point(all_1_5_5, all_1_3_3) = all_52_1_62
% 63.80/20.34 | (207) point(all_52_1_62) = all_52_0_61
% 63.80/20.34 | (208) ~ (all_52_2_63 = 0) | ~ (all_52_3_64 = 0) | all_52_0_61 = 0
% 63.80/20.34 | (209) line(all_1_3_3) = all_52_2_63
% 63.80/20.34 | (210) line(all_1_5_5) = all_52_3_64
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (155) with all_54_0_65, all_54_1_66, all_54_2_67, all_54_3_68 yields:
% 63.80/20.34 | (211) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_54_0_65 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_54_3_68 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_54_1_66 & convergent_lines(all_1_5_5, all_1_4_4) = all_54_2_67 & ( ~ (all_54_3_68 = 0) | all_54_0_65 = 0 | (all_54_1_66 = 0 & all_54_2_67 = 0))
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (211) yields:
% 63.80/20.34 | (212) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_54_0_65
% 63.80/20.34 | (213) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_54_3_68
% 63.80/20.34 | (214) convergent_lines(all_1_5_5, all_1_4_4) = all_54_2_67
% 63.80/20.34 | (215) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_54_1_66
% 63.80/20.34 | (216) ~ (all_54_3_68 = 0) | all_54_0_65 = 0 | (all_54_1_66 = 0 & all_54_2_67 = 0)
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (143) with all_56_0_69, all_56_1_70 yields:
% 63.80/20.34 | (217) apart_point_and_line(all_1_2_2, all_1_5_5) = all_56_0_69 & convergent_lines(all_1_5_5, all_1_4_4) = all_56_1_70 & ( ~ (all_56_0_69 = 0) | ~ (all_56_1_70 = 0))
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (217) yields:
% 63.80/20.34 | (218) apart_point_and_line(all_1_2_2, all_1_5_5) = all_56_0_69
% 63.80/20.34 | (219) convergent_lines(all_1_5_5, all_1_4_4) = all_56_1_70
% 63.80/20.34 | (220) ~ (all_56_0_69 = 0) | ~ (all_56_1_70 = 0)
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (142) with all_58_0_71, all_58_1_72 yields:
% 63.80/20.34 | (221) apart_point_and_line(all_1_2_2, all_1_4_4) = all_58_0_71 & convergent_lines(all_1_5_5, all_1_4_4) = all_58_1_72 & ( ~ (all_58_0_71 = 0) | ~ (all_58_1_72 = 0))
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (221) yields:
% 63.80/20.34 | (222) apart_point_and_line(all_1_2_2, all_1_4_4) = all_58_0_71
% 63.80/20.34 | (223) convergent_lines(all_1_5_5, all_1_4_4) = all_58_1_72
% 63.80/20.34 | (224) ~ (all_58_0_71 = 0) | ~ (all_58_1_72 = 0)
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (160) with all_60_0_73, all_60_1_74, all_60_2_75, all_60_3_76 yields:
% 63.80/20.34 | (225) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_60_0_73 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_60_1_74 & unorthogonal_lines(all_1_5_5, all_1_5_5) = all_60_2_75 & convergent_lines(all_1_5_5, all_1_5_5) = all_60_3_76 & ( ~ (all_60_0_73 = 0) | all_60_1_74 = 0 | (all_60_2_75 = 0 & all_60_3_76 = 0))
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (225) yields:
% 63.80/20.34 | (226) ~ (all_60_0_73 = 0) | all_60_1_74 = 0 | (all_60_2_75 = 0 & all_60_3_76 = 0)
% 63.80/20.34 | (227) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_60_1_74
% 63.80/20.34 | (228) unorthogonal_lines(all_1_5_5, all_1_5_5) = all_60_2_75
% 63.80/20.34 | (229) convergent_lines(all_1_5_5, all_1_5_5) = all_60_3_76
% 63.80/20.34 | (230) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_60_0_73
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (153) with all_66_0_85, all_66_1_86, all_66_2_87, all_66_3_88 yields:
% 63.80/20.34 | (231) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_66_0_85 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_66_1_86 & unorthogonal_lines(all_1_5_5, all_1_5_5) = all_66_2_87 & convergent_lines(all_1_5_5, all_1_5_5) = all_66_3_88 & ( ~ (all_66_0_85 = 0) | all_66_1_86 = 0 | (all_66_2_87 = 0 & all_66_3_88 = 0))
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (231) yields:
% 63.80/20.34 | (232) ~ (all_66_0_85 = 0) | all_66_1_86 = 0 | (all_66_2_87 = 0 & all_66_3_88 = 0)
% 63.80/20.34 | (233) unorthogonal_lines(all_1_5_5, all_1_5_5) = all_66_2_87
% 63.80/20.34 | (234) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_66_1_86
% 63.80/20.34 | (235) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_66_0_85
% 63.80/20.34 | (236) convergent_lines(all_1_5_5, all_1_5_5) = all_66_3_88
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (151) with all_70_0_93, all_70_1_94 yields:
% 63.80/20.34 | (237) ~ (all_70_0_93 = 0) & intersection_point(all_1_3_3, all_1_4_4) = all_70_1_94 & apart_point_and_line(all_70_1_94, all_1_3_3) = all_70_0_93
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (237) yields:
% 63.80/20.34 | (238) ~ (all_70_0_93 = 0)
% 63.80/20.34 | (239) intersection_point(all_1_3_3, all_1_4_4) = all_70_1_94
% 63.80/20.34 | (240) apart_point_and_line(all_70_1_94, all_1_3_3) = all_70_0_93
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (150) with all_72_0_95, all_72_1_96 yields:
% 63.80/20.34 | (241) ~ (all_72_0_95 = 0) & intersection_point(all_1_3_3, all_1_4_4) = all_72_1_96 & apart_point_and_line(all_72_1_96, all_1_4_4) = all_72_0_95
% 63.80/20.34 |
% 63.80/20.34 | Applying alpha-rule on (241) yields:
% 63.80/20.34 | (242) ~ (all_72_0_95 = 0)
% 63.80/20.34 | (243) intersection_point(all_1_3_3, all_1_4_4) = all_72_1_96
% 63.80/20.34 | (244) apart_point_and_line(all_72_1_96, all_1_4_4) = all_72_0_95
% 63.80/20.34 |
% 63.80/20.34 | Instantiating (149) with all_74_0_97, all_74_1_98, all_74_2_99, all_74_3_100 yields:
% 63.80/20.35 | (245) point(all_74_1_98) = all_74_0_97 & line(all_1_3_3) = all_74_3_100 & line(all_1_4_4) = all_74_2_99 & intersection_point(all_1_3_3, all_1_4_4) = all_74_1_98 & ( ~ (all_74_2_99 = 0) | ~ (all_74_3_100 = 0) | all_74_0_97 = 0)
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (245) yields:
% 63.80/20.35 | (246) point(all_74_1_98) = all_74_0_97
% 63.80/20.35 | (247) line(all_1_4_4) = all_74_2_99
% 63.80/20.35 | (248) intersection_point(all_1_3_3, all_1_4_4) = all_74_1_98
% 63.80/20.35 | (249) line(all_1_3_3) = all_74_3_100
% 63.80/20.35 | (250) ~ (all_74_2_99 = 0) | ~ (all_74_3_100 = 0) | all_74_0_97 = 0
% 63.80/20.35 |
% 63.80/20.35 | Instantiating (148) with all_76_0_101, all_76_1_102, all_76_2_103, all_76_3_104 yields:
% 63.80/20.35 | (251) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_76_2_103 & unorthogonal_lines(all_1_3_3, all_1_4_4) = all_76_3_104 & unorthogonal_lines(all_1_4_4, all_1_4_4) = all_76_0_101 & convergent_lines(all_1_4_4, all_1_4_4) = all_76_1_102 & ( ~ (all_76_0_101 = 0) | ~ (all_76_1_102 = 0) | all_76_2_103 = 0 | all_76_3_104 = 0)
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (251) yields:
% 63.80/20.35 | (252) convergent_lines(all_1_4_4, all_1_4_4) = all_76_1_102
% 63.80/20.35 | (253) ~ (all_76_0_101 = 0) | ~ (all_76_1_102 = 0) | all_76_2_103 = 0 | all_76_3_104 = 0
% 63.80/20.35 | (254) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_76_2_103
% 63.80/20.35 | (255) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_76_3_104
% 63.80/20.35 | (256) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_76_0_101
% 63.80/20.35 |
% 63.80/20.35 | Instantiating (152) with all_78_0_105, all_78_1_106, all_78_2_107, all_78_3_108 yields:
% 63.80/20.35 | (257) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_78_0_105 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_78_3_108 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_78_1_106 & convergent_lines(all_1_5_5, all_1_4_4) = all_78_2_107 & ( ~ (all_78_0_105 = 0) | all_78_3_108 = 0 | (all_78_1_106 = 0 & all_78_2_107 = 0))
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (257) yields:
% 63.80/20.35 | (258) ~ (all_78_0_105 = 0) | all_78_3_108 = 0 | (all_78_1_106 = 0 & all_78_2_107 = 0)
% 63.80/20.35 | (259) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_78_1_106
% 63.80/20.35 | (260) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_78_3_108
% 63.80/20.35 | (261) convergent_lines(all_1_5_5, all_1_4_4) = all_78_2_107
% 63.80/20.35 | (262) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_78_0_105
% 63.80/20.35 |
% 63.80/20.35 | Instantiating (154) with all_88_0_122, all_88_1_123, all_88_2_124, all_88_3_125 yields:
% 63.80/20.35 | (263) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_88_0_122 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_88_1_123 & unorthogonal_lines(all_1_5_5, all_1_5_5) = all_88_2_124 & convergent_lines(all_1_5_5, all_1_5_5) = all_88_3_125 & ( ~ (all_88_2_124 = 0) | ~ (all_88_3_125 = 0) | all_88_0_122 = 0 | all_88_1_123 = 0)
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (263) yields:
% 63.80/20.35 | (264) unorthogonal_lines(all_1_5_5, all_1_5_5) = all_88_2_124
% 63.80/20.35 | (265) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_88_1_123
% 63.80/20.35 | (266) convergent_lines(all_1_5_5, all_1_5_5) = all_88_3_125
% 63.80/20.35 | (267) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_88_0_122
% 63.80/20.35 | (268) ~ (all_88_2_124 = 0) | ~ (all_88_3_125 = 0) | all_88_0_122 = 0 | all_88_1_123 = 0
% 63.80/20.35 |
% 63.80/20.35 | Instantiating (141) with all_90_0_126, all_90_1_127, all_90_2_128, all_90_3_129 yields:
% 63.80/20.35 | (269) point(all_1_2_2) = all_90_0_126 & line(all_1_4_4) = all_90_2_128 & line(all_1_5_5) = all_90_3_129 & convergent_lines(all_1_5_5, all_1_4_4) = all_90_1_127 & ( ~ (all_90_1_127 = 0) | ~ (all_90_2_128 = 0) | ~ (all_90_3_129 = 0) | all_90_0_126 = 0)
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (269) yields:
% 63.80/20.35 | (270) convergent_lines(all_1_5_5, all_1_4_4) = all_90_1_127
% 63.80/20.35 | (271) line(all_1_4_4) = all_90_2_128
% 63.80/20.35 | (272) point(all_1_2_2) = all_90_0_126
% 63.80/20.35 | (273) line(all_1_5_5) = all_90_3_129
% 63.80/20.35 | (274) ~ (all_90_1_127 = 0) | ~ (all_90_2_128 = 0) | ~ (all_90_3_129 = 0) | all_90_0_126 = 0
% 63.80/20.35 |
% 63.80/20.35 | Instantiating (140) with all_92_0_130, all_92_1_131 yields:
% 63.80/20.35 | (275) apart_point_and_line(all_1_1_1, all_1_4_4) = all_92_0_130 & convergent_lines(all_1_4_4, all_1_5_5) = all_92_1_131 & ( ~ (all_92_0_130 = 0) | ~ (all_92_1_131 = 0))
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (275) yields:
% 63.80/20.35 | (276) apart_point_and_line(all_1_1_1, all_1_4_4) = all_92_0_130
% 63.80/20.35 | (277) convergent_lines(all_1_4_4, all_1_5_5) = all_92_1_131
% 63.80/20.35 | (278) ~ (all_92_0_130 = 0) | ~ (all_92_1_131 = 0)
% 63.80/20.35 |
% 63.80/20.35 | Instantiating (138) with all_94_0_132, all_94_1_133, all_94_2_134, all_94_3_135 yields:
% 63.80/20.35 | (279) point(all_1_1_1) = all_94_0_132 & line(all_1_4_4) = all_94_3_135 & line(all_1_5_5) = all_94_2_134 & convergent_lines(all_1_4_4, all_1_5_5) = all_94_1_133 & ( ~ (all_94_1_133 = 0) | ~ (all_94_2_134 = 0) | ~ (all_94_3_135 = 0) | all_94_0_132 = 0)
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (279) yields:
% 63.80/20.35 | (280) line(all_1_5_5) = all_94_2_134
% 63.80/20.35 | (281) line(all_1_4_4) = all_94_3_135
% 63.80/20.35 | (282) convergent_lines(all_1_4_4, all_1_5_5) = all_94_1_133
% 63.80/20.35 | (283) point(all_1_1_1) = all_94_0_132
% 63.80/20.35 | (284) ~ (all_94_1_133 = 0) | ~ (all_94_2_134 = 0) | ~ (all_94_3_135 = 0) | all_94_0_132 = 0
% 63.80/20.35 |
% 63.80/20.35 | Instantiating (139) with all_96_0_136, all_96_1_137 yields:
% 63.80/20.35 | (285) apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136 & convergent_lines(all_1_4_4, all_1_5_5) = all_96_1_137 & ( ~ (all_96_0_136 = 0) | ~ (all_96_1_137 = 0))
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (285) yields:
% 63.80/20.35 | (286) apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136
% 63.80/20.35 | (287) convergent_lines(all_1_4_4, all_1_5_5) = all_96_1_137
% 63.80/20.35 | (288) ~ (all_96_0_136 = 0) | ~ (all_96_1_137 = 0)
% 63.80/20.35 |
% 63.80/20.35 +-Applying beta-rule and splitting (146), into two cases.
% 63.80/20.35 |-Branch one:
% 63.80/20.35 | (289) distinct_points(all_1_2_2, all_1_1_1) = 0
% 63.80/20.35 |
% 63.80/20.35 +-Applying beta-rule and splitting (144), into two cases.
% 63.80/20.35 |-Branch one:
% 63.80/20.35 | (290) all_1_0_0 = 0
% 63.80/20.35 |
% 63.80/20.35 | Equations (290) can reduce 135 to:
% 63.80/20.35 | (291) $false
% 63.80/20.35 |
% 63.80/20.35 |-The branch is then unsatisfiable
% 63.80/20.35 |-Branch two:
% 63.80/20.35 | (135) ~ (all_1_0_0 = 0)
% 63.80/20.35 | (293) ? [v0] : ? [v1] : (convergent_lines(all_1_3_3, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 63.80/20.35 |
% 63.80/20.35 +-Applying beta-rule and splitting (145), into two cases.
% 63.80/20.35 |-Branch one:
% 63.80/20.35 | (290) all_1_0_0 = 0
% 63.80/20.35 |
% 63.80/20.35 | Equations (290) can reduce 135 to:
% 63.80/20.35 | (291) $false
% 63.80/20.35 |
% 63.80/20.35 |-The branch is then unsatisfiable
% 63.80/20.35 |-Branch two:
% 63.80/20.35 | (135) ~ (all_1_0_0 = 0)
% 63.80/20.35 | (297) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.35 |
% 63.80/20.35 | Instantiating (297) with all_115_0_140, all_115_1_141, all_115_2_142, all_115_3_143 yields:
% 63.80/20.35 | (298) apart_point_and_line(all_1_1_1, all_1_3_3) = all_115_0_140 & apart_point_and_line(all_1_1_1, all_1_3_3) = all_115_1_141 & distinct_lines(all_1_3_3, all_1_3_3) = all_115_2_142 & distinct_points(all_1_1_1, all_1_1_1) = all_115_3_143 & ( ~ (all_115_2_142 = 0) | ~ (all_115_3_143 = 0) | all_115_0_140 = 0 | all_115_1_141 = 0)
% 63.80/20.35 |
% 63.80/20.35 | Applying alpha-rule on (298) yields:
% 63.80/20.35 | (299) apart_point_and_line(all_1_1_1, all_1_3_3) = all_115_0_140
% 63.80/20.35 | (300) ~ (all_115_2_142 = 0) | ~ (all_115_3_143 = 0) | all_115_0_140 = 0 | all_115_1_141 = 0
% 63.80/20.35 | (301) distinct_lines(all_1_3_3, all_1_3_3) = all_115_2_142
% 63.80/20.35 | (302) distinct_points(all_1_1_1, all_1_1_1) = all_115_3_143
% 63.80/20.36 | (303) apart_point_and_line(all_1_1_1, all_1_3_3) = all_115_1_141
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (61) with all_1_3_3, all_1_4_4, all_72_1_96, all_74_1_98 and discharging atoms intersection_point(all_1_3_3, all_1_4_4) = all_74_1_98, intersection_point(all_1_3_3, all_1_4_4) = all_72_1_96, yields:
% 63.80/20.36 | (304) all_74_1_98 = all_72_1_96
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (61) with all_1_3_3, all_1_4_4, all_70_1_94, all_74_1_98 and discharging atoms intersection_point(all_1_3_3, all_1_4_4) = all_74_1_98, intersection_point(all_1_3_3, all_1_4_4) = all_70_1_94, yields:
% 63.80/20.36 | (305) all_74_1_98 = all_70_1_94
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (61) with all_1_5_5, all_1_3_3, all_46_1_55, all_52_1_62 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_52_1_62, intersection_point(all_1_5_5, all_1_3_3) = all_46_1_55, yields:
% 63.80/20.36 | (306) all_52_1_62 = all_46_1_55
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (61) with all_1_5_5, all_1_3_3, all_44_1_53, all_52_1_62 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_52_1_62, intersection_point(all_1_5_5, all_1_3_3) = all_44_1_53, yields:
% 63.80/20.36 | (307) all_52_1_62 = all_44_1_53
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (61) with all_1_5_5, all_1_4_4, all_28_1_26, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_28_1_26, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 63.80/20.36 | (308) all_28_1_26 = all_1_2_2
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (61) with all_1_5_5, all_1_4_4, all_26_1_24, all_28_1_26 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_28_1_26, intersection_point(all_1_5_5, all_1_4_4) = all_26_1_24, yields:
% 63.80/20.36 | (309) all_28_1_26 = all_26_1_24
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (104) with all_1_1_1, all_1_3_3, all_115_0_140, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_115_0_140, apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, yields:
% 63.80/20.36 | (310) all_115_0_140 = all_1_0_0
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (104) with all_1_1_1, all_1_3_3, all_115_1_141, all_115_0_140 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_115_0_140, apart_point_and_line(all_1_1_1, all_1_3_3) = all_115_1_141, yields:
% 63.80/20.36 | (311) all_115_0_140 = all_115_1_141
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (104) with all_1_2_2, all_1_4_4, all_58_0_71, all_28_0_25 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_58_0_71, yields:
% 63.80/20.36 | (312) all_58_0_71 = all_28_0_25 | ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25)
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (104) with all_1_2_2, all_1_5_5, all_56_0_69, all_26_0_23 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_56_0_69, yields:
% 63.80/20.36 | (313) all_56_0_69 = all_26_0_23 | ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = all_26_0_23)
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_4_4, all_1_4_4, all_48_1_57, all_76_1_102 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = all_76_1_102, convergent_lines(all_1_4_4, all_1_4_4) = all_48_1_57, yields:
% 63.80/20.36 | (314) all_76_1_102 = all_48_1_57
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_4_4, all_1_4_4, all_32_1_32, all_76_1_102 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = all_76_1_102, convergent_lines(all_1_4_4, all_1_4_4) = all_32_1_32, yields:
% 63.80/20.36 | (315) all_76_1_102 = all_32_1_32
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_4_4, all_1_4_4, all_24_1_20, all_76_1_102 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = all_76_1_102, convergent_lines(all_1_4_4, all_1_4_4) = all_24_1_20, yields:
% 63.80/20.36 | (316) all_76_1_102 = all_24_1_20
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_4_4, all_1_5_5, all_94_1_133, all_96_1_137 and discharging atoms convergent_lines(all_1_4_4, all_1_5_5) = all_96_1_137, convergent_lines(all_1_4_4, all_1_5_5) = all_94_1_133, yields:
% 63.80/20.36 | (317) all_96_1_137 = all_94_1_133
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_4_4, all_1_5_5, all_92_1_131, all_96_1_137 and discharging atoms convergent_lines(all_1_4_4, all_1_5_5) = all_96_1_137, convergent_lines(all_1_4_4, all_1_5_5) = all_92_1_131, yields:
% 63.80/20.36 | (318) all_96_1_137 = all_92_1_131
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_5_5, all_1_4_4, all_90_1_127, 0 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_90_1_127, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 63.80/20.36 | (319) all_90_1_127 = 0
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_5_5, all_1_4_4, all_78_2_107, all_90_1_127 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_90_1_127, convergent_lines(all_1_5_5, all_1_4_4) = all_78_2_107, yields:
% 63.80/20.36 | (320) all_90_1_127 = all_78_2_107
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_5_5, all_1_4_4, all_58_1_72, all_78_2_107 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_78_2_107, convergent_lines(all_1_5_5, all_1_4_4) = all_58_1_72, yields:
% 63.80/20.36 | (321) all_78_2_107 = all_58_1_72
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_5_5, all_1_4_4, all_56_1_70, all_78_2_107 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_78_2_107, convergent_lines(all_1_5_5, all_1_4_4) = all_56_1_70, yields:
% 63.80/20.36 | (322) all_78_2_107 = all_56_1_70
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_5_5, all_1_4_4, all_54_2_67, all_78_2_107 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_78_2_107, convergent_lines(all_1_5_5, all_1_4_4) = all_54_2_67, yields:
% 63.80/20.36 | (323) all_78_2_107 = all_54_2_67
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_5_5, all_1_5_5, all_66_3_88, all_88_3_125 and discharging atoms convergent_lines(all_1_5_5, all_1_5_5) = all_88_3_125, convergent_lines(all_1_5_5, all_1_5_5) = all_66_3_88, yields:
% 63.80/20.36 | (324) all_88_3_125 = all_66_3_88
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_5_5, all_1_5_5, all_60_3_76, all_88_3_125 and discharging atoms convergent_lines(all_1_5_5, all_1_5_5) = all_88_3_125, convergent_lines(all_1_5_5, all_1_5_5) = all_60_3_76, yields:
% 63.80/20.36 | (325) all_88_3_125 = all_60_3_76
% 63.80/20.36 |
% 63.80/20.36 | Using (229) and (137) yields:
% 63.80/20.36 | (326) ~ (all_60_3_76 = 0)
% 63.80/20.36 |
% 63.80/20.36 | Instantiating formula (12) with all_1_5_5, all_1_5_5, all_30_3_30, all_88_3_125 and discharging atoms convergent_lines(all_1_5_5, all_1_5_5) = all_88_3_125, convergent_lines(all_1_5_5, all_1_5_5) = all_30_3_30, yields:
% 63.80/20.36 | (327) all_88_3_125 = all_30_3_30
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (311,310) yields a new equation:
% 63.80/20.36 | (328) all_115_1_141 = all_1_0_0
% 63.80/20.36 |
% 63.80/20.36 | Simplifying 328 yields:
% 63.80/20.36 | (329) all_115_1_141 = all_1_0_0
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (317,318) yields a new equation:
% 63.80/20.36 | (330) all_94_1_133 = all_92_1_131
% 63.80/20.36 |
% 63.80/20.36 | Simplifying 330 yields:
% 63.80/20.36 | (331) all_94_1_133 = all_92_1_131
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (320,319) yields a new equation:
% 63.80/20.36 | (332) all_78_2_107 = 0
% 63.80/20.36 |
% 63.80/20.36 | Simplifying 332 yields:
% 63.80/20.36 | (333) all_78_2_107 = 0
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (327,324) yields a new equation:
% 63.80/20.36 | (334) all_66_3_88 = all_30_3_30
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (325,324) yields a new equation:
% 63.80/20.36 | (335) all_66_3_88 = all_60_3_76
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (323,321) yields a new equation:
% 63.80/20.36 | (336) all_58_1_72 = all_54_2_67
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (322,321) yields a new equation:
% 63.80/20.36 | (337) all_58_1_72 = all_56_1_70
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (333,321) yields a new equation:
% 63.80/20.36 | (338) all_58_1_72 = 0
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (316,314) yields a new equation:
% 63.80/20.36 | (339) all_48_1_57 = all_24_1_20
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (315,314) yields a new equation:
% 63.80/20.36 | (340) all_48_1_57 = all_32_1_32
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (305,304) yields a new equation:
% 63.80/20.36 | (341) all_72_1_96 = all_70_1_94
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (334,335) yields a new equation:
% 63.80/20.36 | (342) all_60_3_76 = all_30_3_30
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (336,337) yields a new equation:
% 63.80/20.36 | (343) all_56_1_70 = all_54_2_67
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (338,337) yields a new equation:
% 63.80/20.36 | (344) all_56_1_70 = 0
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (344,343) yields a new equation:
% 63.80/20.36 | (345) all_54_2_67 = 0
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (306,307) yields a new equation:
% 63.80/20.36 | (346) all_46_1_55 = all_44_1_53
% 63.80/20.36 |
% 63.80/20.36 | Simplifying 346 yields:
% 63.80/20.36 | (347) all_46_1_55 = all_44_1_53
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (339,340) yields a new equation:
% 63.80/20.36 | (348) all_32_1_32 = all_24_1_20
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (309,308) yields a new equation:
% 63.80/20.36 | (349) all_26_1_24 = all_1_2_2
% 63.80/20.36 |
% 63.80/20.36 | Simplifying 349 yields:
% 63.80/20.36 | (350) all_26_1_24 = all_1_2_2
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (345,343) yields a new equation:
% 63.80/20.36 | (344) all_56_1_70 = 0
% 63.80/20.36 |
% 63.80/20.36 | Combining equations (344,337) yields a new equation:
% 63.80/20.36 | (338) all_58_1_72 = 0
% 63.80/20.36 |
% 63.80/20.36 | Equations (342) can reduce 326 to:
% 63.80/20.36 | (353) ~ (all_30_3_30 = 0)
% 63.80/20.36 |
% 63.80/20.36 | From (341) and (244) follows:
% 63.80/20.36 | (354) apart_point_and_line(all_70_1_94, all_1_4_4) = all_72_0_95
% 63.80/20.36 |
% 63.80/20.36 | From (347) and (198) follows:
% 63.80/20.36 | (355) apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54
% 63.80/20.36 |
% 63.80/20.36 | From (308) and (178) follows:
% 63.80/20.36 | (356) apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25
% 63.80/20.36 |
% 63.80/20.36 | From (350) and (174) follows:
% 63.80/20.36 | (357) apart_point_and_line(all_1_2_2, all_1_5_5) = all_26_0_23
% 63.80/20.36 |
% 63.80/20.36 | From (329) and (303) follows:
% 63.80/20.36 | (129) apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0
% 63.80/20.36 |
% 63.80/20.36 | From (348) and (189) follows:
% 63.80/20.36 | (166) convergent_lines(all_1_4_4, all_1_4_4) = all_24_1_20
% 63.80/20.36 |
% 63.80/20.36 | From (331) and (282) follows:
% 63.80/20.36 | (277) convergent_lines(all_1_4_4, all_1_5_5) = all_92_1_131
% 63.80/20.36 |
% 63.80/20.36 | From (345) and (214) follows:
% 63.80/20.36 | (133) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 63.80/20.36 |
% 63.80/20.36 | From (342) and (229) follows:
% 63.80/20.36 | (183) convergent_lines(all_1_5_5, all_1_5_5) = all_30_3_30
% 63.80/20.36 |
% 63.80/20.36 +-Applying beta-rule and splitting (220), into two cases.
% 63.80/20.36 |-Branch one:
% 63.80/20.36 | (363) ~ (all_56_0_69 = 0)
% 63.80/20.36 |
% 63.80/20.36 +-Applying beta-rule and splitting (224), into two cases.
% 63.80/20.36 |-Branch one:
% 63.80/20.36 | (364) ~ (all_58_0_71 = 0)
% 63.80/20.36 |
% 63.80/20.36 +-Applying beta-rule and splitting (313), into two cases.
% 63.80/20.36 |-Branch one:
% 63.80/20.36 | (365) ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = all_26_0_23)
% 63.80/20.36 |
% 63.80/20.36 | Using (357) and (365) yields:
% 63.80/20.36 | (366) $false
% 63.80/20.36 |
% 63.80/20.36 |-The branch is then unsatisfiable
% 63.80/20.36 |-Branch two:
% 63.80/20.36 | (357) apart_point_and_line(all_1_2_2, all_1_5_5) = all_26_0_23
% 63.80/20.36 | (368) all_56_0_69 = all_26_0_23
% 63.80/20.36 |
% 63.80/20.36 | Equations (368) can reduce 363 to:
% 63.80/20.36 | (172) ~ (all_26_0_23 = 0)
% 63.80/20.36 |
% 63.80/20.36 | From (368) and (218) follows:
% 63.80/20.36 | (357) apart_point_and_line(all_1_2_2, all_1_5_5) = all_26_0_23
% 63.80/20.36 |
% 63.80/20.36 +-Applying beta-rule and splitting (312), into two cases.
% 63.80/20.36 |-Branch one:
% 63.80/20.36 | (371) ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25)
% 63.80/20.36 |
% 63.80/20.36 | Using (356) and (371) yields:
% 63.80/20.36 | (366) $false
% 63.80/20.36 |
% 63.80/20.36 |-The branch is then unsatisfiable
% 63.80/20.36 |-Branch two:
% 63.80/20.36 | (356) apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25
% 63.80/20.37 | (374) all_58_0_71 = all_28_0_25
% 63.80/20.37 |
% 63.80/20.37 | Equations (374) can reduce 364 to:
% 63.80/20.37 | (176) ~ (all_28_0_25 = 0)
% 63.80/20.37 |
% 63.80/20.37 | From (374) and (222) follows:
% 63.80/20.37 | (356) apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_44_0_52, all_72_0_95, all_1_5_5, all_1_4_4, all_44_1_53, all_70_1_94 and discharging atoms apart_point_and_line(all_70_1_94, all_1_4_4) = all_72_0_95, apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, yields:
% 63.80/20.37 | (377) all_72_0_95 = 0 | all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v2 & apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_70_1_94, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_72_0_95, all_44_0_52, all_1_4_4, all_1_5_5, all_70_1_94, all_44_1_53 and discharging atoms apart_point_and_line(all_70_1_94, all_1_4_4) = all_72_0_95, apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, yields:
% 63.80/20.37 | (378) all_72_0_95 = 0 | all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v3 & apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_44_1_53, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (52) with all_44_0_52, all_72_0_95, all_1_4_4, all_1_5_5, all_44_1_53, all_70_1_94 and discharging atoms apart_point_and_line(all_70_1_94, all_1_4_4) = all_72_0_95, apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, yields:
% 63.80/20.37 | (379) all_72_0_95 = 0 | all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v2 & apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_70_1_94, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (52) with all_72_0_95, all_44_0_52, all_1_5_5, all_1_4_4, all_70_1_94, all_44_1_53 and discharging atoms apart_point_and_line(all_70_1_94, all_1_4_4) = all_72_0_95, apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, yields:
% 63.80/20.37 | (380) all_72_0_95 = 0 | all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v3 & apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_44_0_52, all_44_0_52, all_1_5_5, all_1_5_5, all_44_1_53, all_44_1_53 and discharging atoms apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, yields:
% 63.80/20.37 | (381) all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v3 & apart_point_and_line(all_44_1_53, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_44_0_52, all_92_0_130, all_1_5_5, all_1_4_4, all_44_1_53, all_1_1_1 and discharging atoms apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, apart_point_and_line(all_1_1_1, all_1_4_4) = all_92_0_130, yields:
% 63.80/20.37 | (382) all_92_0_130 = 0 | all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (54) with all_96_0_136, all_1_0_0, all_1_5_5, all_1_3_3, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (383) all_96_0_136 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_3_3, all_1_5_5) = v1 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (54) with all_1_0_0, all_96_0_136, all_1_3_3, all_1_5_5, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (384) all_96_0_136 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_5_5, all_1_3_3) = v1 & distinct_lines(all_1_5_5, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_96_0_136, all_1_0_0, all_1_5_5, all_1_3_3, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (385) all_96_0_136 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (52) with all_1_0_0, all_96_0_136, all_1_5_5, all_1_3_3, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (386) all_96_0_136 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_96_0_136, all_46_0_54, all_1_5_5, all_1_3_3, all_1_1_1, all_44_1_53 and discharging atoms apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (387) all_96_0_136 = 0 | all_46_0_54 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_46_0_54, all_96_0_136, all_1_3_3, all_1_5_5, all_44_1_53, all_1_1_1 and discharging atoms apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (388) all_96_0_136 = 0 | all_46_0_54 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (52) with all_96_0_136, all_46_0_54, all_1_3_3, all_1_5_5, all_1_1_1, all_44_1_53 and discharging atoms apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (389) all_96_0_136 = 0 | all_46_0_54 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_53, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (52) with all_46_0_54, all_96_0_136, all_1_5_5, all_1_3_3, all_44_1_53, all_1_1_1 and discharging atoms apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (390) all_96_0_136 = 0 | all_46_0_54 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_92_0_130, all_96_0_136, all_1_4_4, all_1_5_5, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_92_0_130, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (391) all_96_0_136 = 0 | all_92_0_130 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (52) with all_96_0_136, all_92_0_130, all_1_4_4, all_1_5_5, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_92_0_130, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (392) all_96_0_136 = 0 | all_92_0_130 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (54) with all_96_0_136, all_96_0_136, all_1_5_5, all_1_5_5, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 63.80/20.37 | (393) all_96_0_136 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_5_5, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_28_0_25, all_1_0_0, all_1_4_4, all_1_3_3, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.37 | (394) all_28_0_25 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_1_0_0, all_28_0_25, all_1_3_3, all_1_4_4, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.37 | (395) all_28_0_25 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (52) with all_28_0_25, all_1_0_0, all_1_3_3, all_1_4_4, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.37 | (396) all_28_0_25 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_28_0_25, all_72_0_95, all_1_4_4, all_1_4_4, all_1_2_2, all_70_1_94 and discharging atoms apart_point_and_line(all_70_1_94, all_1_4_4) = all_72_0_95, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.37 | (397) all_72_0_95 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_70_1_94, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_72_0_95, all_28_0_25, all_1_4_4, all_1_4_4, all_70_1_94, all_1_2_2 and discharging atoms apart_point_and_line(all_70_1_94, all_1_4_4) = all_72_0_95, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.37 | (398) all_72_0_95 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_28_0_25, all_46_0_54, all_1_4_4, all_1_3_3, all_1_2_2, all_44_1_53 and discharging atoms apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.37 | (399) all_46_0_54 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.37 |
% 63.80/20.37 | Instantiating formula (118) with all_46_0_54, all_28_0_25, all_1_3_3, all_1_4_4, all_44_1_53, all_1_2_2 and discharging atoms apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.38 | (400) all_46_0_54 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (52) with all_28_0_25, all_46_0_54, all_1_3_3, all_1_4_4, all_1_2_2, all_44_1_53 and discharging atoms apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.38 | (401) all_46_0_54 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (52) with all_46_0_54, all_28_0_25, all_1_4_4, all_1_3_3, all_44_1_53, all_1_2_2 and discharging atoms apart_point_and_line(all_44_1_53, all_1_3_3) = all_46_0_54, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.38 | (402) all_46_0_54 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (118) with all_28_0_25, all_44_0_52, all_1_4_4, all_1_5_5, all_1_2_2, all_44_1_53 and discharging atoms apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.38 | (403) all_44_0_52 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (118) with all_44_0_52, all_28_0_25, all_1_5_5, all_1_4_4, all_44_1_53, all_1_2_2 and discharging atoms apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.38 | (404) all_44_0_52 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (52) with all_28_0_25, all_44_0_52, all_1_5_5, all_1_4_4, all_1_2_2, all_44_1_53 and discharging atoms apart_point_and_line(all_44_1_53, all_1_5_5) = all_44_0_52, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.38 | (405) all_44_0_52 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (52) with all_96_0_136, all_28_0_25, all_1_4_4, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.38 | (406) all_96_0_136 = 0 | all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (118) with all_28_0_25, all_28_0_25, all_1_4_4, all_1_4_4, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, yields:
% 63.80/20.38 | (407) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (118) with all_26_0_23, all_92_0_130, all_1_5_5, all_1_4_4, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_92_0_130, apart_point_and_line(all_1_2_2, all_1_5_5) = all_26_0_23, yields:
% 63.80/20.38 | (408) all_92_0_130 = 0 | all_26_0_23 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (87) with all_92_1_131, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_4_4, all_1_5_5) = all_92_1_131, convergent_lines(all_1_5_5, all_1_4_4) = 0, ~ (convergent_lines(all_1_5_5, all_1_5_5) = 0), yields:
% 63.80/20.38 | (409) all_92_1_131 = 0
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (83) with all_24_1_20, all_1_4_4, all_1_5_5, all_1_4_4 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = all_24_1_20, yields:
% 63.80/20.38 | (410) all_24_1_20 = 0 | ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) | distinct_lines(all_1_5_5, all_1_4_4) = 0
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (82) with all_1_5_5, all_1_4_4 yields:
% 63.80/20.38 | (411) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(v2) = v3 & line(all_1_4_4) = v0 & line(all_1_5_5) = v1 & intersection_point(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (1) with all_1_5_5, all_1_4_4 yields:
% 63.80/20.38 | (412) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(v0, all_1_5_5) = v1)
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (70) with all_1_5_5, all_1_4_4 yields:
% 63.80/20.38 | (413) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(v0, all_1_4_4) = v1)
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (123) with all_1_5_5, all_1_4_4 yields:
% 63.80/20.38 | (414) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & parallel_lines(all_1_4_4, all_1_5_5) = v0)
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (83) with all_30_3_30, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, convergent_lines(all_1_5_5, all_1_5_5) = all_30_3_30, yields:
% 63.80/20.38 | (415) all_30_3_30 = 0 | distinct_lines(all_1_4_4, all_1_5_5) = 0
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (56) with all_30_3_30, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_5_5) = all_30_3_30, yields:
% 63.80/20.38 | (416) all_30_3_30 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_5_5) = v0)
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (40) with all_92_0_130, all_96_0_136, all_1_4_4, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_92_0_130, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 63.80/20.38 | (417) all_96_0_136 = 0 | all_92_0_130 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Instantiating formula (10) with all_26_0_23, all_28_0_25, all_1_5_5, all_1_4_4, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_28_0_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_26_0_23, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 63.80/20.38 | (418) all_28_0_25 = 0 | all_26_0_23 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 63.80/20.38 |
% 63.80/20.38 | Combining equations (409,318) yields a new equation:
% 63.80/20.38 | (419) all_96_1_137 = 0
% 63.80/20.38 |
% 63.80/20.38 | From (409) and (277) follows:
% 63.80/20.38 | (420) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 63.80/20.38 |
% 63.80/20.38 +-Applying beta-rule and splitting (288), into two cases.
% 63.80/20.38 |-Branch one:
% 63.80/20.38 | (421) ~ (all_96_0_136 = 0)
% 63.80/20.38 |
% 63.80/20.38 +-Applying beta-rule and splitting (278), into two cases.
% 63.80/20.38 |-Branch one:
% 63.80/20.38 | (422) ~ (all_92_0_130 = 0)
% 63.80/20.38 |
% 63.80/20.38 +-Applying beta-rule and splitting (393), into two cases.
% 63.80/20.38 |-Branch one:
% 63.80/20.38 | (423) all_96_0_136 = 0
% 63.80/20.38 |
% 63.80/20.38 | Equations (423) can reduce 421 to:
% 63.80/20.38 | (291) $false
% 63.80/20.38 |
% 63.80/20.38 |-The branch is then unsatisfiable
% 63.80/20.38 |-Branch two:
% 63.80/20.38 | (421) ~ (all_96_0_136 = 0)
% 63.80/20.38 | (426) ? [v0] : ? [v1] : (convergent_lines(all_1_5_5, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 63.80/20.38 |
% 63.80/20.38 +-Applying beta-rule and splitting (407), into two cases.
% 63.80/20.38 |-Branch one:
% 63.80/20.38 | (427) all_28_0_25 = 0
% 63.80/20.38 |
% 63.80/20.38 | Equations (427) can reduce 176 to:
% 63.80/20.38 | (291) $false
% 63.80/20.38 |
% 63.80/20.38 |-The branch is then unsatisfiable
% 63.80/20.38 |-Branch two:
% 63.80/20.38 | (176) ~ (all_28_0_25 = 0)
% 63.80/20.38 | (430) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 +-Applying beta-rule and splitting (391), into two cases.
% 63.80/20.38 |-Branch one:
% 63.80/20.38 | (423) all_96_0_136 = 0
% 63.80/20.38 |
% 63.80/20.38 | Equations (423) can reduce 421 to:
% 63.80/20.38 | (291) $false
% 63.80/20.38 |
% 63.80/20.38 |-The branch is then unsatisfiable
% 63.80/20.38 |-Branch two:
% 63.80/20.38 | (421) ~ (all_96_0_136 = 0)
% 63.80/20.38 | (434) all_92_0_130 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 +-Applying beta-rule and splitting (392), into two cases.
% 63.80/20.38 |-Branch one:
% 63.80/20.38 | (423) all_96_0_136 = 0
% 63.80/20.38 |
% 63.80/20.38 | Equations (423) can reduce 421 to:
% 63.80/20.38 | (291) $false
% 63.80/20.38 |
% 63.80/20.38 |-The branch is then unsatisfiable
% 63.80/20.38 |-Branch two:
% 63.80/20.38 | (421) ~ (all_96_0_136 = 0)
% 63.80/20.38 | (438) all_92_0_130 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 +-Applying beta-rule and splitting (404), into two cases.
% 63.80/20.38 |-Branch one:
% 63.80/20.38 | (439) all_44_0_52 = 0
% 63.80/20.38 |
% 63.80/20.38 | Equations (439) can reduce 192 to:
% 63.80/20.38 | (291) $false
% 63.80/20.38 |
% 63.80/20.38 |-The branch is then unsatisfiable
% 63.80/20.38 |-Branch two:
% 63.80/20.38 | (192) ~ (all_44_0_52 = 0)
% 63.80/20.38 | (442) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.38 |
% 63.80/20.38 +-Applying beta-rule and splitting (405), into two cases.
% 63.80/20.38 |-Branch one:
% 63.80/20.38 | (439) all_44_0_52 = 0
% 63.80/20.38 |
% 63.80/20.39 | Equations (439) can reduce 192 to:
% 63.80/20.39 | (291) $false
% 63.80/20.39 |
% 63.80/20.39 |-The branch is then unsatisfiable
% 63.80/20.39 |-Branch two:
% 63.80/20.39 | (192) ~ (all_44_0_52 = 0)
% 63.80/20.39 | (446) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.39 |
% 63.80/20.39 +-Applying beta-rule and splitting (398), into two cases.
% 63.80/20.39 |-Branch one:
% 63.80/20.39 | (447) all_72_0_95 = 0
% 63.80/20.39 |
% 63.80/20.39 | Equations (447) can reduce 242 to:
% 63.80/20.39 | (291) $false
% 63.80/20.39 |
% 63.80/20.39 |-The branch is then unsatisfiable
% 63.80/20.39 |-Branch two:
% 63.80/20.39 | (242) ~ (all_72_0_95 = 0)
% 63.80/20.39 | (450) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 63.80/20.39 |
% 63.80/20.39 +-Applying beta-rule and splitting (397), into two cases.
% 63.80/20.39 |-Branch one:
% 63.80/20.39 | (447) all_72_0_95 = 0
% 63.80/20.39 |
% 63.80/20.39 | Equations (447) can reduce 242 to:
% 63.80/20.39 | (291) $false
% 63.80/20.39 |
% 63.80/20.39 |-The branch is then unsatisfiable
% 63.80/20.39 |-Branch two:
% 63.80/20.39 | (242) ~ (all_72_0_95 = 0)
% 63.80/20.39 | (454) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_70_1_94, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (399), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (455) all_46_0_54 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (455) can reduce 196 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (196) ~ (all_46_0_54 = 0)
% 64.04/20.39 | (458) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (402), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (455) all_46_0_54 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (455) can reduce 196 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (196) ~ (all_46_0_54 = 0)
% 64.04/20.39 | (462) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (403), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (439) all_44_0_52 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (439) can reduce 192 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (192) ~ (all_44_0_52 = 0)
% 64.04/20.39 | (466) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (400), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (455) all_46_0_54 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (455) can reduce 196 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (196) ~ (all_46_0_54 = 0)
% 64.04/20.39 | (470) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (401), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (455) all_46_0_54 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (455) can reduce 196 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (196) ~ (all_46_0_54 = 0)
% 64.04/20.39 | (474) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (394), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (478) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (395), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (482) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (396), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (486) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (434), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (487) all_92_0_130 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (487) can reduce 422 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (422) ~ (all_92_0_130 = 0)
% 64.04/20.39 | (490) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 | Instantiating (490) with all_653_0_850, all_653_1_851, all_653_2_852, all_653_3_853 yields:
% 64.04/20.39 | (491) apart_point_and_line(all_1_1_1, all_1_4_4) = all_653_1_851 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_653_0_850 & distinct_lines(all_1_5_5, all_1_4_4) = all_653_2_852 & distinct_points(all_1_1_1, all_1_1_1) = all_653_3_853 & ( ~ (all_653_2_852 = 0) | ~ (all_653_3_853 = 0) | all_653_0_850 = 0 | all_653_1_851 = 0)
% 64.04/20.39 |
% 64.04/20.39 | Applying alpha-rule on (491) yields:
% 64.04/20.39 | (492) distinct_points(all_1_1_1, all_1_1_1) = all_653_3_853
% 64.04/20.39 | (493) ~ (all_653_2_852 = 0) | ~ (all_653_3_853 = 0) | all_653_0_850 = 0 | all_653_1_851 = 0
% 64.04/20.39 | (494) apart_point_and_line(all_1_1_1, all_1_5_5) = all_653_0_850
% 64.04/20.39 | (495) distinct_lines(all_1_5_5, all_1_4_4) = all_653_2_852
% 64.04/20.39 | (496) apart_point_and_line(all_1_1_1, all_1_4_4) = all_653_1_851
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (438), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (487) all_92_0_130 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (487) can reduce 422 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (422) ~ (all_92_0_130 = 0)
% 64.04/20.39 | (500) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 | Instantiating (500) with all_658_0_854, all_658_1_855, all_658_2_856, all_658_3_857 yields:
% 64.04/20.39 | (501) apart_point_and_line(all_1_1_1, all_1_4_4) = all_658_0_854 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_658_1_855 & distinct_lines(all_1_5_5, all_1_4_4) = all_658_2_856 & distinct_points(all_1_1_1, all_1_1_1) = all_658_3_857 & ( ~ (all_658_2_856 = 0) | ~ (all_658_3_857 = 0) | all_658_0_854 = 0 | all_658_1_855 = 0)
% 64.04/20.39 |
% 64.04/20.39 | Applying alpha-rule on (501) yields:
% 64.04/20.39 | (502) ~ (all_658_2_856 = 0) | ~ (all_658_3_857 = 0) | all_658_0_854 = 0 | all_658_1_855 = 0
% 64.04/20.39 | (503) distinct_points(all_1_1_1, all_1_1_1) = all_658_3_857
% 64.04/20.39 | (504) distinct_lines(all_1_5_5, all_1_4_4) = all_658_2_856
% 64.04/20.39 | (505) apart_point_and_line(all_1_1_1, all_1_5_5) = all_658_1_855
% 64.04/20.39 | (506) apart_point_and_line(all_1_1_1, all_1_4_4) = all_658_0_854
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (450), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (510) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (454), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (514) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_70_1_94, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (462), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (518) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (470), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (522) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (474), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (526) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_44_1_53, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.39 |
% 64.04/20.39 +-Applying beta-rule and splitting (418), into two cases.
% 64.04/20.39 |-Branch one:
% 64.04/20.39 | (427) all_28_0_25 = 0
% 64.04/20.39 |
% 64.04/20.39 | Equations (427) can reduce 176 to:
% 64.04/20.39 | (291) $false
% 64.04/20.39 |
% 64.04/20.39 |-The branch is then unsatisfiable
% 64.04/20.39 |-Branch two:
% 64.04/20.39 | (176) ~ (all_28_0_25 = 0)
% 64.04/20.39 | (530) all_26_0_23 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 64.04/20.39 |
% 64.04/20.40 +-Applying beta-rule and splitting (478), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (290) all_1_0_0 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (290) can reduce 135 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (135) ~ (all_1_0_0 = 0)
% 64.04/20.40 | (534) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.40 |
% 64.04/20.40 | Instantiating (534) with all_699_0_878, all_699_1_879, all_699_2_880, all_699_3_881 yields:
% 64.04/20.40 | (535) apart_point_and_line(all_1_1_1, all_1_4_4) = all_699_1_879 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_699_0_878 & distinct_lines(all_1_3_3, all_1_4_4) = all_699_2_880 & distinct_points(all_1_1_1, all_1_2_2) = all_699_3_881 & ( ~ (all_699_2_880 = 0) | ~ (all_699_3_881 = 0) | all_699_0_878 = 0 | all_699_1_879 = 0)
% 64.04/20.40 |
% 64.04/20.40 | Applying alpha-rule on (535) yields:
% 64.04/20.40 | (536) apart_point_and_line(all_1_1_1, all_1_4_4) = all_699_1_879
% 64.04/20.40 | (537) apart_point_and_line(all_1_2_2, all_1_3_3) = all_699_0_878
% 64.04/20.40 | (538) ~ (all_699_2_880 = 0) | ~ (all_699_3_881 = 0) | all_699_0_878 = 0 | all_699_1_879 = 0
% 64.04/20.40 | (539) distinct_points(all_1_1_1, all_1_2_2) = all_699_3_881
% 64.04/20.40 | (540) distinct_lines(all_1_3_3, all_1_4_4) = all_699_2_880
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (486), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (290) all_1_0_0 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (290) can reduce 135 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (135) ~ (all_1_0_0 = 0)
% 64.04/20.40 | (544) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.40 |
% 64.04/20.40 | Instantiating (544) with all_704_0_882, all_704_1_883, all_704_2_884, all_704_3_885 yields:
% 64.04/20.40 | (545) apart_point_and_line(all_1_1_1, all_1_4_4) = all_704_1_883 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_704_0_882 & distinct_lines(all_1_4_4, all_1_3_3) = all_704_2_884 & distinct_points(all_1_1_1, all_1_2_2) = all_704_3_885 & ( ~ (all_704_2_884 = 0) | ~ (all_704_3_885 = 0) | all_704_0_882 = 0 | all_704_1_883 = 0)
% 64.04/20.40 |
% 64.04/20.40 | Applying alpha-rule on (545) yields:
% 64.04/20.40 | (546) ~ (all_704_2_884 = 0) | ~ (all_704_3_885 = 0) | all_704_0_882 = 0 | all_704_1_883 = 0
% 64.04/20.40 | (547) apart_point_and_line(all_1_2_2, all_1_3_3) = all_704_0_882
% 64.04/20.40 | (548) apart_point_and_line(all_1_1_1, all_1_4_4) = all_704_1_883
% 64.04/20.40 | (549) distinct_points(all_1_1_1, all_1_2_2) = all_704_3_885
% 64.04/20.40 | (550) distinct_lines(all_1_4_4, all_1_3_3) = all_704_2_884
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (410), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (551) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 64.04/20.40 |
% 64.04/20.40 | Using (420) and (551) yields:
% 64.04/20.40 | (366) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (420) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 64.04/20.40 | (554) all_24_1_20 = 0 | distinct_lines(all_1_5_5, all_1_4_4) = 0
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (414), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (551) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 64.04/20.40 |
% 64.04/20.40 | Using (420) and (551) yields:
% 64.04/20.40 | (366) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (420) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 64.04/20.40 | (558) ? [v0] : ( ~ (v0 = 0) & parallel_lines(all_1_4_4, all_1_5_5) = v0)
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (530), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (559) all_26_0_23 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (559) can reduce 172 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (172) ~ (all_26_0_23 = 0)
% 64.04/20.40 | (562) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 64.04/20.40 |
% 64.04/20.40 | Instantiating (562) with all_728_0_895, all_728_1_896, all_728_2_897 yields:
% 64.04/20.40 | (563) apart_point_and_line(all_1_1_1, all_1_4_4) = all_728_1_896 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_728_0_895 & distinct_lines(all_1_4_4, all_1_5_5) = all_728_2_897 & ( ~ (all_728_2_897 = 0) | all_728_0_895 = 0 | all_728_1_896 = 0)
% 64.04/20.40 |
% 64.04/20.40 | Applying alpha-rule on (563) yields:
% 64.04/20.40 | (564) apart_point_and_line(all_1_1_1, all_1_4_4) = all_728_1_896
% 64.04/20.40 | (565) apart_point_and_line(all_1_1_1, all_1_5_5) = all_728_0_895
% 64.04/20.40 | (566) distinct_lines(all_1_4_4, all_1_5_5) = all_728_2_897
% 64.04/20.40 | (567) ~ (all_728_2_897 = 0) | all_728_0_895 = 0 | all_728_1_896 = 0
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (413), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (551) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 64.04/20.40 |
% 64.04/20.40 | Using (420) and (551) yields:
% 64.04/20.40 | (366) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (420) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 64.04/20.40 | (571) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(v0, all_1_4_4) = v1)
% 64.04/20.40 |
% 64.04/20.40 | Instantiating (571) with all_734_0_898, all_734_1_899 yields:
% 64.04/20.40 | (572) ~ (all_734_0_898 = 0) & intersection_point(all_1_4_4, all_1_5_5) = all_734_1_899 & apart_point_and_line(all_734_1_899, all_1_4_4) = all_734_0_898
% 64.04/20.40 |
% 64.04/20.40 | Applying alpha-rule on (572) yields:
% 64.04/20.40 | (573) ~ (all_734_0_898 = 0)
% 64.04/20.40 | (574) intersection_point(all_1_4_4, all_1_5_5) = all_734_1_899
% 64.04/20.40 | (575) apart_point_and_line(all_734_1_899, all_1_4_4) = all_734_0_898
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (416), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (576) all_30_3_30 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (576) can reduce 353 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (353) ~ (all_30_3_30 = 0)
% 64.04/20.40 | (579) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_5_5) = v0)
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (415), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (580) distinct_lines(all_1_4_4, all_1_5_5) = 0
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (382), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (487) all_92_0_130 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (487) can reduce 422 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (422) ~ (all_92_0_130 = 0)
% 64.04/20.40 | (584) all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (384), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (423) all_96_0_136 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (423) can reduce 421 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.40 | (588) all_1_0_0 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_5_5, all_1_3_3) = v1 & distinct_lines(all_1_5_5, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (584), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (439) all_44_0_52 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (439) can reduce 192 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (192) ~ (all_44_0_52 = 0)
% 64.04/20.40 | (592) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.40 |
% 64.04/20.40 | Instantiating (592) with all_767_0_901, all_767_1_902, all_767_2_903, all_767_3_904 yields:
% 64.04/20.40 | (593) apart_point_and_line(all_44_1_53, all_1_4_4) = all_767_0_901 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_767_1_902 & distinct_lines(all_1_4_4, all_1_5_5) = all_767_2_903 & distinct_points(all_1_1_1, all_44_1_53) = all_767_3_904 & ( ~ (all_767_2_903 = 0) | ~ (all_767_3_904 = 0) | all_767_0_901 = 0 | all_767_1_902 = 0)
% 64.04/20.40 |
% 64.04/20.40 | Applying alpha-rule on (593) yields:
% 64.04/20.40 | (594) apart_point_and_line(all_44_1_53, all_1_4_4) = all_767_0_901
% 64.04/20.40 | (595) apart_point_and_line(all_1_1_1, all_1_5_5) = all_767_1_902
% 64.04/20.40 | (596) distinct_points(all_1_1_1, all_44_1_53) = all_767_3_904
% 64.04/20.40 | (597) distinct_lines(all_1_4_4, all_1_5_5) = all_767_2_903
% 64.04/20.40 | (598) ~ (all_767_2_903 = 0) | ~ (all_767_3_904 = 0) | all_767_0_901 = 0 | all_767_1_902 = 0
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (388), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (423) all_96_0_136 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (423) can reduce 421 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.40 | (602) all_46_0_54 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (383), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (423) all_96_0_136 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (423) can reduce 421 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.40 | (606) all_1_0_0 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_3_3, all_1_5_5) = v1 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (389), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (423) all_96_0_136 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (423) can reduce 421 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.40 | (610) all_46_0_54 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_53, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (385), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (423) all_96_0_136 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (423) can reduce 421 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.40 | (614) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (387), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (423) all_96_0_136 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (423) can reduce 421 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.40 | (618) all_46_0_54 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.40 |
% 64.04/20.40 +-Applying beta-rule and splitting (390), into two cases.
% 64.04/20.40 |-Branch one:
% 64.04/20.40 | (423) all_96_0_136 = 0
% 64.04/20.40 |
% 64.04/20.40 | Equations (423) can reduce 421 to:
% 64.04/20.40 | (291) $false
% 64.04/20.40 |
% 64.04/20.40 |-The branch is then unsatisfiable
% 64.04/20.40 |-Branch two:
% 64.04/20.40 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.40 | (622) all_46_0_54 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (386), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (423) all_96_0_136 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (423) can reduce 421 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.41 | (626) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (411), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (551) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 64.04/20.41 |
% 64.04/20.41 | Using (420) and (551) yields:
% 64.04/20.41 | (366) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (420) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 64.04/20.41 | (630) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(v2) = v3 & line(all_1_4_4) = v0 & line(all_1_5_5) = v1 & intersection_point(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 64.04/20.41 |
% 64.04/20.41 | Instantiating (630) with all_813_0_909, all_813_1_910, all_813_2_911, all_813_3_912 yields:
% 64.04/20.41 | (631) point(all_813_1_910) = all_813_0_909 & line(all_1_4_4) = all_813_3_912 & line(all_1_5_5) = all_813_2_911 & intersection_point(all_1_4_4, all_1_5_5) = all_813_1_910 & ( ~ (all_813_2_911 = 0) | ~ (all_813_3_912 = 0) | all_813_0_909 = 0)
% 64.04/20.41 |
% 64.04/20.41 | Applying alpha-rule on (631) yields:
% 64.04/20.41 | (632) point(all_813_1_910) = all_813_0_909
% 64.04/20.41 | (633) line(all_1_4_4) = all_813_3_912
% 64.04/20.41 | (634) intersection_point(all_1_4_4, all_1_5_5) = all_813_1_910
% 64.04/20.41 | (635) ~ (all_813_2_911 = 0) | ~ (all_813_3_912 = 0) | all_813_0_909 = 0
% 64.04/20.41 | (636) line(all_1_5_5) = all_813_2_911
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (606), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (290) all_1_0_0 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (290) can reduce 135 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (135) ~ (all_1_0_0 = 0)
% 64.04/20.41 | (640) ? [v0] : ? [v1] : (convergent_lines(all_1_3_3, all_1_5_5) = v1 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (614), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (290) all_1_0_0 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (290) can reduce 135 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (135) ~ (all_1_0_0 = 0)
% 64.04/20.41 | (644) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 | Instantiating (644) with all_828_0_919, all_828_1_920, all_828_2_921, all_828_3_922 yields:
% 64.04/20.41 | (645) apart_point_and_line(all_1_1_1, all_1_3_3) = all_828_0_919 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_828_1_920 & distinct_lines(all_1_3_3, all_1_5_5) = all_828_2_921 & distinct_points(all_1_1_1, all_1_1_1) = all_828_3_922 & ( ~ (all_828_2_921 = 0) | ~ (all_828_3_922 = 0) | all_828_0_919 = 0 | all_828_1_920 = 0)
% 64.04/20.41 |
% 64.04/20.41 | Applying alpha-rule on (645) yields:
% 64.04/20.41 | (646) distinct_points(all_1_1_1, all_1_1_1) = all_828_3_922
% 64.04/20.41 | (647) ~ (all_828_2_921 = 0) | ~ (all_828_3_922 = 0) | all_828_0_919 = 0 | all_828_1_920 = 0
% 64.04/20.41 | (648) apart_point_and_line(all_1_1_1, all_1_3_3) = all_828_0_919
% 64.04/20.41 | (649) apart_point_and_line(all_1_1_1, all_1_5_5) = all_828_1_920
% 64.04/20.41 | (650) distinct_lines(all_1_3_3, all_1_5_5) = all_828_2_921
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (626), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (290) all_1_0_0 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (290) can reduce 135 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (135) ~ (all_1_0_0 = 0)
% 64.04/20.41 | (654) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 | Instantiating (654) with all_843_0_931, all_843_1_932, all_843_2_933, all_843_3_934 yields:
% 64.04/20.41 | (655) apart_point_and_line(all_1_1_1, all_1_3_3) = all_843_1_932 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_843_0_931 & distinct_lines(all_1_3_3, all_1_5_5) = all_843_2_933 & distinct_points(all_1_1_1, all_1_1_1) = all_843_3_934 & ( ~ (all_843_2_933 = 0) | ~ (all_843_3_934 = 0) | all_843_0_931 = 0 | all_843_1_932 = 0)
% 64.04/20.41 |
% 64.04/20.41 | Applying alpha-rule on (655) yields:
% 64.04/20.41 | (656) apart_point_and_line(all_1_1_1, all_1_3_3) = all_843_1_932
% 64.04/20.41 | (657) ~ (all_843_2_933 = 0) | ~ (all_843_3_934 = 0) | all_843_0_931 = 0 | all_843_1_932 = 0
% 64.04/20.41 | (658) distinct_points(all_1_1_1, all_1_1_1) = all_843_3_934
% 64.04/20.41 | (659) apart_point_and_line(all_1_1_1, all_1_5_5) = all_843_0_931
% 64.04/20.41 | (660) distinct_lines(all_1_3_3, all_1_5_5) = all_843_2_933
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (412), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (551) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 64.04/20.41 |
% 64.04/20.41 | Using (420) and (551) yields:
% 64.04/20.41 | (366) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (420) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 64.04/20.41 | (664) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(v0, all_1_5_5) = v1)
% 64.04/20.41 |
% 64.04/20.41 | Instantiating (664) with all_899_0_947, all_899_1_948 yields:
% 64.04/20.41 | (665) ~ (all_899_0_947 = 0) & intersection_point(all_1_4_4, all_1_5_5) = all_899_1_948 & apart_point_and_line(all_899_1_948, all_1_5_5) = all_899_0_947
% 64.04/20.41 |
% 64.04/20.41 | Applying alpha-rule on (665) yields:
% 64.04/20.41 | (666) ~ (all_899_0_947 = 0)
% 64.04/20.41 | (667) intersection_point(all_1_4_4, all_1_5_5) = all_899_1_948
% 64.04/20.41 | (668) apart_point_and_line(all_899_1_948, all_1_5_5) = all_899_0_947
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (381), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (439) all_44_0_52 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (439) can reduce 192 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (192) ~ (all_44_0_52 = 0)
% 64.04/20.41 | (672) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_44_1_53, all_1_5_5) = v3 & apart_point_and_line(all_44_1_53, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (377), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (447) all_72_0_95 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (447) can reduce 242 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (242) ~ (all_72_0_95 = 0)
% 64.04/20.41 | (676) all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v2 & apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_70_1_94, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (378), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (447) all_72_0_95 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (447) can reduce 242 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (242) ~ (all_72_0_95 = 0)
% 64.04/20.41 | (680) all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v3 & apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_44_1_53, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (379), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (447) all_72_0_95 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (447) can reduce 242 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (242) ~ (all_72_0_95 = 0)
% 64.04/20.41 | (684) all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v2 & apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_70_1_94, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (380), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (447) all_72_0_95 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (447) can reduce 242 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (242) ~ (all_72_0_95 = 0)
% 64.04/20.41 | (688) all_44_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v3 & apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (676), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (439) all_44_0_52 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (439) can reduce 192 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (192) ~ (all_44_0_52 = 0)
% 64.04/20.41 | (692) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v2 & apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_70_1_94, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 | Instantiating (692) with all_973_0_957, all_973_1_958, all_973_2_959, all_973_3_960 yields:
% 64.04/20.41 | (693) apart_point_and_line(all_70_1_94, all_1_5_5) = all_973_1_958 & apart_point_and_line(all_44_1_53, all_1_4_4) = all_973_0_957 & distinct_lines(all_1_4_4, all_1_5_5) = all_973_2_959 & distinct_points(all_70_1_94, all_44_1_53) = all_973_3_960 & ( ~ (all_973_2_959 = 0) | ~ (all_973_3_960 = 0) | all_973_0_957 = 0 | all_973_1_958 = 0)
% 64.04/20.41 |
% 64.04/20.41 | Applying alpha-rule on (693) yields:
% 64.04/20.41 | (694) distinct_points(all_70_1_94, all_44_1_53) = all_973_3_960
% 64.04/20.41 | (695) distinct_lines(all_1_4_4, all_1_5_5) = all_973_2_959
% 64.04/20.41 | (696) ~ (all_973_2_959 = 0) | ~ (all_973_3_960 = 0) | all_973_0_957 = 0 | all_973_1_958 = 0
% 64.04/20.41 | (697) apart_point_and_line(all_70_1_94, all_1_5_5) = all_973_1_958
% 64.04/20.41 | (698) apart_point_and_line(all_44_1_53, all_1_4_4) = all_973_0_957
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (680), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (439) all_44_0_52 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (439) can reduce 192 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (192) ~ (all_44_0_52 = 0)
% 64.04/20.41 | (702) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v3 & apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_44_1_53, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (684), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (439) all_44_0_52 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (439) can reduce 192 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (192) ~ (all_44_0_52 = 0)
% 64.04/20.41 | (706) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v2 & apart_point_and_line(all_44_1_53, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_70_1_94, all_44_1_53) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.41 |
% 64.04/20.41 +-Applying beta-rule and splitting (688), into two cases.
% 64.04/20.41 |-Branch one:
% 64.04/20.41 | (439) all_44_0_52 = 0
% 64.04/20.41 |
% 64.04/20.41 | Equations (439) can reduce 192 to:
% 64.04/20.41 | (291) $false
% 64.04/20.41 |
% 64.04/20.41 |-The branch is then unsatisfiable
% 64.04/20.41 |-Branch two:
% 64.04/20.41 | (192) ~ (all_44_0_52 = 0)
% 64.04/20.42 | (710) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_70_1_94, all_1_5_5) = v3 & apart_point_and_line(all_44_1_53, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_44_1_53, all_70_1_94) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.42 |
% 64.04/20.42 | Instantiating (710) with all_988_0_969, all_988_1_970, all_988_2_971, all_988_3_972 yields:
% 64.04/20.42 | (711) apart_point_and_line(all_70_1_94, all_1_5_5) = all_988_0_969 & apart_point_and_line(all_44_1_53, all_1_4_4) = all_988_1_970 & distinct_lines(all_1_4_4, all_1_5_5) = all_988_2_971 & distinct_points(all_44_1_53, all_70_1_94) = all_988_3_972 & ( ~ (all_988_2_971 = 0) | ~ (all_988_3_972 = 0) | all_988_0_969 = 0 | all_988_1_970 = 0)
% 64.04/20.42 |
% 64.04/20.42 | Applying alpha-rule on (711) yields:
% 64.04/20.42 | (712) distinct_lines(all_1_4_4, all_1_5_5) = all_988_2_971
% 64.04/20.42 | (713) distinct_points(all_44_1_53, all_70_1_94) = all_988_3_972
% 64.04/20.42 | (714) ~ (all_988_2_971 = 0) | ~ (all_988_3_972 = 0) | all_988_0_969 = 0 | all_988_1_970 = 0
% 64.04/20.42 | (715) apart_point_and_line(all_44_1_53, all_1_4_4) = all_988_1_970
% 64.04/20.42 | (716) apart_point_and_line(all_70_1_94, all_1_5_5) = all_988_0_969
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (61) with all_1_4_4, all_1_5_5, all_813_1_910, all_1_1_1 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_813_1_910, intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1, yields:
% 64.04/20.42 | (717) all_813_1_910 = all_1_1_1
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (61) with all_1_4_4, all_1_5_5, all_813_1_910, all_899_1_948 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_899_1_948, intersection_point(all_1_4_4, all_1_5_5) = all_813_1_910, yields:
% 64.04/20.42 | (718) all_899_1_948 = all_813_1_910
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (61) with all_1_4_4, all_1_5_5, all_734_1_899, all_899_1_948 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_899_1_948, intersection_point(all_1_4_4, all_1_5_5) = all_734_1_899, yields:
% 64.04/20.42 | (719) all_899_1_948 = all_734_1_899
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_5_5, all_899_0_947, all_96_0_136 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 64.04/20.42 | (720) all_899_0_947 = all_96_0_136 | ~ (apart_point_and_line(all_1_1_1, all_1_5_5) = all_899_0_947)
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_4_4, all_728_1_896, all_734_0_898 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_728_1_896, yields:
% 64.04/20.42 | (721) all_734_0_898 = all_728_1_896 | ~ (apart_point_and_line(all_1_1_1, all_1_4_4) = all_734_0_898)
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_4_4, all_699_1_879, all_92_0_130 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_699_1_879, apart_point_and_line(all_1_1_1, all_1_4_4) = all_92_0_130, yields:
% 64.04/20.42 | (722) all_699_1_879 = all_92_0_130
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_4_4, all_699_1_879, all_728_1_896 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_728_1_896, apart_point_and_line(all_1_1_1, all_1_4_4) = all_699_1_879, yields:
% 64.04/20.42 | (723) all_728_1_896 = all_699_1_879
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_4_4, all_699_1_879, all_704_1_883 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_704_1_883, apart_point_and_line(all_1_1_1, all_1_4_4) = all_699_1_879, yields:
% 64.04/20.42 | (724) all_704_1_883 = all_699_1_879
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_4_4, all_658_0_854, all_728_1_896 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_728_1_896, apart_point_and_line(all_1_1_1, all_1_4_4) = all_658_0_854, yields:
% 64.04/20.42 | (725) all_728_1_896 = all_658_0_854
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_4_4, all_653_1_851, all_704_1_883 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_704_1_883, apart_point_and_line(all_1_1_1, all_1_4_4) = all_653_1_851, yields:
% 64.04/20.42 | (726) all_704_1_883 = all_653_1_851
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_5_5, all_828_1_920, all_843_0_931 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_843_0_931, apart_point_and_line(all_1_1_1, all_1_5_5) = all_828_1_920, yields:
% 64.04/20.42 | (727) all_843_0_931 = all_828_1_920
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_5_5, all_767_1_902, all_96_0_136 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_767_1_902, apart_point_and_line(all_1_1_1, all_1_5_5) = all_96_0_136, yields:
% 64.04/20.42 | (728) all_767_1_902 = all_96_0_136
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_5_5, all_767_1_902, all_843_0_931 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_843_0_931, apart_point_and_line(all_1_1_1, all_1_5_5) = all_767_1_902, yields:
% 64.04/20.42 | (729) all_843_0_931 = all_767_1_902
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (104) with all_1_1_1, all_1_5_5, all_728_0_895, all_843_0_931 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_843_0_931, apart_point_and_line(all_1_1_1, all_1_5_5) = all_728_0_895, yields:
% 64.04/20.42 | (730) all_843_0_931 = all_728_0_895
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (20) with all_1_4_4, all_1_5_5, all_973_2_959, all_988_2_971 and discharging atoms distinct_lines(all_1_4_4, all_1_5_5) = all_988_2_971, distinct_lines(all_1_4_4, all_1_5_5) = all_973_2_959, yields:
% 64.04/20.42 | (731) all_988_2_971 = all_973_2_959
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (20) with all_1_4_4, all_1_5_5, all_767_2_903, all_973_2_959 and discharging atoms distinct_lines(all_1_4_4, all_1_5_5) = all_973_2_959, distinct_lines(all_1_4_4, all_1_5_5) = all_767_2_903, yields:
% 64.04/20.42 | (732) all_973_2_959 = all_767_2_903
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (20) with all_1_4_4, all_1_5_5, all_728_2_897, all_767_2_903 and discharging atoms distinct_lines(all_1_4_4, all_1_5_5) = all_767_2_903, distinct_lines(all_1_4_4, all_1_5_5) = all_728_2_897, yields:
% 64.04/20.42 | (733) all_767_2_903 = all_728_2_897
% 64.04/20.42 |
% 64.04/20.42 | Instantiating formula (20) with all_1_4_4, all_1_5_5, 0, all_988_2_971 and discharging atoms distinct_lines(all_1_4_4, all_1_5_5) = all_988_2_971, distinct_lines(all_1_4_4, all_1_5_5) = 0, yields:
% 64.04/20.42 | (734) all_988_2_971 = 0
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (731,734) yields a new equation:
% 64.04/20.42 | (735) all_973_2_959 = 0
% 64.04/20.42 |
% 64.04/20.42 | Simplifying 735 yields:
% 64.04/20.42 | (736) all_973_2_959 = 0
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (732,736) yields a new equation:
% 64.04/20.42 | (737) all_767_2_903 = 0
% 64.04/20.42 |
% 64.04/20.42 | Simplifying 737 yields:
% 64.04/20.42 | (738) all_767_2_903 = 0
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (718,719) yields a new equation:
% 64.04/20.42 | (739) all_813_1_910 = all_734_1_899
% 64.04/20.42 |
% 64.04/20.42 | Simplifying 739 yields:
% 64.04/20.42 | (740) all_813_1_910 = all_734_1_899
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (730,727) yields a new equation:
% 64.04/20.42 | (741) all_828_1_920 = all_728_0_895
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (729,727) yields a new equation:
% 64.04/20.42 | (742) all_828_1_920 = all_767_1_902
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (742,741) yields a new equation:
% 64.04/20.42 | (743) all_767_1_902 = all_728_0_895
% 64.04/20.42 |
% 64.04/20.42 | Simplifying 743 yields:
% 64.04/20.42 | (744) all_767_1_902 = all_728_0_895
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (717,740) yields a new equation:
% 64.04/20.42 | (745) all_734_1_899 = all_1_1_1
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (744,728) yields a new equation:
% 64.04/20.42 | (746) all_728_0_895 = all_96_0_136
% 64.04/20.42 |
% 64.04/20.42 | Simplifying 746 yields:
% 64.04/20.42 | (747) all_728_0_895 = all_96_0_136
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (733,738) yields a new equation:
% 64.04/20.42 | (748) all_728_2_897 = 0
% 64.04/20.42 |
% 64.04/20.42 | Simplifying 748 yields:
% 64.04/20.42 | (749) all_728_2_897 = 0
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (723,725) yields a new equation:
% 64.04/20.42 | (750) all_699_1_879 = all_658_0_854
% 64.04/20.42 |
% 64.04/20.42 | Simplifying 750 yields:
% 64.04/20.42 | (751) all_699_1_879 = all_658_0_854
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (724,726) yields a new equation:
% 64.04/20.42 | (752) all_699_1_879 = all_653_1_851
% 64.04/20.42 |
% 64.04/20.42 | Simplifying 752 yields:
% 64.04/20.42 | (753) all_699_1_879 = all_653_1_851
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (722,751) yields a new equation:
% 64.04/20.42 | (754) all_658_0_854 = all_92_0_130
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (753,751) yields a new equation:
% 64.04/20.42 | (755) all_658_0_854 = all_653_1_851
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (754,755) yields a new equation:
% 64.04/20.42 | (756) all_653_1_851 = all_92_0_130
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (756,755) yields a new equation:
% 64.04/20.42 | (754) all_658_0_854 = all_92_0_130
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (754,725) yields a new equation:
% 64.04/20.42 | (758) all_728_1_896 = all_92_0_130
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (745,719) yields a new equation:
% 64.04/20.42 | (759) all_899_1_948 = all_1_1_1
% 64.04/20.42 |
% 64.04/20.42 | From (759) and (668) follows:
% 64.04/20.42 | (760) apart_point_and_line(all_1_1_1, all_1_5_5) = all_899_0_947
% 64.04/20.42 |
% 64.04/20.42 | From (745) and (575) follows:
% 64.04/20.42 | (761) apart_point_and_line(all_1_1_1, all_1_4_4) = all_734_0_898
% 64.04/20.42 |
% 64.04/20.42 +-Applying beta-rule and splitting (721), into two cases.
% 64.04/20.42 |-Branch one:
% 64.04/20.42 | (762) ~ (apart_point_and_line(all_1_1_1, all_1_4_4) = all_734_0_898)
% 64.04/20.42 |
% 64.04/20.42 | Using (761) and (762) yields:
% 64.04/20.42 | (366) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.42 |-Branch two:
% 64.04/20.42 | (761) apart_point_and_line(all_1_1_1, all_1_4_4) = all_734_0_898
% 64.04/20.42 | (765) all_734_0_898 = all_728_1_896
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (758,765) yields a new equation:
% 64.04/20.42 | (766) all_734_0_898 = all_92_0_130
% 64.04/20.42 |
% 64.04/20.42 | Equations (766) can reduce 573 to:
% 64.04/20.42 | (422) ~ (all_92_0_130 = 0)
% 64.04/20.42 |
% 64.04/20.42 +-Applying beta-rule and splitting (720), into two cases.
% 64.04/20.42 |-Branch one:
% 64.04/20.42 | (768) ~ (apart_point_and_line(all_1_1_1, all_1_5_5) = all_899_0_947)
% 64.04/20.42 |
% 64.04/20.42 | Using (760) and (768) yields:
% 64.04/20.42 | (366) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.42 |-Branch two:
% 64.04/20.42 | (760) apart_point_and_line(all_1_1_1, all_1_5_5) = all_899_0_947
% 64.04/20.42 | (771) all_899_0_947 = all_96_0_136
% 64.04/20.42 |
% 64.04/20.42 | Equations (771) can reduce 666 to:
% 64.04/20.42 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.42 |
% 64.04/20.42 +-Applying beta-rule and splitting (408), into two cases.
% 64.04/20.42 |-Branch one:
% 64.04/20.42 | (487) all_92_0_130 = 0
% 64.04/20.42 |
% 64.04/20.42 | Equations (487) can reduce 422 to:
% 64.04/20.42 | (291) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.42 |-Branch two:
% 64.04/20.42 | (422) ~ (all_92_0_130 = 0)
% 64.04/20.42 | (776) all_26_0_23 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.42 |
% 64.04/20.42 +-Applying beta-rule and splitting (417), into two cases.
% 64.04/20.42 |-Branch one:
% 64.04/20.42 | (423) all_96_0_136 = 0
% 64.04/20.42 |
% 64.04/20.42 | Equations (423) can reduce 421 to:
% 64.04/20.42 | (291) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.42 |-Branch two:
% 64.04/20.42 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.42 | (780) all_92_0_130 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 64.04/20.42 |
% 64.04/20.42 +-Applying beta-rule and splitting (406), into two cases.
% 64.04/20.42 |-Branch one:
% 64.04/20.42 | (423) all_96_0_136 = 0
% 64.04/20.42 |
% 64.04/20.42 | Equations (423) can reduce 421 to:
% 64.04/20.42 | (291) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.42 |-Branch two:
% 64.04/20.42 | (421) ~ (all_96_0_136 = 0)
% 64.04/20.42 | (784) all_28_0_25 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 64.04/20.42 |
% 64.04/20.42 +-Applying beta-rule and splitting (567), into two cases.
% 64.04/20.42 |-Branch one:
% 64.04/20.42 | (785) ~ (all_728_2_897 = 0)
% 64.04/20.42 |
% 64.04/20.42 | Equations (749) can reduce 785 to:
% 64.04/20.42 | (291) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.42 |-Branch two:
% 64.04/20.42 | (749) all_728_2_897 = 0
% 64.04/20.42 | (788) all_728_0_895 = 0 | all_728_1_896 = 0
% 64.04/20.42 |
% 64.04/20.42 +-Applying beta-rule and splitting (788), into two cases.
% 64.04/20.42 |-Branch one:
% 64.04/20.42 | (789) all_728_0_895 = 0
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (789,747) yields a new equation:
% 64.04/20.42 | (423) all_96_0_136 = 0
% 64.04/20.42 |
% 64.04/20.42 | Equations (423) can reduce 421 to:
% 64.04/20.42 | (291) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.42 |-Branch two:
% 64.04/20.42 | (792) ~ (all_728_0_895 = 0)
% 64.04/20.42 | (793) all_728_1_896 = 0
% 64.04/20.42 |
% 64.04/20.42 | Combining equations (793,758) yields a new equation:
% 64.04/20.42 | (487) all_92_0_130 = 0
% 64.04/20.42 |
% 64.04/20.42 | Equations (487) can reduce 422 to:
% 64.04/20.42 | (291) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.42 |-Branch two:
% 64.04/20.42 | (796) ~ (distinct_lines(all_1_4_4, all_1_5_5) = 0)
% 64.04/20.42 | (576) all_30_3_30 = 0
% 64.04/20.42 |
% 64.04/20.42 | Equations (576) can reduce 353 to:
% 64.04/20.42 | (291) $false
% 64.04/20.42 |
% 64.04/20.42 |-The branch is then unsatisfiable
% 64.04/20.43 |-Branch two:
% 64.04/20.43 | (487) all_92_0_130 = 0
% 64.04/20.43 | (800) ~ (all_92_1_131 = 0)
% 64.04/20.43 |
% 64.04/20.43 | Equations (409) can reduce 800 to:
% 64.04/20.43 | (291) $false
% 64.04/20.43 |
% 64.04/20.43 |-The branch is then unsatisfiable
% 64.04/20.43 |-Branch two:
% 64.04/20.43 | (423) all_96_0_136 = 0
% 64.04/20.43 | (803) ~ (all_96_1_137 = 0)
% 64.04/20.43 |
% 64.04/20.43 | Equations (419) can reduce 803 to:
% 64.04/20.43 | (291) $false
% 64.04/20.43 |
% 64.04/20.43 |-The branch is then unsatisfiable
% 64.04/20.43 |-Branch two:
% 64.04/20.43 | (805) all_58_0_71 = 0
% 64.04/20.43 | (806) ~ (all_58_1_72 = 0)
% 64.04/20.43 |
% 64.04/20.43 | Equations (338) can reduce 806 to:
% 64.04/20.43 | (291) $false
% 64.04/20.43 |
% 64.04/20.43 |-The branch is then unsatisfiable
% 64.04/20.43 |-Branch two:
% 64.04/20.43 | (808) all_56_0_69 = 0
% 64.04/20.43 | (809) ~ (all_56_1_70 = 0)
% 64.04/20.43 |
% 64.04/20.43 | Equations (344) can reduce 809 to:
% 64.04/20.43 | (291) $false
% 64.04/20.43 |
% 64.04/20.43 |-The branch is then unsatisfiable
% 64.04/20.43 |-Branch two:
% 64.04/20.43 | (811) ~ (distinct_points(all_1_2_2, all_1_1_1) = 0)
% 64.04/20.43 | (290) all_1_0_0 = 0
% 64.04/20.43 |
% 64.04/20.43 | Equations (290) can reduce 135 to:
% 64.04/20.43 | (291) $false
% 64.04/20.43 |
% 64.04/20.43 |-The branch is then unsatisfiable
% 64.04/20.43 % SZS output end Proof for theBenchmark
% 64.04/20.43
% 64.04/20.43 19850ms
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