TSTP Solution File: GEO199+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO199+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 03:48:35 EDT 2022
% Result : Theorem 23.00s 6.42s
% Output : Proof 32.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO199+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 01:31:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.67/0.67 ____ _
% 0.67/0.67 ___ / __ \_____(_)___ ________ __________
% 0.67/0.67 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.67/0.67 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.67/0.67 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.67/0.67
% 0.67/0.67 A Theorem Prover for First-Order Logic
% 0.67/0.67 (ePrincess v.1.0)
% 0.67/0.67
% 0.67/0.67 (c) Philipp Rümmer, 2009-2015
% 0.67/0.67 (c) Peter Backeman, 2014-2015
% 0.67/0.67 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.67/0.67 Free software under GNU Lesser General Public License (LGPL).
% 0.67/0.67 Bug reports to peter@backeman.se
% 0.67/0.67
% 0.67/0.67 For more information, visit http://user.uu.se/~petba168/breu/
% 0.67/0.67
% 0.67/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.79/0.73 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.79/1.09 Prover 0: Preprocessing ...
% 2.16/1.26 Prover 0: Warning: ignoring some quantifiers
% 2.16/1.29 Prover 0: Constructing countermodel ...
% 3.59/1.74 Prover 0: gave up
% 3.59/1.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.80/1.78 Prover 1: Preprocessing ...
% 3.98/1.90 Prover 1: Constructing countermodel ...
% 4.26/1.95 Prover 1: gave up
% 4.26/1.95 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.26/1.98 Prover 2: Preprocessing ...
% 5.21/2.15 Prover 2: Warning: ignoring some quantifiers
% 5.21/2.16 Prover 2: Constructing countermodel ...
% 13.63/4.18 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 13.63/4.20 Prover 3: Preprocessing ...
% 13.63/4.22 Prover 3: Warning: ignoring some quantifiers
% 13.63/4.22 Prover 3: Constructing countermodel ...
% 14.17/4.29 Prover 3: gave up
% 14.17/4.29 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 14.17/4.32 Prover 4: Preprocessing ...
% 14.76/4.41 Prover 4: Warning: ignoring some quantifiers
% 14.76/4.42 Prover 4: Constructing countermodel ...
% 18.39/5.32 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 18.39/5.34 Prover 5: Preprocessing ...
% 18.69/5.41 Prover 5: Constructing countermodel ...
% 23.00/6.42 Prover 5: proved (1104ms)
% 23.00/6.42 Prover 4: stopped
% 23.00/6.42 Prover 2: stopped
% 23.00/6.42
% 23.00/6.42 No countermodel exists, formula is valid
% 23.00/6.42 % SZS status Theorem for theBenchmark
% 23.00/6.42
% 23.00/6.42 Generating proof ... found it (size 558)
% 31.17/8.38
% 31.17/8.38 % SZS output start Proof for theBenchmark
% 31.17/8.38 Assumed formulas after preprocessing and simplification:
% 31.17/8.38 | (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 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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] : ( ~ (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] : ( ~ (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] : (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] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & intersection_point(v1, v0) = v5 & intersection_point(v0, v1) = v3 & apart_point_and_line(v5, v2) = 0 & apart_point_and_line(v3, v2) = v4 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0)
% 31.17/8.43 | Applying alpha-rule on (0) yields:
% 31.17/8.43 | (1) ! [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)))
% 31.17/8.43 | (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))))
% 31.17/8.43 | (3) ! [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))
% 31.17/8.43 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 31.17/8.43 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 31.17/8.43 | (6) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & intersection_point(v1, v0) = v5 & intersection_point(v0, v1) = v3 & apart_point_and_line(v5, v2) = 0 & apart_point_and_line(v3, v2) = v4 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0)
% 31.17/8.43 | (7) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 31.17/8.43 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 31.17/8.43 | (9) ! [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))))
% 31.17/8.43 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 31.17/8.43 | (11) ! [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))))
% 31.17/8.43 | (12) ! [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)))
% 31.17/8.43 | (13) ! [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))))
% 31.17/8.43 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 31.17/8.43 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 31.17/8.43 | (16) ! [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))
% 31.17/8.44 | (17) ! [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)
% 31.17/8.44 | (18) ! [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))
% 31.17/8.44 | (19) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 31.17/8.44 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 31.17/8.44 | (21) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 31.17/8.44 | (22) ! [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))
% 31.17/8.44 | (23) ! [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)))
% 31.17/8.44 | (24) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 31.17/8.44 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 31.17/8.44 | (26) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 31.17/8.44 | (27) ! [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)))
% 31.17/8.44 | (28) ! [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))
% 31.17/8.44 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 31.17/8.44 | (30) ! [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)))
% 31.17/8.44 | (31) ! [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))
% 31.17/8.44 | (32) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 31.17/8.44 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 31.17/8.44 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 31.17/8.44 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 31.17/8.44 | (36) ! [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)))
% 31.17/8.44 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 31.17/8.44 | (38) ! [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)))
% 31.17/8.45 | (39) ! [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)
% 31.17/8.45 | (40) ! [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)
% 31.17/8.45 | (41) ! [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)
% 31.17/8.45 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 31.17/8.45 | (43) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 31.17/8.45 |
% 31.17/8.45 | Instantiating (6) 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:
% 31.17/8.45 | (44) ~ (all_1_1_1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = all_1_0_0 & intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2 & apart_point_and_line(all_1_0_0, all_1_3_3) = 0 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1 & 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
% 31.17/8.45 |
% 31.17/8.45 | Applying alpha-rule on (44) yields:
% 31.17/8.45 | (45) convergent_lines(all_1_5_5, all_1_3_3) = 0
% 31.17/8.45 | (46) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 31.17/8.45 | (47) apart_point_and_line(all_1_0_0, all_1_3_3) = 0
% 31.17/8.45 | (48) ~ (all_1_1_1 = 0)
% 31.17/8.45 | (49) apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1
% 31.17/8.45 | (50) intersection_point(all_1_4_4, all_1_5_5) = all_1_0_0
% 31.17/8.45 | (51) convergent_lines(all_1_3_3, all_1_4_4) = 0
% 31.17/8.45 | (52) intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (7) with all_1_4_4 yields:
% 31.17/8.45 | (53) ~ (convergent_lines(all_1_4_4, all_1_4_4) = 0)
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (7) with all_1_5_5 yields:
% 31.17/8.45 | (54) ~ (convergent_lines(all_1_5_5, all_1_5_5) = 0)
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (11) with all_1_0_0, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1_0_0, yields:
% 31.17/8.45 | (55) ? [v0] : ? [v1] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (2) with all_1_0_0, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1_0_0, yields:
% 31.17/8.45 | (56) ? [v0] : ? [v1] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (11) 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:
% 31.17/8.45 | (57) ? [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)))
% 31.17/8.45 |
% 31.17/8.45 | 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:
% 31.17/8.45 | (58) ? [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)))
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (40) with all_1_1_1, all_1_2_2, all_1_3_3, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = 0, apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, yields:
% 31.17/8.45 | (59) all_1_1_1 = 0 | distinct_points(all_1_0_0, all_1_2_2) = 0
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (27) with all_1_1_1, all_1_1_1, all_1_3_3, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, yields:
% 31.17/8.45 | (60) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (43) with all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 31.17/8.45 | (61) ? [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)
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (19) with all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 31.17/8.45 | (62) ? [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)
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (43) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 31.17/8.45 | (63) ? [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)
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (19) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 31.17/8.45 | (64) ? [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)
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (43) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.17/8.45 | (65) ? [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)
% 31.17/8.45 |
% 31.17/8.45 | Instantiating formula (19) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.17/8.45 | (66) ? [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)
% 31.17/8.45 |
% 31.17/8.45 | Instantiating (66) with all_16_0_6, all_16_1_7 yields:
% 31.17/8.45 | (67) ~ (all_16_0_6 = 0) & intersection_point(all_1_5_5, all_1_4_4) = all_16_1_7 & apart_point_and_line(all_16_1_7, all_1_5_5) = all_16_0_6
% 31.17/8.46 |
% 31.17/8.46 | Applying alpha-rule on (67) yields:
% 31.17/8.46 | (68) ~ (all_16_0_6 = 0)
% 31.17/8.46 | (69) intersection_point(all_1_5_5, all_1_4_4) = all_16_1_7
% 31.17/8.46 | (70) apart_point_and_line(all_16_1_7, all_1_5_5) = all_16_0_6
% 31.17/8.46 |
% 31.17/8.46 | Instantiating (64) with all_18_0_8, all_18_1_9 yields:
% 31.17/8.46 | (71) ~ (all_18_0_8 = 0) & intersection_point(all_1_5_5, all_1_3_3) = all_18_1_9 & apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8
% 31.17/8.46 |
% 31.17/8.46 | Applying alpha-rule on (71) yields:
% 31.17/8.46 | (72) ~ (all_18_0_8 = 0)
% 31.17/8.46 | (73) intersection_point(all_1_5_5, all_1_3_3) = all_18_1_9
% 31.17/8.46 | (74) apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8
% 31.17/8.46 |
% 31.17/8.46 | Instantiating (62) with all_20_0_10, all_20_1_11 yields:
% 31.17/8.46 | (75) ~ (all_20_0_10 = 0) & intersection_point(all_1_3_3, all_1_4_4) = all_20_1_11 & apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10
% 31.17/8.46 |
% 31.17/8.46 | Applying alpha-rule on (75) yields:
% 31.17/8.46 | (76) ~ (all_20_0_10 = 0)
% 31.17/8.46 | (77) intersection_point(all_1_3_3, all_1_4_4) = all_20_1_11
% 31.17/8.46 | (78) apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10
% 31.17/8.46 |
% 31.17/8.46 | Instantiating (61) with all_22_0_12, all_22_1_13 yields:
% 31.17/8.46 | (79) ~ (all_22_0_12 = 0) & intersection_point(all_1_3_3, all_1_4_4) = all_22_1_13 & apart_point_and_line(all_22_1_13, all_1_4_4) = all_22_0_12
% 31.64/8.46 |
% 31.64/8.46 | Applying alpha-rule on (79) yields:
% 31.64/8.46 | (80) ~ (all_22_0_12 = 0)
% 31.64/8.46 | (81) intersection_point(all_1_3_3, all_1_4_4) = all_22_1_13
% 31.64/8.46 | (82) apart_point_and_line(all_22_1_13, all_1_4_4) = all_22_0_12
% 31.64/8.46 |
% 31.64/8.46 | Instantiating (63) with all_24_0_14, all_24_1_15 yields:
% 31.64/8.46 | (83) ~ (all_24_0_14 = 0) & intersection_point(all_1_5_5, all_1_3_3) = all_24_1_15 & apart_point_and_line(all_24_1_15, all_1_3_3) = all_24_0_14
% 31.64/8.46 |
% 31.64/8.46 | Applying alpha-rule on (83) yields:
% 31.64/8.46 | (84) ~ (all_24_0_14 = 0)
% 31.64/8.46 | (85) intersection_point(all_1_5_5, all_1_3_3) = all_24_1_15
% 31.64/8.46 | (86) apart_point_and_line(all_24_1_15, all_1_3_3) = all_24_0_14
% 31.64/8.46 |
% 31.64/8.46 | Instantiating (65) with all_26_0_16, all_26_1_17 yields:
% 31.64/8.46 | (87) ~ (all_26_0_16 = 0) & intersection_point(all_1_5_5, all_1_4_4) = all_26_1_17 & apart_point_and_line(all_26_1_17, all_1_4_4) = all_26_0_16
% 31.64/8.46 |
% 31.64/8.46 | Applying alpha-rule on (87) yields:
% 31.64/8.46 | (88) ~ (all_26_0_16 = 0)
% 31.64/8.46 | (89) intersection_point(all_1_5_5, all_1_4_4) = all_26_1_17
% 31.64/8.46 | (90) apart_point_and_line(all_26_1_17, all_1_4_4) = all_26_0_16
% 31.64/8.46 |
% 31.64/8.46 | Instantiating (58) with all_28_0_18, all_28_1_19 yields:
% 31.64/8.46 | (91) apart_point_and_line(all_1_2_2, all_1_5_5) = all_28_0_18 & convergent_lines(all_1_5_5, all_1_4_4) = all_28_1_19 & ( ~ (all_28_0_18 = 0) | ~ (all_28_1_19 = 0))
% 31.64/8.46 |
% 31.64/8.46 | Applying alpha-rule on (91) yields:
% 31.64/8.46 | (92) apart_point_and_line(all_1_2_2, all_1_5_5) = all_28_0_18
% 31.64/8.46 | (93) convergent_lines(all_1_5_5, all_1_4_4) = all_28_1_19
% 31.64/8.46 | (94) ~ (all_28_0_18 = 0) | ~ (all_28_1_19 = 0)
% 31.64/8.46 |
% 31.64/8.46 | Instantiating (57) with all_30_0_20, all_30_1_21 yields:
% 31.64/8.46 | (95) apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_20 & convergent_lines(all_1_5_5, all_1_4_4) = all_30_1_21 & ( ~ (all_30_0_20 = 0) | ~ (all_30_1_21 = 0))
% 31.64/8.46 |
% 31.64/8.46 | Applying alpha-rule on (95) yields:
% 31.64/8.46 | (96) apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_20
% 31.64/8.46 | (97) convergent_lines(all_1_5_5, all_1_4_4) = all_30_1_21
% 31.64/8.46 | (98) ~ (all_30_0_20 = 0) | ~ (all_30_1_21 = 0)
% 31.64/8.46 |
% 31.64/8.46 | Instantiating (56) with all_32_0_22, all_32_1_23 yields:
% 31.64/8.46 | (99) apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22 & convergent_lines(all_1_4_4, all_1_5_5) = all_32_1_23 & ( ~ (all_32_0_22 = 0) | ~ (all_32_1_23 = 0))
% 31.64/8.46 |
% 31.64/8.46 | Applying alpha-rule on (99) yields:
% 31.64/8.46 | (100) apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22
% 31.64/8.46 | (101) convergent_lines(all_1_4_4, all_1_5_5) = all_32_1_23
% 31.64/8.46 | (102) ~ (all_32_0_22 = 0) | ~ (all_32_1_23 = 0)
% 31.64/8.46 |
% 31.64/8.46 | Instantiating (55) with all_34_0_24, all_34_1_25 yields:
% 31.64/8.46 | (103) apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24 & convergent_lines(all_1_4_4, all_1_5_5) = all_34_1_25 & ( ~ (all_34_0_24 = 0) | ~ (all_34_1_25 = 0))
% 31.64/8.46 |
% 31.64/8.46 | Applying alpha-rule on (103) yields:
% 31.64/8.46 | (104) apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24
% 31.64/8.46 | (105) convergent_lines(all_1_4_4, all_1_5_5) = all_34_1_25
% 31.64/8.46 | (106) ~ (all_34_0_24 = 0) | ~ (all_34_1_25 = 0)
% 31.64/8.46 |
% 31.64/8.46 +-Applying beta-rule and splitting (59), into two cases.
% 31.64/8.46 |-Branch one:
% 31.64/8.46 | (107) distinct_points(all_1_0_0, all_1_2_2) = 0
% 31.64/8.46 |
% 31.64/8.46 +-Applying beta-rule and splitting (60), into two cases.
% 31.64/8.46 |-Branch one:
% 31.64/8.46 | (108) all_1_1_1 = 0
% 31.64/8.46 |
% 31.64/8.46 | Equations (108) can reduce 48 to:
% 31.64/8.46 | (109) $false
% 31.64/8.46 |
% 31.64/8.46 |-The branch is then unsatisfiable
% 31.64/8.46 |-Branch two:
% 31.64/8.46 | (48) ~ (all_1_1_1 = 0)
% 31.64/8.46 | (111) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.46 |
% 31.64/8.46 | Instantiating (111) with all_43_0_26, all_43_1_27, all_43_2_28, all_43_3_29 yields:
% 31.64/8.46 | (112) apart_point_and_line(all_1_2_2, all_1_3_3) = all_43_0_26 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_43_1_27 & distinct_lines(all_1_3_3, all_1_3_3) = all_43_2_28 & distinct_points(all_1_2_2, all_1_2_2) = all_43_3_29 & ( ~ (all_43_2_28 = 0) | ~ (all_43_3_29 = 0) | all_43_0_26 = 0 | all_43_1_27 = 0)
% 31.64/8.46 |
% 31.64/8.46 | Applying alpha-rule on (112) yields:
% 31.64/8.46 | (113) apart_point_and_line(all_1_2_2, all_1_3_3) = all_43_0_26
% 31.64/8.46 | (114) distinct_points(all_1_2_2, all_1_2_2) = all_43_3_29
% 31.64/8.46 | (115) distinct_lines(all_1_3_3, all_1_3_3) = all_43_2_28
% 31.64/8.47 | (116) ~ (all_43_2_28 = 0) | ~ (all_43_3_29 = 0) | all_43_0_26 = 0 | all_43_1_27 = 0
% 31.64/8.47 | (117) apart_point_and_line(all_1_2_2, all_1_3_3) = all_43_1_27
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (34) with all_1_3_3, all_1_4_4, all_20_1_11, all_22_1_13 and discharging atoms intersection_point(all_1_3_3, all_1_4_4) = all_22_1_13, intersection_point(all_1_3_3, all_1_4_4) = all_20_1_11, yields:
% 31.64/8.47 | (118) all_22_1_13 = all_20_1_11
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (34) with all_1_5_5, all_1_3_3, all_18_1_9, all_24_1_15 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_24_1_15, intersection_point(all_1_5_5, all_1_3_3) = all_18_1_9, yields:
% 31.64/8.47 | (119) all_24_1_15 = all_18_1_9
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (34) with all_1_5_5, all_1_4_4, all_26_1_17, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_26_1_17, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 31.64/8.47 | (120) all_26_1_17 = all_1_2_2
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (34) with all_1_5_5, all_1_4_4, all_16_1_7, all_26_1_17 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_26_1_17, intersection_point(all_1_5_5, all_1_4_4) = all_16_1_7, yields:
% 31.64/8.47 | (121) all_26_1_17 = all_16_1_7
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (35) with all_1_2_2, all_1_3_3, all_43_0_26, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_43_0_26, apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, yields:
% 31.64/8.47 | (122) all_43_0_26 = all_1_1_1
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (35) with all_1_2_2, all_1_3_3, all_43_1_27, all_43_0_26 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_43_0_26, apart_point_and_line(all_1_2_2, all_1_3_3) = all_43_1_27, yields:
% 31.64/8.47 | (123) all_43_0_26 = all_43_1_27
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (35) with all_1_2_2, all_1_4_4, all_30_0_20, all_26_0_16 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_20, yields:
% 31.64/8.47 | (124) all_30_0_20 = all_26_0_16 | ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16)
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (35) with all_1_2_2, all_1_5_5, all_28_0_18, all_16_0_6 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_28_0_18, yields:
% 31.64/8.47 | (125) all_28_0_18 = all_16_0_6 | ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6)
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (15) with all_1_4_4, all_1_5_5, all_32_1_23, all_34_1_25 and discharging atoms convergent_lines(all_1_4_4, all_1_5_5) = all_34_1_25, convergent_lines(all_1_4_4, all_1_5_5) = all_32_1_23, yields:
% 31.64/8.47 | (126) all_34_1_25 = all_32_1_23
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (15) with all_1_5_5, all_1_4_4, all_30_1_21, 0 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_30_1_21, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.64/8.47 | (127) all_30_1_21 = 0
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (15) with all_1_5_5, all_1_4_4, all_28_1_19, all_30_1_21 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_30_1_21, convergent_lines(all_1_5_5, all_1_4_4) = all_28_1_19, yields:
% 31.64/8.47 | (128) all_30_1_21 = all_28_1_19
% 31.64/8.47 |
% 31.64/8.47 | Combining equations (122,123) yields a new equation:
% 31.64/8.47 | (129) all_43_1_27 = all_1_1_1
% 31.64/8.47 |
% 31.64/8.47 | Combining equations (128,127) yields a new equation:
% 31.64/8.47 | (130) all_28_1_19 = 0
% 31.64/8.47 |
% 31.64/8.47 | Simplifying 130 yields:
% 31.64/8.47 | (131) all_28_1_19 = 0
% 31.64/8.47 |
% 31.64/8.47 | Combining equations (121,120) yields a new equation:
% 31.64/8.47 | (132) all_16_1_7 = all_1_2_2
% 31.64/8.47 |
% 31.64/8.47 | Simplifying 132 yields:
% 31.64/8.47 | (133) all_16_1_7 = all_1_2_2
% 31.64/8.47 |
% 31.64/8.47 | From (120) and (90) follows:
% 31.64/8.47 | (134) apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16
% 31.64/8.47 |
% 31.64/8.47 | From (119) and (86) follows:
% 31.64/8.47 | (135) apart_point_and_line(all_18_1_9, all_1_3_3) = all_24_0_14
% 31.64/8.47 |
% 31.64/8.47 | From (118) and (82) follows:
% 31.64/8.47 | (136) apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12
% 31.64/8.47 |
% 31.64/8.47 | From (133) and (70) follows:
% 31.64/8.47 | (137) apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6
% 31.64/8.47 |
% 31.64/8.47 | From (129) and (117) follows:
% 31.64/8.47 | (49) apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1
% 31.64/8.47 |
% 31.64/8.47 | From (126) and (105) follows:
% 31.64/8.47 | (101) convergent_lines(all_1_4_4, all_1_5_5) = all_32_1_23
% 31.64/8.47 |
% 31.64/8.47 | From (131) and (93) follows:
% 31.64/8.47 | (46) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 31.64/8.47 |
% 31.64/8.47 +-Applying beta-rule and splitting (98), into two cases.
% 31.64/8.47 |-Branch one:
% 31.64/8.47 | (141) ~ (all_30_0_20 = 0)
% 31.64/8.47 |
% 31.64/8.47 +-Applying beta-rule and splitting (94), into two cases.
% 31.64/8.47 |-Branch one:
% 31.64/8.47 | (142) ~ (all_28_0_18 = 0)
% 31.64/8.47 |
% 31.64/8.47 +-Applying beta-rule and splitting (125), into two cases.
% 31.64/8.47 |-Branch one:
% 31.64/8.47 | (143) ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6)
% 31.64/8.47 |
% 31.64/8.47 | Using (137) and (143) yields:
% 31.64/8.47 | (144) $false
% 31.64/8.47 |
% 31.64/8.47 |-The branch is then unsatisfiable
% 31.64/8.47 |-Branch two:
% 31.64/8.47 | (137) apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6
% 31.64/8.47 | (146) all_28_0_18 = all_16_0_6
% 31.64/8.47 |
% 31.64/8.47 | Equations (146) can reduce 142 to:
% 31.64/8.47 | (68) ~ (all_16_0_6 = 0)
% 31.64/8.47 |
% 31.64/8.47 | From (146) and (92) follows:
% 31.64/8.47 | (137) apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6
% 31.64/8.47 |
% 31.64/8.47 +-Applying beta-rule and splitting (124), into two cases.
% 31.64/8.47 |-Branch one:
% 31.64/8.47 | (149) ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16)
% 31.64/8.47 |
% 31.64/8.47 | Using (134) and (149) yields:
% 31.64/8.47 | (144) $false
% 31.64/8.47 |
% 31.64/8.47 |-The branch is then unsatisfiable
% 31.64/8.47 |-Branch two:
% 31.64/8.47 | (134) apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16
% 31.64/8.47 | (152) all_30_0_20 = all_26_0_16
% 31.64/8.47 |
% 31.64/8.47 | Equations (152) can reduce 141 to:
% 31.64/8.47 | (88) ~ (all_26_0_16 = 0)
% 31.64/8.47 |
% 31.64/8.47 | From (152) and (96) follows:
% 31.64/8.47 | (134) apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (27) with all_18_0_8, all_22_0_12, all_1_5_5, all_1_4_4, all_18_1_9, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, yields:
% 31.64/8.47 | (155) all_22_0_12 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_18_1_9, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.47 |
% 31.64/8.47 | Instantiating formula (27) with all_22_0_12, all_18_0_8, all_1_4_4, all_1_5_5, all_20_1_11, all_18_1_9 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, yields:
% 31.64/8.48 | (156) all_22_0_12 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_18_1_9, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_18_1_9, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (1) with all_18_0_8, all_22_0_12, all_1_4_4, all_1_5_5, all_18_1_9, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, yields:
% 31.64/8.48 | (157) all_22_0_12 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_18_1_9, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_20_1_11, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (1) with all_22_0_12, all_18_0_8, all_1_5_5, all_1_4_4, all_20_1_11, all_18_1_9 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, yields:
% 31.64/8.48 | (158) all_22_0_12 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_18_1_9, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (27) with all_18_0_8, all_18_0_8, all_1_5_5, all_1_5_5, all_18_1_9, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, yields:
% 31.64/8.48 | (159) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v3 & apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (27) with all_32_0_22, all_32_0_22, all_1_4_4, all_1_4_4, all_1_0_0, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22, yields:
% 31.64/8.48 | (160) all_32_0_22 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (27) with all_34_0_24, all_1_1_1, all_1_5_5, all_1_3_3, all_1_0_0, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, yields:
% 31.64/8.48 | (161) all_34_0_24 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (27) with all_34_0_24, all_20_0_10, all_1_5_5, all_1_3_3, all_1_0_0, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.48 | (162) all_34_0_24 = 0 | all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (27) with all_20_0_10, all_34_0_24, all_1_3_3, all_1_5_5, all_20_1_11, all_1_0_0 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.48 | (163) all_34_0_24 = 0 | all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (1) with all_34_0_24, all_20_0_10, all_1_3_3, all_1_5_5, all_1_0_0, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.48 | (164) all_34_0_24 = 0 | all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (1) with all_20_0_10, all_34_0_24, all_1_5_5, all_1_3_3, all_20_1_11, all_1_0_0 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.48 | (165) all_34_0_24 = 0 | all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (27) with all_34_0_24, all_22_0_12, all_1_5_5, all_1_4_4, all_1_0_0, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.48 | (166) all_34_0_24 = 0 | all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (27) with all_22_0_12, all_34_0_24, all_1_4_4, all_1_5_5, all_20_1_11, all_1_0_0 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.48 | (167) all_34_0_24 = 0 | all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.48 |
% 31.64/8.48 | Instantiating formula (1) with all_34_0_24, all_22_0_12, all_1_4_4, all_1_5_5, all_1_0_0, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.48 | (168) all_34_0_24 = 0 | all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (1) with all_22_0_12, all_34_0_24, all_1_5_5, all_1_4_4, all_20_1_11, all_1_0_0 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.49 | (169) all_34_0_24 = 0 | all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (27) with all_34_0_24, all_24_0_14, all_1_5_5, all_1_3_3, all_1_0_0, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_3_3) = all_24_0_14, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.49 | (170) all_34_0_24 = 0 | all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (27) with all_24_0_14, all_34_0_24, all_1_3_3, all_1_5_5, all_18_1_9, all_1_0_0 and discharging atoms apart_point_and_line(all_18_1_9, all_1_3_3) = all_24_0_14, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.49 | (171) all_34_0_24 = 0 | all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_0_0, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (1) with all_34_0_24, all_24_0_14, all_1_3_3, all_1_5_5, all_1_0_0, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_3_3) = all_24_0_14, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.49 | (172) all_34_0_24 = 0 | all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_18_1_9, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (27) with all_34_0_24, all_18_0_8, all_1_5_5, all_1_5_5, all_1_0_0, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.49 | (173) all_34_0_24 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (27) with all_32_0_22, all_34_0_24, all_1_4_4, all_1_5_5, all_1_0_0, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.49 | (174) all_34_0_24 = 0 | all_32_0_22 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (1) with all_34_0_24, all_32_0_22, all_1_4_4, all_1_5_5, all_1_0_0, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.49 | (175) all_34_0_24 = 0 | all_32_0_22 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & apart_point_and_line(all_1_0_0, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (1) with all_32_0_22, all_34_0_24, all_1_5_5, all_1_4_4, all_1_0_0, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.64/8.49 | (176) all_34_0_24 = 0 | all_32_0_22 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.64/8.49 |
% 31.64/8.49 | Instantiating formula (27) with all_34_0_24, all_34_0_24, all_1_5_5, all_1_5_5, all_1_0_0, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 31.81/8.49 | (177) all_34_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.49 |
% 31.81/8.49 | Instantiating formula (27) with all_26_0_16, all_1_1_1, all_1_4_4, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.49 | (178) all_26_0_16 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.49 |
% 31.81/8.49 | Instantiating formula (27) with all_1_1_1, all_26_0_16, all_1_3_3, 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_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.49 | (179) all_26_0_16 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.49 |
% 31.81/8.49 | Instantiating formula (1) with all_26_0_16, all_1_1_1, all_1_3_3, 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_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.49 | (180) all_26_0_16 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.49 |
% 31.81/8.49 | Instantiating formula (1) with all_1_1_1, all_26_0_16, all_1_4_4, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (181) all_26_0_16 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (27) with all_26_0_16, all_20_0_10, all_1_4_4, all_1_3_3, all_1_2_2, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (182) all_26_0_16 = 0 | all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (27) with all_20_0_10, all_26_0_16, all_1_3_3, all_1_4_4, all_20_1_11, all_1_2_2 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (183) all_26_0_16 = 0 | all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (1) with all_26_0_16, all_20_0_10, all_1_3_3, all_1_4_4, all_1_2_2, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (184) all_26_0_16 = 0 | all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (1) with all_20_0_10, all_26_0_16, all_1_4_4, all_1_3_3, all_20_1_11, all_1_2_2 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (185) all_26_0_16 = 0 | all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (27) with all_26_0_16, all_22_0_12, all_1_4_4, all_1_4_4, all_1_2_2, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (186) all_26_0_16 = 0 | all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (27) with all_22_0_12, all_26_0_16, all_1_4_4, all_1_4_4, all_20_1_11, all_1_2_2 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (187) all_26_0_16 = 0 | all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (27) with all_26_0_16, all_24_0_14, all_1_4_4, all_1_3_3, all_1_2_2, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_3_3) = all_24_0_14, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (188) all_26_0_16 = 0 | all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (27) with all_24_0_14, all_26_0_16, all_1_3_3, all_1_4_4, all_18_1_9, all_1_2_2 and discharging atoms apart_point_and_line(all_18_1_9, all_1_3_3) = all_24_0_14, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (189) all_26_0_16 = 0 | all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (1) with all_26_0_16, all_24_0_14, all_1_3_3, all_1_4_4, all_1_2_2, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_3_3) = all_24_0_14, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (190) all_26_0_16 = 0 | all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (1) with all_24_0_14, all_26_0_16, all_1_4_4, all_1_3_3, all_18_1_9, all_1_2_2 and discharging atoms apart_point_and_line(all_18_1_9, all_1_3_3) = all_24_0_14, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (191) all_26_0_16 = 0 | all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (27) with all_26_0_16, all_18_0_8, all_1_4_4, all_1_5_5, all_1_2_2, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (192) all_26_0_16 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.50 |
% 31.81/8.50 | Instantiating formula (27) with all_18_0_8, all_26_0_16, all_1_5_5, all_1_4_4, all_18_1_9, all_1_2_2 and discharging atoms apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.50 | (193) all_26_0_16 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (1) with all_26_0_16, all_18_0_8, all_1_5_5, all_1_4_4, all_1_2_2, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.51 | (194) all_26_0_16 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (1) with all_18_0_8, all_26_0_16, all_1_4_4, all_1_5_5, all_18_1_9, all_1_2_2 and discharging atoms apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.51 | (195) all_26_0_16 = 0 | all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (27) with all_32_0_22, all_26_0_16, all_1_4_4, all_1_4_4, all_1_0_0, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.51 | (196) all_32_0_22 = 0 | all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (27) with all_26_0_16, all_34_0_24, all_1_4_4, all_1_5_5, all_1_2_2, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.51 | (197) all_34_0_24 = 0 | all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_1_0_0, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (27) with all_34_0_24, all_26_0_16, all_1_5_5, all_1_4_4, all_1_0_0, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.51 | (198) all_34_0_24 = 0 | all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (1) with all_34_0_24, all_26_0_16, all_1_4_4, all_1_5_5, all_1_0_0, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, yields:
% 31.81/8.51 | (199) all_34_0_24 = 0 | all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (27) with all_16_0_6, all_1_1_1, all_1_5_5, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.51 | (200) all_16_0_6 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (1) with all_1_1_1, all_16_0_6, all_1_5_5, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.51 | (201) all_16_0_6 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (27) with all_16_0_6, all_20_0_10, all_1_5_5, all_1_3_3, all_1_2_2, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.51 | (202) all_20_0_10 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (27) with all_20_0_10, all_16_0_6, all_1_3_3, all_1_5_5, all_20_1_11, all_1_2_2 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.51 | (203) all_20_0_10 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (1) with all_16_0_6, all_20_0_10, all_1_3_3, all_1_5_5, all_1_2_2, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.51 | (204) all_20_0_10 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (1) with all_20_0_10, all_16_0_6, all_1_5_5, all_1_3_3, all_20_1_11, all_1_2_2 and discharging atoms apart_point_and_line(all_20_1_11, all_1_3_3) = all_20_0_10, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.51 | (205) all_20_0_10 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (27) with all_16_0_6, all_22_0_12, all_1_5_5, all_1_4_4, all_1_2_2, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.51 | (206) all_22_0_12 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.51 |
% 31.81/8.51 | Instantiating formula (27) with all_22_0_12, all_16_0_6, all_1_4_4, all_1_5_5, all_20_1_11, all_1_2_2 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (207) all_22_0_12 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (1) with all_16_0_6, all_22_0_12, all_1_4_4, all_1_5_5, all_1_2_2, all_20_1_11 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (208) all_22_0_12 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (1) with all_22_0_12, all_16_0_6, all_1_5_5, all_1_4_4, all_20_1_11, all_1_2_2 and discharging atoms apart_point_and_line(all_20_1_11, all_1_4_4) = all_22_0_12, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (209) all_22_0_12 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (27) with all_16_0_6, all_18_0_8, all_1_5_5, all_1_5_5, all_1_2_2, all_18_1_9 and discharging atoms apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (210) all_18_0_8 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (27) with all_18_0_8, all_16_0_6, all_1_5_5, all_1_5_5, all_18_1_9, all_1_2_2 and discharging atoms apart_point_and_line(all_18_1_9, all_1_5_5) = all_18_0_8, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (211) all_18_0_8 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (27) with all_32_0_22, all_16_0_6, all_1_4_4, all_1_5_5, all_1_0_0, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (212) all_32_0_22 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (1) with all_32_0_22, all_16_0_6, all_1_5_5, all_1_4_4, all_1_0_0, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (213) all_32_0_22 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (27) with all_34_0_24, all_16_0_6, all_1_5_5, all_1_5_5, all_1_0_0, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (214) all_34_0_24 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (1) with all_26_0_16, all_16_0_6, all_1_5_5, 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_26_0_16, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (215) all_26_0_16 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (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) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (27) with all_16_0_6, all_16_0_6, all_1_5_5, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, yields:
% 31.81/8.52 | (216) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (37) with all_32_1_23, 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_32_1_23, convergent_lines(all_1_5_5, all_1_4_4) = 0, ~ (convergent_lines(all_1_5_5, all_1_5_5) = 0), yields:
% 31.81/8.52 | (217) all_32_1_23 = 0
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (43) with all_1_5_5, all_1_4_4 yields:
% 31.81/8.52 | (218) ~ (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)
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (19) with all_1_5_5, all_1_4_4 yields:
% 31.81/8.52 | (219) ~ (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)
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (30) with all_1_1_1, all_26_0_16, all_1_3_3, all_1_4_4, all_1_2_2, all_1_0_0 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, distinct_points(all_1_0_0, all_1_2_2) = 0, yields:
% 31.81/8.52 | (220) all_26_0_16 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.81/8.52 |
% 31.81/8.52 | Instantiating formula (30) with all_1_1_1, all_16_0_6, all_1_3_3, all_1_5_5, all_1_2_2, all_1_0_0 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, distinct_points(all_1_0_0, all_1_2_2) = 0, yields:
% 31.81/8.52 | (221) all_16_0_6 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.81/8.53 |
% 31.81/8.53 | Instantiating formula (30) with all_26_0_16, all_1_1_1, all_1_4_4, all_1_3_3, all_1_2_2, all_1_0_0 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, distinct_points(all_1_0_0, all_1_2_2) = 0, yields:
% 31.81/8.53 | (222) all_26_0_16 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.81/8.53 |
% 31.81/8.53 | Instantiating formula (30) with all_26_0_16, all_26_0_16, all_1_4_4, all_1_4_4, all_1_2_2, all_1_0_0 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, distinct_points(all_1_0_0, all_1_2_2) = 0, yields:
% 31.81/8.53 | (223) all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.81/8.53 |
% 31.81/8.53 | Instantiating formula (30) with all_26_0_16, all_16_0_6, all_1_4_4, all_1_5_5, all_1_2_2, all_1_0_0 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_26_0_16, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, distinct_points(all_1_0_0, all_1_2_2) = 0, yields:
% 31.81/8.53 | (224) all_26_0_16 = 0 | all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.81/8.53 |
% 31.81/8.53 | Instantiating formula (30) with all_16_0_6, all_1_1_1, all_1_5_5, all_1_3_3, all_1_2_2, all_1_0_0 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_5_5) = all_16_0_6, distinct_points(all_1_0_0, all_1_2_2) = 0, yields:
% 31.81/8.53 | (225) all_16_0_6 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & apart_point_and_line(all_1_0_0, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.81/8.53 |
% 31.81/8.53 | Combining equations (217,126) yields a new equation:
% 31.81/8.53 | (226) all_34_1_25 = 0
% 31.81/8.53 |
% 31.81/8.53 | From (217) and (101) follows:
% 31.81/8.53 | (227) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 31.81/8.53 |
% 31.81/8.53 +-Applying beta-rule and splitting (106), into two cases.
% 31.81/8.53 |-Branch one:
% 31.81/8.53 | (228) ~ (all_34_0_24 = 0)
% 31.81/8.53 |
% 31.81/8.53 +-Applying beta-rule and splitting (216), into two cases.
% 31.81/8.53 |-Branch one:
% 31.81/8.53 | (229) all_16_0_6 = 0
% 31.81/8.53 |
% 31.81/8.53 | Equations (229) can reduce 68 to:
% 31.81/8.53 | (109) $false
% 31.81/8.53 |
% 31.81/8.53 |-The branch is then unsatisfiable
% 31.81/8.53 |-Branch two:
% 31.81/8.53 | (68) ~ (all_16_0_6 = 0)
% 31.81/8.53 | (232) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.81/8.53 |
% 31.81/8.53 +-Applying beta-rule and splitting (223), into two cases.
% 31.81/8.53 |-Branch one:
% 31.81/8.53 | (233) all_26_0_16 = 0
% 31.81/8.53 |
% 31.81/8.53 | Equations (233) can reduce 88 to:
% 31.81/8.53 | (109) $false
% 31.81/8.53 |
% 31.81/8.53 |-The branch is then unsatisfiable
% 31.81/8.53 |-Branch two:
% 31.81/8.53 | (88) ~ (all_26_0_16 = 0)
% 31.81/8.53 | (236) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.81/8.53 |
% 31.81/8.53 | Instantiating (236) with all_91_0_38, all_91_1_39, all_91_2_40 yields:
% 31.81/8.53 | (237) apart_point_and_line(all_1_0_0, all_1_4_4) = all_91_0_38 & apart_point_and_line(all_1_0_0, all_1_4_4) = all_91_1_39 & distinct_lines(all_1_4_4, all_1_4_4) = all_91_2_40 & ( ~ (all_91_2_40 = 0) | all_91_0_38 = 0 | all_91_1_39 = 0)
% 31.81/8.53 |
% 31.81/8.53 | Applying alpha-rule on (237) yields:
% 31.81/8.53 | (238) apart_point_and_line(all_1_0_0, all_1_4_4) = all_91_0_38
% 31.81/8.53 | (239) apart_point_and_line(all_1_0_0, all_1_4_4) = all_91_1_39
% 32.01/8.53 | (240) distinct_lines(all_1_4_4, all_1_4_4) = all_91_2_40
% 32.01/8.53 | (241) ~ (all_91_2_40 = 0) | all_91_0_38 = 0 | all_91_1_39 = 0
% 32.01/8.53 |
% 32.01/8.53 +-Applying beta-rule and splitting (222), into two cases.
% 32.01/8.53 |-Branch one:
% 32.01/8.53 | (233) all_26_0_16 = 0
% 32.01/8.53 |
% 32.01/8.53 | Equations (233) can reduce 88 to:
% 32.01/8.53 | (109) $false
% 32.01/8.53 |
% 32.01/8.53 |-The branch is then unsatisfiable
% 32.01/8.53 |-Branch two:
% 32.01/8.53 | (88) ~ (all_26_0_16 = 0)
% 32.01/8.53 | (245) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.01/8.53 |
% 32.01/8.53 +-Applying beta-rule and splitting (221), into two cases.
% 32.01/8.53 |-Branch one:
% 32.01/8.53 | (229) all_16_0_6 = 0
% 32.01/8.53 |
% 32.01/8.53 | Equations (229) can reduce 68 to:
% 32.01/8.53 | (109) $false
% 32.01/8.53 |
% 32.01/8.53 |-The branch is then unsatisfiable
% 32.01/8.53 |-Branch two:
% 32.01/8.53 | (68) ~ (all_16_0_6 = 0)
% 32.01/8.53 | (249) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.01/8.53 |
% 32.01/8.53 +-Applying beta-rule and splitting (224), into two cases.
% 32.01/8.53 |-Branch one:
% 32.01/8.53 | (233) all_26_0_16 = 0
% 32.01/8.53 |
% 32.01/8.53 | Equations (233) can reduce 88 to:
% 32.01/8.53 | (109) $false
% 32.01/8.53 |
% 32.01/8.53 |-The branch is then unsatisfiable
% 32.01/8.53 |-Branch two:
% 32.01/8.53 | (88) ~ (all_26_0_16 = 0)
% 32.01/8.53 | (253) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.01/8.53 |
% 32.01/8.53 +-Applying beta-rule and splitting (215), into two cases.
% 32.01/8.53 |-Branch one:
% 32.01/8.53 | (233) all_26_0_16 = 0
% 32.01/8.53 |
% 32.01/8.53 | Equations (233) can reduce 88 to:
% 32.01/8.53 | (109) $false
% 32.01/8.53 |
% 32.01/8.53 |-The branch is then unsatisfiable
% 32.01/8.53 |-Branch two:
% 32.01/8.53 | (88) ~ (all_26_0_16 = 0)
% 32.01/8.53 | (257) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (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) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.01/8.53 |
% 32.01/8.53 +-Applying beta-rule and splitting (102), into two cases.
% 32.01/8.53 |-Branch one:
% 32.01/8.53 | (258) ~ (all_32_0_22 = 0)
% 32.01/8.53 |
% 32.01/8.53 +-Applying beta-rule and splitting (249), into two cases.
% 32.01/8.53 |-Branch one:
% 32.01/8.53 | (108) all_1_1_1 = 0
% 32.01/8.53 |
% 32.01/8.53 | Equations (108) can reduce 48 to:
% 32.01/8.53 | (109) $false
% 32.01/8.53 |
% 32.01/8.53 |-The branch is then unsatisfiable
% 32.01/8.53 |-Branch two:
% 32.01/8.53 | (48) ~ (all_1_1_1 = 0)
% 32.01/8.53 | (262) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.01/8.54 |
% 32.01/8.54 | Instantiating (262) with all_112_0_41, all_112_1_42, all_112_2_43 yields:
% 32.01/8.54 | (263) apart_point_and_line(all_1_0_0, all_1_3_3) = all_112_0_41 & apart_point_and_line(all_1_0_0, all_1_5_5) = all_112_1_42 & distinct_lines(all_1_5_5, all_1_3_3) = all_112_2_43 & ( ~ (all_112_2_43 = 0) | all_112_0_41 = 0 | all_112_1_42 = 0)
% 32.03/8.54 |
% 32.03/8.54 | Applying alpha-rule on (263) yields:
% 32.03/8.54 | (264) apart_point_and_line(all_1_0_0, all_1_3_3) = all_112_0_41
% 32.03/8.54 | (265) apart_point_and_line(all_1_0_0, all_1_5_5) = all_112_1_42
% 32.03/8.54 | (266) distinct_lines(all_1_5_5, all_1_3_3) = all_112_2_43
% 32.03/8.54 | (267) ~ (all_112_2_43 = 0) | all_112_0_41 = 0 | all_112_1_42 = 0
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (253), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (229) all_16_0_6 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (229) can reduce 68 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.54 | (271) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.03/8.54 |
% 32.03/8.54 | Instantiating (271) with all_117_0_44, all_117_1_45, all_117_2_46 yields:
% 32.03/8.54 | (272) apart_point_and_line(all_1_0_0, all_1_4_4) = all_117_0_44 & apart_point_and_line(all_1_0_0, all_1_5_5) = all_117_1_45 & distinct_lines(all_1_5_5, all_1_4_4) = all_117_2_46 & ( ~ (all_117_2_46 = 0) | all_117_0_44 = 0 | all_117_1_45 = 0)
% 32.03/8.54 |
% 32.03/8.54 | Applying alpha-rule on (272) yields:
% 32.03/8.54 | (273) apart_point_and_line(all_1_0_0, all_1_4_4) = all_117_0_44
% 32.03/8.54 | (274) apart_point_and_line(all_1_0_0, all_1_5_5) = all_117_1_45
% 32.03/8.54 | (275) distinct_lines(all_1_5_5, all_1_4_4) = all_117_2_46
% 32.03/8.54 | (276) ~ (all_117_2_46 = 0) | all_117_0_44 = 0 | all_117_1_45 = 0
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (257), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (229) all_16_0_6 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (229) can reduce 68 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.54 | (280) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (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) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (219), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (281) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 32.03/8.54 |
% 32.03/8.54 | Using (227) and (281) yields:
% 32.03/8.54 | (144) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (227) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 32.03/8.54 | (284) ? [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)
% 32.03/8.54 |
% 32.03/8.54 | Instantiating (284) with all_132_0_51, all_132_1_52 yields:
% 32.03/8.54 | (285) ~ (all_132_0_51 = 0) & intersection_point(all_1_4_4, all_1_5_5) = all_132_1_52 & apart_point_and_line(all_132_1_52, all_1_4_4) = all_132_0_51
% 32.03/8.54 |
% 32.03/8.54 | Applying alpha-rule on (285) yields:
% 32.03/8.54 | (286) ~ (all_132_0_51 = 0)
% 32.03/8.54 | (287) intersection_point(all_1_4_4, all_1_5_5) = all_132_1_52
% 32.03/8.54 | (288) apart_point_and_line(all_132_1_52, all_1_4_4) = all_132_0_51
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (225), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (229) all_16_0_6 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (229) can reduce 68 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.54 | (292) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & apart_point_and_line(all_1_0_0, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (218), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (281) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 32.03/8.54 |
% 32.03/8.54 | Using (227) and (281) yields:
% 32.03/8.54 | (144) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (227) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 32.03/8.54 | (296) ? [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)
% 32.03/8.54 |
% 32.03/8.54 | Instantiating (296) with all_144_0_53, all_144_1_54 yields:
% 32.03/8.54 | (297) ~ (all_144_0_53 = 0) & intersection_point(all_1_4_4, all_1_5_5) = all_144_1_54 & apart_point_and_line(all_144_1_54, all_1_5_5) = all_144_0_53
% 32.03/8.54 |
% 32.03/8.54 | Applying alpha-rule on (297) yields:
% 32.03/8.54 | (298) ~ (all_144_0_53 = 0)
% 32.03/8.54 | (299) intersection_point(all_1_4_4, all_1_5_5) = all_144_1_54
% 32.03/8.54 | (300) apart_point_and_line(all_144_1_54, all_1_5_5) = all_144_0_53
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (220), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (233) all_26_0_16 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (233) can reduce 88 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.54 | (304) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (205), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (305) all_20_0_10 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (305) can reduce 76 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (76) ~ (all_20_0_10 = 0)
% 32.03/8.54 | (308) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (206), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (309) all_22_0_12 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (309) can reduce 80 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.54 | (312) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (201), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (229) all_16_0_6 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (229) can reduce 68 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.54 | (316) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (209), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (309) all_22_0_12 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (309) can reduce 80 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.54 | (320) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (202), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (305) all_20_0_10 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (305) can reduce 76 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (76) ~ (all_20_0_10 = 0)
% 32.03/8.54 | (324) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (203), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (305) all_20_0_10 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (305) can reduce 76 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (76) ~ (all_20_0_10 = 0)
% 32.03/8.54 | (328) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.54 |
% 32.03/8.54 +-Applying beta-rule and splitting (204), into two cases.
% 32.03/8.54 |-Branch one:
% 32.03/8.54 | (305) all_20_0_10 = 0
% 32.03/8.54 |
% 32.03/8.54 | Equations (305) can reduce 76 to:
% 32.03/8.54 | (109) $false
% 32.03/8.54 |
% 32.03/8.54 |-The branch is then unsatisfiable
% 32.03/8.54 |-Branch two:
% 32.03/8.54 | (76) ~ (all_20_0_10 = 0)
% 32.03/8.55 | (332) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (207), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (309) all_22_0_12 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (309) can reduce 80 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.55 | (336) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (208), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (309) all_22_0_12 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (309) can reduce 80 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.55 | (340) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (211), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (341) all_18_0_8 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (341) can reduce 72 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (72) ~ (all_18_0_8 = 0)
% 32.03/8.55 | (344) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (210), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (341) all_18_0_8 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (341) can reduce 72 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (72) ~ (all_18_0_8 = 0)
% 32.03/8.55 | (348) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (182), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (352) all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (183), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (356) all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (184), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (360) all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (185), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (364) all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (214), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (365) all_34_0_24 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (365) can reduce 228 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.55 | (368) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (212), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (369) all_32_0_22 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (369) can reduce 258 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (258) ~ (all_32_0_22 = 0)
% 32.03/8.55 | (372) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (188), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (376) all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (186), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (380) all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (187), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (384) all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (189), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (388) all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (213), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (369) all_32_0_22 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (369) can reduce 258 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (258) ~ (all_32_0_22 = 0)
% 32.03/8.55 | (392) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (194), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (396) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (195), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (400) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.55 |
% 32.03/8.55 +-Applying beta-rule and splitting (190), into two cases.
% 32.03/8.55 |-Branch one:
% 32.03/8.55 | (233) all_26_0_16 = 0
% 32.03/8.55 |
% 32.03/8.55 | Equations (233) can reduce 88 to:
% 32.03/8.55 | (109) $false
% 32.03/8.55 |
% 32.03/8.55 |-The branch is then unsatisfiable
% 32.03/8.55 |-Branch two:
% 32.03/8.55 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.55 | (404) all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (191), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (233) all_26_0_16 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (233) can reduce 88 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.56 | (408) all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (192), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (233) all_26_0_16 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (233) can reduce 88 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.56 | (412) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (193), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (233) all_26_0_16 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (233) can reduce 88 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.56 | (416) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (196), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (369) all_32_0_22 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (369) can reduce 258 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (258) ~ (all_32_0_22 = 0)
% 32.03/8.56 | (420) all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (198), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (424) all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (199), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (428) all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (200), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (229) all_16_0_6 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (229) can reduce 68 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.56 | (432) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (292), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (108) all_1_1_1 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (108) can reduce 48 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (48) ~ (all_1_1_1 = 0)
% 32.03/8.56 | (436) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & apart_point_and_line(all_1_0_0, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.03/8.56 |
% 32.03/8.56 | Instantiating (436) with all_260_0_55, all_260_1_56, all_260_2_57 yields:
% 32.03/8.56 | (437) apart_point_and_line(all_1_0_0, all_1_3_3) = all_260_1_56 & apart_point_and_line(all_1_0_0, all_1_5_5) = all_260_0_55 & distinct_lines(all_1_3_3, all_1_5_5) = all_260_2_57 & ( ~ (all_260_2_57 = 0) | all_260_0_55 = 0 | all_260_1_56 = 0)
% 32.03/8.56 |
% 32.03/8.56 | Applying alpha-rule on (437) yields:
% 32.03/8.56 | (438) apart_point_and_line(all_1_0_0, all_1_3_3) = all_260_1_56
% 32.03/8.56 | (439) apart_point_and_line(all_1_0_0, all_1_5_5) = all_260_0_55
% 32.03/8.56 | (440) distinct_lines(all_1_3_3, all_1_5_5) = all_260_2_57
% 32.03/8.56 | (441) ~ (all_260_2_57 = 0) | all_260_0_55 = 0 | all_260_1_56 = 0
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (161), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (445) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (168), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (449) all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (169), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (453) all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (164), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (457) all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (165), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (461) all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (166), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (465) all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (167), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (469) all_22_0_12 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (170), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.56 | Equations (365) can reduce 228 to:
% 32.03/8.56 | (109) $false
% 32.03/8.56 |
% 32.03/8.56 |-The branch is then unsatisfiable
% 32.03/8.56 |-Branch two:
% 32.03/8.56 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.56 | (473) all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.56 |
% 32.03/8.56 +-Applying beta-rule and splitting (171), into two cases.
% 32.03/8.56 |-Branch one:
% 32.03/8.56 | (365) all_34_0_24 = 0
% 32.03/8.56 |
% 32.03/8.57 | Equations (365) can reduce 228 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.57 | (477) all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_0_0, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (180), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (233) all_26_0_16 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (233) can reduce 88 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.57 | (481) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (178), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (233) all_26_0_16 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (233) can reduce 88 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.57 | (485) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (179), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (233) all_26_0_16 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (233) can reduce 88 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.57 | (489) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (181), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (233) all_26_0_16 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (233) can reduce 88 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.57 | (493) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (308), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (229) all_16_0_6 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (229) can reduce 68 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.57 | (497) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (312), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (229) all_16_0_6 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (229) can reduce 68 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.57 | (501) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, 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_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (320), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (229) all_16_0_6 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (229) can reduce 68 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.57 | (505) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (332), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (229) all_16_0_6 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (229) can reduce 68 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.57 | (509) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_20_1_11, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (344), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (229) all_16_0_6 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (229) can reduce 68 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.57 | (513) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (372), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (229) all_16_0_6 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (229) can reduce 68 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (68) ~ (all_16_0_6 = 0)
% 32.03/8.57 | (517) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 | Instantiating (517) with all_343_0_86, all_343_1_87, all_343_2_88, all_343_3_89 yields:
% 32.03/8.57 | (518) apart_point_and_line(all_1_0_0, all_1_5_5) = all_343_0_86 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_343_1_87 & distinct_lines(all_1_5_5, all_1_4_4) = all_343_2_88 & distinct_points(all_1_2_2, all_1_0_0) = all_343_3_89 & ( ~ (all_343_2_88 = 0) | ~ (all_343_3_89 = 0) | all_343_0_86 = 0 | all_343_1_87 = 0)
% 32.03/8.57 |
% 32.03/8.57 | Applying alpha-rule on (518) yields:
% 32.03/8.57 | (519) apart_point_and_line(all_1_2_2, all_1_4_4) = all_343_1_87
% 32.03/8.57 | (520) apart_point_and_line(all_1_0_0, all_1_5_5) = all_343_0_86
% 32.03/8.57 | (521) ~ (all_343_2_88 = 0) | ~ (all_343_3_89 = 0) | all_343_0_86 = 0 | all_343_1_87 = 0
% 32.03/8.57 | (522) distinct_points(all_1_2_2, all_1_0_0) = all_343_3_89
% 32.03/8.57 | (523) distinct_lines(all_1_5_5, all_1_4_4) = all_343_2_88
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (396), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (341) all_18_0_8 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (341) can reduce 72 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (72) ~ (all_18_0_8 = 0)
% 32.03/8.57 | (527) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, 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_18_1_9, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (420), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (233) all_26_0_16 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (233) can reduce 88 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (88) ~ (all_26_0_16 = 0)
% 32.03/8.57 | (531) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 | Instantiating (531) with all_363_0_102, all_363_1_103, all_363_2_104, all_363_3_105 yields:
% 32.03/8.57 | (532) apart_point_and_line(all_1_0_0, all_1_4_4) = all_363_0_102 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_363_1_103 & distinct_lines(all_1_4_4, all_1_4_4) = all_363_2_104 & distinct_points(all_1_2_2, all_1_0_0) = all_363_3_105 & ( ~ (all_363_2_104 = 0) | ~ (all_363_3_105 = 0) | all_363_0_102 = 0 | all_363_1_103 = 0)
% 32.03/8.57 |
% 32.03/8.57 | Applying alpha-rule on (532) yields:
% 32.03/8.57 | (533) distinct_lines(all_1_4_4, all_1_4_4) = all_363_2_104
% 32.03/8.57 | (534) apart_point_and_line(all_1_2_2, all_1_4_4) = all_363_1_103
% 32.03/8.57 | (535) ~ (all_363_2_104 = 0) | ~ (all_363_3_105 = 0) | all_363_0_102 = 0 | all_363_1_103 = 0
% 32.03/8.57 | (536) apart_point_and_line(all_1_0_0, all_1_4_4) = all_363_0_102
% 32.03/8.57 | (537) distinct_points(all_1_2_2, all_1_0_0) = all_363_3_105
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (159), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (341) all_18_0_8 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (341) can reduce 72 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (72) ~ (all_18_0_8 = 0)
% 32.03/8.57 | (541) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v3 & apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 +-Applying beta-rule and splitting (160), into two cases.
% 32.03/8.57 |-Branch one:
% 32.03/8.57 | (369) all_32_0_22 = 0
% 32.03/8.57 |
% 32.03/8.57 | Equations (369) can reduce 258 to:
% 32.03/8.57 | (109) $false
% 32.03/8.57 |
% 32.03/8.57 |-The branch is then unsatisfiable
% 32.03/8.57 |-Branch two:
% 32.03/8.57 | (258) ~ (all_32_0_22 = 0)
% 32.03/8.57 | (545) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.57 |
% 32.03/8.57 | Instantiating (545) with all_377_0_110, all_377_1_111, all_377_2_112, all_377_3_113 yields:
% 32.03/8.57 | (546) apart_point_and_line(all_1_0_0, all_1_4_4) = all_377_0_110 & apart_point_and_line(all_1_0_0, all_1_4_4) = all_377_1_111 & distinct_lines(all_1_4_4, all_1_4_4) = all_377_2_112 & distinct_points(all_1_0_0, all_1_0_0) = all_377_3_113 & ( ~ (all_377_2_112 = 0) | ~ (all_377_3_113 = 0) | all_377_0_110 = 0 | all_377_1_111 = 0)
% 32.03/8.58 |
% 32.03/8.58 | Applying alpha-rule on (546) yields:
% 32.03/8.58 | (547) distinct_points(all_1_0_0, all_1_0_0) = all_377_3_113
% 32.03/8.58 | (548) apart_point_and_line(all_1_0_0, all_1_4_4) = all_377_1_111
% 32.03/8.58 | (549) ~ (all_377_2_112 = 0) | ~ (all_377_3_113 = 0) | all_377_0_110 = 0 | all_377_1_111 = 0
% 32.03/8.58 | (550) distinct_lines(all_1_4_4, all_1_4_4) = all_377_2_112
% 32.03/8.58 | (551) apart_point_and_line(all_1_0_0, all_1_4_4) = all_377_0_110
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (177), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (365) all_34_0_24 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (365) can reduce 228 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.58 | (555) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 | Instantiating (555) with all_382_0_114, all_382_1_115, all_382_2_116, all_382_3_117 yields:
% 32.03/8.58 | (556) apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_0_114 & apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_1_115 & distinct_lines(all_1_5_5, all_1_5_5) = all_382_2_116 & distinct_points(all_1_0_0, all_1_0_0) = all_382_3_117 & ( ~ (all_382_2_116 = 0) | ~ (all_382_3_117 = 0) | all_382_0_114 = 0 | all_382_1_115 = 0)
% 32.03/8.58 |
% 32.03/8.58 | Applying alpha-rule on (556) yields:
% 32.03/8.58 | (557) distinct_lines(all_1_5_5, all_1_5_5) = all_382_2_116
% 32.03/8.58 | (558) apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_1_115
% 32.03/8.58 | (559) apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_0_114
% 32.03/8.58 | (560) ~ (all_382_2_116 = 0) | ~ (all_382_3_117 = 0) | all_382_0_114 = 0 | all_382_1_115 = 0
% 32.03/8.58 | (561) distinct_points(all_1_0_0, all_1_0_0) = all_382_3_117
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (162), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (365) all_34_0_24 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (365) can reduce 228 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.58 | (565) all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (163), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (365) all_34_0_24 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (365) can reduce 228 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.58 | (569) all_20_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (174), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (365) all_34_0_24 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (365) can reduce 228 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.58 | (573) all_32_0_22 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (155), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (309) all_22_0_12 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (309) can reduce 80 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.58 | (577) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_18_1_9, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (158), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (309) all_22_0_12 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (309) can reduce 80 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.58 | (581) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_18_1_9, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (156), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (309) all_22_0_12 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (309) can reduce 80 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.58 | (585) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_18_1_9, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_18_1_9, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (157), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (309) all_22_0_12 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (309) can reduce 80 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.58 | (589) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_18_1_9, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_20_1_11, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (175), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (365) all_34_0_24 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (365) can reduce 228 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.58 | (593) all_32_0_22 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & apart_point_and_line(all_1_0_0, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (176), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (365) all_34_0_24 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (365) can reduce 228 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.58 | (597) all_32_0_22 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (449), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (309) all_22_0_12 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (309) can reduce 80 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.58 | (601) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_20_1_11, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 | Instantiating (601) with all_432_0_118, all_432_1_119, all_432_2_120, all_432_3_121 yields:
% 32.03/8.58 | (602) apart_point_and_line(all_20_1_11, all_1_5_5) = all_432_1_119 & apart_point_and_line(all_1_0_0, all_1_4_4) = all_432_0_118 & distinct_lines(all_1_5_5, all_1_4_4) = all_432_2_120 & distinct_points(all_20_1_11, all_1_0_0) = all_432_3_121 & ( ~ (all_432_2_120 = 0) | ~ (all_432_3_121 = 0) | all_432_0_118 = 0 | all_432_1_119 = 0)
% 32.03/8.58 |
% 32.03/8.58 | Applying alpha-rule on (602) yields:
% 32.03/8.58 | (603) apart_point_and_line(all_1_0_0, all_1_4_4) = all_432_0_118
% 32.03/8.58 | (604) ~ (all_432_2_120 = 0) | ~ (all_432_3_121 = 0) | all_432_0_118 = 0 | all_432_1_119 = 0
% 32.03/8.58 | (605) distinct_lines(all_1_5_5, all_1_4_4) = all_432_2_120
% 32.03/8.58 | (606) distinct_points(all_20_1_11, all_1_0_0) = all_432_3_121
% 32.03/8.58 | (607) apart_point_and_line(all_20_1_11, all_1_5_5) = all_432_1_119
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (453), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (309) all_22_0_12 = 0
% 32.03/8.58 |
% 32.03/8.58 | Equations (309) can reduce 80 to:
% 32.03/8.58 | (109) $false
% 32.03/8.58 |
% 32.03/8.58 |-The branch is then unsatisfiable
% 32.03/8.58 |-Branch two:
% 32.03/8.58 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.58 | (611) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.58 |
% 32.03/8.58 | Instantiating (611) with all_437_0_122, all_437_1_123, all_437_2_124, all_437_3_125 yields:
% 32.03/8.58 | (612) apart_point_and_line(all_20_1_11, all_1_5_5) = all_437_0_122 & apart_point_and_line(all_1_0_0, all_1_4_4) = all_437_1_123 & distinct_lines(all_1_4_4, all_1_5_5) = all_437_2_124 & distinct_points(all_1_0_0, all_20_1_11) = all_437_3_125 & ( ~ (all_437_2_124 = 0) | ~ (all_437_3_125 = 0) | all_437_0_122 = 0 | all_437_1_123 = 0)
% 32.03/8.58 |
% 32.03/8.58 | Applying alpha-rule on (612) yields:
% 32.03/8.58 | (613) ~ (all_437_2_124 = 0) | ~ (all_437_3_125 = 0) | all_437_0_122 = 0 | all_437_1_123 = 0
% 32.03/8.58 | (614) distinct_points(all_1_0_0, all_20_1_11) = all_437_3_125
% 32.03/8.58 | (615) distinct_lines(all_1_4_4, all_1_5_5) = all_437_2_124
% 32.03/8.58 | (616) apart_point_and_line(all_20_1_11, all_1_5_5) = all_437_0_122
% 32.03/8.58 | (617) apart_point_and_line(all_1_0_0, all_1_4_4) = all_437_1_123
% 32.03/8.58 |
% 32.03/8.58 +-Applying beta-rule and splitting (469), into two cases.
% 32.03/8.58 |-Branch one:
% 32.03/8.58 | (309) all_22_0_12 = 0
% 32.03/8.59 |
% 32.03/8.59 | Equations (309) can reduce 80 to:
% 32.03/8.59 | (109) $false
% 32.03/8.59 |
% 32.03/8.59 |-The branch is then unsatisfiable
% 32.03/8.59 |-Branch two:
% 32.03/8.59 | (80) ~ (all_22_0_12 = 0)
% 32.03/8.59 | (621) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_1_0_0, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_0_0, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.59 |
% 32.03/8.59 | Instantiating (621) with all_447_0_130, all_447_1_131, all_447_2_132, all_447_3_133 yields:
% 32.03/8.59 | (622) apart_point_and_line(all_20_1_11, all_1_5_5) = all_447_0_130 & apart_point_and_line(all_1_0_0, all_1_4_4) = all_447_1_131 & distinct_lines(all_1_5_5, all_1_4_4) = all_447_2_132 & distinct_points(all_1_0_0, all_20_1_11) = all_447_3_133 & ( ~ (all_447_2_132 = 0) | ~ (all_447_3_133 = 0) | all_447_0_130 = 0 | all_447_1_131 = 0)
% 32.03/8.59 |
% 32.03/8.59 | Applying alpha-rule on (622) yields:
% 32.03/8.59 | (623) distinct_points(all_1_0_0, all_20_1_11) = all_447_3_133
% 32.03/8.59 | (624) apart_point_and_line(all_20_1_11, all_1_5_5) = all_447_0_130
% 32.03/8.59 | (625) ~ (all_447_2_132 = 0) | ~ (all_447_3_133 = 0) | all_447_0_130 = 0 | all_447_1_131 = 0
% 32.03/8.59 | (626) distinct_lines(all_1_5_5, all_1_4_4) = all_447_2_132
% 32.03/8.59 | (627) apart_point_and_line(all_1_0_0, all_1_4_4) = all_447_1_131
% 32.03/8.59 |
% 32.03/8.59 +-Applying beta-rule and splitting (173), into two cases.
% 32.03/8.59 |-Branch one:
% 32.03/8.59 | (365) all_34_0_24 = 0
% 32.03/8.59 |
% 32.03/8.59 | Equations (365) can reduce 228 to:
% 32.03/8.59 | (109) $false
% 32.03/8.59 |
% 32.03/8.59 |-The branch is then unsatisfiable
% 32.03/8.59 |-Branch two:
% 32.03/8.59 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.59 | (631) all_18_0_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.59 |
% 32.03/8.59 +-Applying beta-rule and splitting (172), into two cases.
% 32.03/8.59 |-Branch one:
% 32.03/8.59 | (365) all_34_0_24 = 0
% 32.03/8.59 |
% 32.03/8.59 | Equations (365) can reduce 228 to:
% 32.03/8.59 | (109) $false
% 32.03/8.59 |
% 32.03/8.59 |-The branch is then unsatisfiable
% 32.03/8.59 |-Branch two:
% 32.03/8.59 | (228) ~ (all_34_0_24 = 0)
% 32.03/8.59 | (635) all_24_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_18_1_9, all_1_5_5) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_18_1_9, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.59 |
% 32.03/8.59 +-Applying beta-rule and splitting (577), into two cases.
% 32.03/8.59 |-Branch one:
% 32.03/8.59 | (341) all_18_0_8 = 0
% 32.03/8.59 |
% 32.03/8.59 | Equations (341) can reduce 72 to:
% 32.03/8.59 | (109) $false
% 32.03/8.59 |
% 32.03/8.59 |-The branch is then unsatisfiable
% 32.03/8.59 |-Branch two:
% 32.03/8.59 | (72) ~ (all_18_0_8 = 0)
% 32.03/8.59 | (639) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_18_1_9, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_20_1_11, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.59 |
% 32.03/8.59 +-Applying beta-rule and splitting (581), into two cases.
% 32.03/8.59 |-Branch one:
% 32.03/8.59 | (341) all_18_0_8 = 0
% 32.03/8.59 |
% 32.03/8.59 | Equations (341) can reduce 72 to:
% 32.03/8.59 | (109) $false
% 32.03/8.59 |
% 32.03/8.59 |-The branch is then unsatisfiable
% 32.03/8.59 |-Branch two:
% 32.03/8.59 | (72) ~ (all_18_0_8 = 0)
% 32.03/8.59 | (643) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_18_1_9, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_18_1_9, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.59 |
% 32.03/8.59 +-Applying beta-rule and splitting (585), into two cases.
% 32.03/8.59 |-Branch one:
% 32.03/8.59 | (341) all_18_0_8 = 0
% 32.03/8.59 |
% 32.03/8.59 | Equations (341) can reduce 72 to:
% 32.03/8.59 | (109) $false
% 32.03/8.59 |
% 32.03/8.59 |-The branch is then unsatisfiable
% 32.03/8.59 |-Branch two:
% 32.03/8.59 | (72) ~ (all_18_0_8 = 0)
% 32.03/8.59 | (647) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v3 & apart_point_and_line(all_18_1_9, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_18_1_9, all_20_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.59 |
% 32.03/8.59 | Instantiating (647) with all_493_0_154, all_493_1_155, all_493_2_156, all_493_3_157 yields:
% 32.03/8.59 | (648) apart_point_and_line(all_20_1_11, all_1_5_5) = all_493_0_154 & apart_point_and_line(all_18_1_9, all_1_4_4) = all_493_1_155 & distinct_lines(all_1_5_5, all_1_4_4) = all_493_2_156 & distinct_points(all_18_1_9, all_20_1_11) = all_493_3_157 & ( ~ (all_493_2_156 = 0) | ~ (all_493_3_157 = 0) | all_493_0_154 = 0 | all_493_1_155 = 0)
% 32.03/8.59 |
% 32.03/8.59 | Applying alpha-rule on (648) yields:
% 32.03/8.59 | (649) apart_point_and_line(all_18_1_9, all_1_4_4) = all_493_1_155
% 32.03/8.59 | (650) distinct_points(all_18_1_9, all_20_1_11) = all_493_3_157
% 32.03/8.59 | (651) distinct_lines(all_1_5_5, all_1_4_4) = all_493_2_156
% 32.03/8.59 | (652) ~ (all_493_2_156 = 0) | ~ (all_493_3_157 = 0) | all_493_0_154 = 0 | all_493_1_155 = 0
% 32.03/8.59 | (653) apart_point_and_line(all_20_1_11, all_1_5_5) = all_493_0_154
% 32.03/8.59 |
% 32.03/8.59 +-Applying beta-rule and splitting (589), into two cases.
% 32.03/8.59 |-Branch one:
% 32.03/8.59 | (341) all_18_0_8 = 0
% 32.03/8.59 |
% 32.03/8.59 | Equations (341) can reduce 72 to:
% 32.03/8.59 | (109) $false
% 32.03/8.59 |
% 32.03/8.59 |-The branch is then unsatisfiable
% 32.03/8.59 |-Branch two:
% 32.03/8.59 | (72) ~ (all_18_0_8 = 0)
% 32.03/8.59 | (657) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_20_1_11, all_1_5_5) = v2 & apart_point_and_line(all_18_1_9, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_20_1_11, all_18_1_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.03/8.59 |
% 32.03/8.59 | Instantiating (657) with all_498_0_158, all_498_1_159, all_498_2_160, all_498_3_161 yields:
% 32.03/8.59 | (658) apart_point_and_line(all_20_1_11, all_1_5_5) = all_498_1_159 & apart_point_and_line(all_18_1_9, all_1_4_4) = all_498_0_158 & distinct_lines(all_1_5_5, all_1_4_4) = all_498_2_160 & distinct_points(all_20_1_11, all_18_1_9) = all_498_3_161 & ( ~ (all_498_2_160 = 0) | ~ (all_498_3_161 = 0) | all_498_0_158 = 0 | all_498_1_159 = 0)
% 32.03/8.59 |
% 32.03/8.59 | Applying alpha-rule on (658) yields:
% 32.03/8.59 | (659) apart_point_and_line(all_20_1_11, all_1_5_5) = all_498_1_159
% 32.03/8.59 | (660) distinct_points(all_20_1_11, all_18_1_9) = all_498_3_161
% 32.03/8.59 | (661) distinct_lines(all_1_5_5, all_1_4_4) = all_498_2_160
% 32.03/8.59 | (662) ~ (all_498_2_160 = 0) | ~ (all_498_3_161 = 0) | all_498_0_158 = 0 | all_498_1_159 = 0
% 32.03/8.59 | (663) apart_point_and_line(all_18_1_9, all_1_4_4) = all_498_0_158
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (34) with all_1_4_4, all_1_5_5, all_144_1_54, all_1_0_0 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_144_1_54, intersection_point(all_1_4_4, all_1_5_5) = all_1_0_0, yields:
% 32.03/8.59 | (664) all_144_1_54 = all_1_0_0
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (34) with all_1_4_4, all_1_5_5, all_132_1_52, all_144_1_54 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_144_1_54, intersection_point(all_1_4_4, all_1_5_5) = all_132_1_52, yields:
% 32.03/8.59 | (665) all_144_1_54 = all_132_1_52
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_437_1_123, all_447_1_131 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_447_1_131, apart_point_and_line(all_1_0_0, all_1_4_4) = all_437_1_123, yields:
% 32.03/8.59 | (666) all_447_1_131 = all_437_1_123
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_432_0_118, all_437_1_123 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_437_1_123, apart_point_and_line(all_1_0_0, all_1_4_4) = all_432_0_118, yields:
% 32.03/8.59 | (667) all_437_1_123 = all_432_0_118
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_377_0_110, all_432_0_118 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_432_0_118, apart_point_and_line(all_1_0_0, all_1_4_4) = all_377_0_110, yields:
% 32.03/8.59 | (668) all_432_0_118 = all_377_0_110
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_377_1_111, all_377_0_110 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_377_0_110, apart_point_and_line(all_1_0_0, all_1_4_4) = all_377_1_111, yields:
% 32.03/8.59 | (669) all_377_0_110 = all_377_1_111
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_363_0_102, all_132_0_51 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_363_0_102, yields:
% 32.03/8.59 | (670) all_363_0_102 = all_132_0_51 | ~ (apart_point_and_line(all_1_0_0, all_1_4_4) = all_132_0_51)
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_363_0_102, all_377_1_111 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_377_1_111, apart_point_and_line(all_1_0_0, all_1_4_4) = all_363_0_102, yields:
% 32.03/8.59 | (671) all_377_1_111 = all_363_0_102
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_117_0_44, all_363_0_102 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_363_0_102, apart_point_and_line(all_1_0_0, all_1_4_4) = all_117_0_44, yields:
% 32.03/8.59 | (672) all_363_0_102 = all_117_0_44
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_91_0_38, all_32_0_22 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_91_0_38, apart_point_and_line(all_1_0_0, all_1_4_4) = all_32_0_22, yields:
% 32.03/8.59 | (673) all_91_0_38 = all_32_0_22
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_91_0_38, all_117_0_44 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_117_0_44, apart_point_and_line(all_1_0_0, all_1_4_4) = all_91_0_38, yields:
% 32.03/8.59 | (674) all_117_0_44 = all_91_0_38
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_4_4, all_91_1_39, all_447_1_131 and discharging atoms apart_point_and_line(all_1_0_0, all_1_4_4) = all_447_1_131, apart_point_and_line(all_1_0_0, all_1_4_4) = all_91_1_39, yields:
% 32.03/8.59 | (675) all_447_1_131 = all_91_1_39
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_5_5, all_382_0_114, all_144_0_53 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_0_114, yields:
% 32.03/8.59 | (676) all_382_0_114 = all_144_0_53 | ~ (apart_point_and_line(all_1_0_0, all_1_5_5) = all_144_0_53)
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_5_5, all_382_1_115, all_382_0_114 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_0_114, apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_1_115, yields:
% 32.03/8.59 | (677) all_382_0_114 = all_382_1_115
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_5_5, all_343_0_86, all_34_0_24 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_343_0_86, apart_point_and_line(all_1_0_0, all_1_5_5) = all_34_0_24, yields:
% 32.03/8.59 | (678) all_343_0_86 = all_34_0_24
% 32.03/8.59 |
% 32.03/8.59 | Instantiating formula (35) with all_1_0_0, all_1_5_5, all_343_0_86, all_382_1_115 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_1_115, apart_point_and_line(all_1_0_0, all_1_5_5) = all_343_0_86, yields:
% 32.03/8.60 | (679) all_382_1_115 = all_343_0_86
% 32.03/8.60 |
% 32.03/8.60 | Instantiating formula (35) with all_1_0_0, all_1_5_5, all_260_0_55, all_343_0_86 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_343_0_86, apart_point_and_line(all_1_0_0, all_1_5_5) = all_260_0_55, yields:
% 32.03/8.60 | (680) all_343_0_86 = all_260_0_55
% 32.03/8.60 |
% 32.03/8.60 | Instantiating formula (35) with all_1_0_0, all_1_5_5, all_117_1_45, all_382_0_114 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_382_0_114, apart_point_and_line(all_1_0_0, all_1_5_5) = all_117_1_45, yields:
% 32.03/8.60 | (681) all_382_0_114 = all_117_1_45
% 32.03/8.60 |
% 32.03/8.60 | Instantiating formula (35) with all_1_0_0, all_1_5_5, all_112_1_42, all_343_0_86 and discharging atoms apart_point_and_line(all_1_0_0, all_1_5_5) = all_343_0_86, apart_point_and_line(all_1_0_0, all_1_5_5) = all_112_1_42, yields:
% 32.03/8.60 | (682) all_343_0_86 = all_112_1_42
% 32.03/8.60 |
% 32.03/8.60 | Instantiating formula (42) with all_1_5_5, all_1_4_4, all_493_2_156, all_498_2_160 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_498_2_160, distinct_lines(all_1_5_5, all_1_4_4) = all_493_2_156, yields:
% 32.03/8.60 | (683) all_498_2_160 = all_493_2_156
% 32.03/8.60 |
% 32.03/8.60 | Instantiating formula (42) with all_1_5_5, all_1_4_4, all_447_2_132, all_493_2_156 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_493_2_156, distinct_lines(all_1_5_5, all_1_4_4) = all_447_2_132, yields:
% 32.03/8.60 | (684) all_493_2_156 = all_447_2_132
% 32.03/8.60 |
% 32.03/8.60 | Instantiating formula (42) with all_1_5_5, all_1_4_4, all_432_2_120, all_447_2_132 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_447_2_132, distinct_lines(all_1_5_5, all_1_4_4) = all_432_2_120, yields:
% 32.03/8.60 | (685) all_447_2_132 = all_432_2_120
% 32.03/8.60 |
% 32.03/8.60 | Instantiating formula (42) with all_1_5_5, all_1_4_4, all_343_2_88, all_432_2_120 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_432_2_120, distinct_lines(all_1_5_5, all_1_4_4) = all_343_2_88, yields:
% 32.03/8.60 | (686) all_432_2_120 = all_343_2_88
% 32.03/8.60 |
% 32.03/8.60 | Instantiating formula (42) with all_1_5_5, all_1_4_4, all_117_2_46, all_498_2_160 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_498_2_160, distinct_lines(all_1_5_5, all_1_4_4) = all_117_2_46, yields:
% 32.03/8.60 | (687) all_498_2_160 = all_117_2_46
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (683,687) yields a new equation:
% 32.03/8.60 | (688) all_493_2_156 = all_117_2_46
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 688 yields:
% 32.03/8.60 | (689) all_493_2_156 = all_117_2_46
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (684,689) yields a new equation:
% 32.03/8.60 | (690) all_447_2_132 = all_117_2_46
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 690 yields:
% 32.03/8.60 | (691) all_447_2_132 = all_117_2_46
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (666,675) yields a new equation:
% 32.03/8.60 | (692) all_437_1_123 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 692 yields:
% 32.03/8.60 | (693) all_437_1_123 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (685,691) yields a new equation:
% 32.03/8.60 | (694) all_432_2_120 = all_117_2_46
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 694 yields:
% 32.03/8.60 | (695) all_432_2_120 = all_117_2_46
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (667,693) yields a new equation:
% 32.03/8.60 | (696) all_432_0_118 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 696 yields:
% 32.03/8.60 | (697) all_432_0_118 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (668,697) yields a new equation:
% 32.03/8.60 | (698) all_377_0_110 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 698 yields:
% 32.03/8.60 | (699) all_377_0_110 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (695,686) yields a new equation:
% 32.03/8.60 | (700) all_343_2_88 = all_117_2_46
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (677,681) yields a new equation:
% 32.03/8.60 | (701) all_382_1_115 = all_117_1_45
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 701 yields:
% 32.03/8.60 | (702) all_382_1_115 = all_117_1_45
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (679,702) yields a new equation:
% 32.03/8.60 | (703) all_343_0_86 = all_117_1_45
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 703 yields:
% 32.03/8.60 | (704) all_343_0_86 = all_117_1_45
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (669,699) yields a new equation:
% 32.03/8.60 | (705) all_377_1_111 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 705 yields:
% 32.03/8.60 | (706) all_377_1_111 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (671,706) yields a new equation:
% 32.03/8.60 | (707) all_363_0_102 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 707 yields:
% 32.03/8.60 | (708) all_363_0_102 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (672,708) yields a new equation:
% 32.03/8.60 | (709) all_117_0_44 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Simplifying 709 yields:
% 32.03/8.60 | (710) all_117_0_44 = all_91_1_39
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (682,680) yields a new equation:
% 32.03/8.60 | (711) all_260_0_55 = all_112_1_42
% 32.03/8.60 |
% 32.03/8.60 | Combining equations (704,680) yields a new equation:
% 32.03/8.60 | (712) all_260_0_55 = all_117_1_45
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (678,680) yields a new equation:
% 32.33/8.60 | (713) all_260_0_55 = all_34_0_24
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (713,712) yields a new equation:
% 32.33/8.60 | (714) all_117_1_45 = all_34_0_24
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (711,712) yields a new equation:
% 32.33/8.60 | (715) all_117_1_45 = all_112_1_42
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (665,664) yields a new equation:
% 32.33/8.60 | (716) all_132_1_52 = all_1_0_0
% 32.33/8.60 |
% 32.33/8.60 | Simplifying 716 yields:
% 32.33/8.60 | (717) all_132_1_52 = all_1_0_0
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (674,710) yields a new equation:
% 32.33/8.60 | (718) all_91_0_38 = all_91_1_39
% 32.33/8.60 |
% 32.33/8.60 | Simplifying 718 yields:
% 32.33/8.60 | (719) all_91_0_38 = all_91_1_39
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (714,715) yields a new equation:
% 32.33/8.60 | (720) all_112_1_42 = all_34_0_24
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (719,673) yields a new equation:
% 32.33/8.60 | (721) all_91_1_39 = all_32_0_22
% 32.33/8.60 |
% 32.33/8.60 | Simplifying 721 yields:
% 32.33/8.60 | (722) all_91_1_39 = all_32_0_22
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (720,715) yields a new equation:
% 32.33/8.60 | (714) all_117_1_45 = all_34_0_24
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (722,710) yields a new equation:
% 32.33/8.60 | (724) all_117_0_44 = all_32_0_22
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (722,708) yields a new equation:
% 32.33/8.60 | (725) all_363_0_102 = all_32_0_22
% 32.33/8.60 |
% 32.33/8.60 | Combining equations (714,681) yields a new equation:
% 32.33/8.60 | (726) all_382_0_114 = all_34_0_24
% 32.33/8.60 |
% 32.33/8.60 | From (664) and (300) follows:
% 32.33/8.60 | (727) apart_point_and_line(all_1_0_0, all_1_5_5) = all_144_0_53
% 32.33/8.60 |
% 32.33/8.60 | From (717) and (288) follows:
% 32.33/8.60 | (728) apart_point_and_line(all_1_0_0, all_1_4_4) = all_132_0_51
% 32.33/8.60 |
% 32.33/8.60 | From (700) and (523) follows:
% 32.33/8.60 | (275) distinct_lines(all_1_5_5, all_1_4_4) = all_117_2_46
% 32.33/8.60 |
% 32.33/8.60 +-Applying beta-rule and splitting (197), into two cases.
% 32.33/8.60 |-Branch one:
% 32.33/8.60 | (365) all_34_0_24 = 0
% 32.33/8.60 |
% 32.33/8.60 | Equations (365) can reduce 228 to:
% 32.33/8.60 | (109) $false
% 32.33/8.60 |
% 32.33/8.60 |-The branch is then unsatisfiable
% 32.33/8.60 |-Branch two:
% 32.33/8.60 | (228) ~ (all_34_0_24 = 0)
% 32.33/8.60 | (733) all_26_0_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_1_0_0, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.33/8.60 |
% 32.33/8.60 +-Applying beta-rule and splitting (733), into two cases.
% 32.33/8.60 |-Branch one:
% 32.33/8.60 | (233) all_26_0_16 = 0
% 32.33/8.60 |
% 32.33/8.61 | Equations (233) can reduce 88 to:
% 32.33/8.61 | (109) $false
% 32.33/8.61 |
% 32.33/8.61 |-The branch is then unsatisfiable
% 32.33/8.61 |-Branch two:
% 32.33/8.61 | (88) ~ (all_26_0_16 = 0)
% 32.33/8.61 | (737) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, 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_1_0_0, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.33/8.61 |
% 32.33/8.61 | Instantiating (737) with all_526_0_166, all_526_1_167, all_526_2_168, all_526_3_169 yields:
% 32.33/8.61 | (738) apart_point_and_line(all_1_0_0, all_1_4_4) = all_526_1_167 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_526_0_166 & distinct_lines(all_1_5_5, all_1_4_4) = all_526_2_168 & distinct_points(all_1_0_0, all_1_2_2) = all_526_3_169 & ( ~ (all_526_2_168 = 0) | ~ (all_526_3_169 = 0) | all_526_0_166 = 0 | all_526_1_167 = 0)
% 32.33/8.61 |
% 32.33/8.61 | Applying alpha-rule on (738) yields:
% 32.33/8.61 | (739) ~ (all_526_2_168 = 0) | ~ (all_526_3_169 = 0) | all_526_0_166 = 0 | all_526_1_167 = 0
% 32.33/8.61 | (740) apart_point_and_line(all_1_2_2, all_1_5_5) = all_526_0_166
% 32.33/8.61 | (741) distinct_lines(all_1_5_5, all_1_4_4) = all_526_2_168
% 32.33/8.61 | (742) distinct_points(all_1_0_0, all_1_2_2) = all_526_3_169
% 32.33/8.61 | (743) apart_point_and_line(all_1_0_0, all_1_4_4) = all_526_1_167
% 32.33/8.61 |
% 32.33/8.61 +-Applying beta-rule and splitting (670), into two cases.
% 32.33/8.61 |-Branch one:
% 32.33/8.61 | (744) ~ (apart_point_and_line(all_1_0_0, all_1_4_4) = all_132_0_51)
% 32.33/8.61 |
% 32.33/8.61 | Using (728) and (744) yields:
% 32.33/8.61 | (144) $false
% 32.33/8.61 |
% 32.33/8.61 |-The branch is then unsatisfiable
% 32.33/8.61 |-Branch two:
% 32.33/8.61 | (728) apart_point_and_line(all_1_0_0, all_1_4_4) = all_132_0_51
% 32.33/8.61 | (747) all_363_0_102 = all_132_0_51
% 32.33/8.61 |
% 32.33/8.61 | Combining equations (747,725) yields a new equation:
% 32.33/8.61 | (748) all_132_0_51 = all_32_0_22
% 32.33/8.61 |
% 32.33/8.61 | Simplifying 748 yields:
% 32.33/8.61 | (749) all_132_0_51 = all_32_0_22
% 32.33/8.61 |
% 32.33/8.61 | Equations (749) can reduce 286 to:
% 32.33/8.61 | (258) ~ (all_32_0_22 = 0)
% 32.33/8.61 |
% 32.33/8.61 +-Applying beta-rule and splitting (676), into two cases.
% 32.33/8.61 |-Branch one:
% 32.33/8.61 | (751) ~ (apart_point_and_line(all_1_0_0, all_1_5_5) = all_144_0_53)
% 32.33/8.61 |
% 32.33/8.61 | Using (727) and (751) yields:
% 32.33/8.61 | (144) $false
% 32.33/8.61 |
% 32.33/8.61 |-The branch is then unsatisfiable
% 32.33/8.61 |-Branch two:
% 32.33/8.61 | (727) apart_point_and_line(all_1_0_0, all_1_5_5) = all_144_0_53
% 32.33/8.61 | (754) all_382_0_114 = all_144_0_53
% 32.33/8.61 |
% 32.33/8.61 | Combining equations (754,726) yields a new equation:
% 32.33/8.61 | (755) all_144_0_53 = all_34_0_24
% 32.33/8.61 |
% 32.33/8.61 | Simplifying 755 yields:
% 32.33/8.61 | (756) all_144_0_53 = all_34_0_24
% 32.33/8.61 |
% 32.33/8.61 | Equations (756) can reduce 298 to:
% 32.33/8.61 | (228) ~ (all_34_0_24 = 0)
% 32.33/8.61 |
% 32.33/8.61 +-Applying beta-rule and splitting (276), into two cases.
% 32.33/8.61 |-Branch one:
% 32.33/8.61 | (758) ~ (all_117_2_46 = 0)
% 32.33/8.61 |
% 32.33/8.61 | Instantiating formula (42) with all_1_5_5, all_1_4_4, all_526_2_168, all_117_2_46 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_526_2_168, distinct_lines(all_1_5_5, all_1_4_4) = all_117_2_46, yields:
% 32.33/8.61 | (759) all_526_2_168 = all_117_2_46
% 32.33/8.61 |
% 32.33/8.61 | From (759) and (741) follows:
% 32.33/8.61 | (275) distinct_lines(all_1_5_5, all_1_4_4) = all_117_2_46
% 32.33/8.61 |
% 32.33/8.61 | Instantiating formula (20) with all_117_2_46, all_1_4_4, all_1_5_5, all_1_4_4 and discharging atoms convergent_lines(all_1_4_4, all_1_5_5) = 0, distinct_lines(all_1_5_5, all_1_4_4) = all_117_2_46, ~ (convergent_lines(all_1_4_4, all_1_4_4) = 0), yields:
% 32.33/8.61 | (761) all_117_2_46 = 0
% 32.33/8.61 |
% 32.33/8.61 | Equations (761) can reduce 758 to:
% 32.33/8.61 | (109) $false
% 32.33/8.61 |
% 32.33/8.61 |-The branch is then unsatisfiable
% 32.33/8.61 |-Branch two:
% 32.33/8.61 | (761) all_117_2_46 = 0
% 32.33/8.61 | (764) all_117_0_44 = 0 | all_117_1_45 = 0
% 32.33/8.61 |
% 32.33/8.61 +-Applying beta-rule and splitting (764), into two cases.
% 32.33/8.61 |-Branch one:
% 32.33/8.61 | (765) all_117_0_44 = 0
% 32.33/8.61 |
% 32.33/8.61 | Combining equations (724,765) yields a new equation:
% 32.33/8.61 | (766) all_32_0_22 = 0
% 32.33/8.61 |
% 32.33/8.61 | Simplifying 766 yields:
% 32.33/8.61 | (369) all_32_0_22 = 0
% 32.33/8.61 |
% 32.33/8.61 | Equations (369) can reduce 258 to:
% 32.33/8.61 | (109) $false
% 32.33/8.61 |
% 32.33/8.61 |-The branch is then unsatisfiable
% 32.33/8.61 |-Branch two:
% 32.33/8.61 | (769) ~ (all_117_0_44 = 0)
% 32.33/8.61 | (770) all_117_1_45 = 0
% 32.33/8.61 |
% 32.33/8.61 | Combining equations (714,770) yields a new equation:
% 32.33/8.61 | (771) all_34_0_24 = 0
% 32.33/8.61 |
% 32.33/8.61 | Simplifying 771 yields:
% 32.33/8.61 | (365) all_34_0_24 = 0
% 32.33/8.61 |
% 32.33/8.61 | Equations (365) can reduce 228 to:
% 32.33/8.61 | (109) $false
% 32.33/8.61 |
% 32.33/8.61 |-The branch is then unsatisfiable
% 32.33/8.62 |-Branch two:
% 32.33/8.62 | (369) all_32_0_22 = 0
% 32.33/8.62 | (775) ~ (all_32_1_23 = 0)
% 32.33/8.62 |
% 32.33/8.62 | Equations (217) can reduce 775 to:
% 32.33/8.62 | (109) $false
% 32.33/8.62 |
% 32.33/8.62 |-The branch is then unsatisfiable
% 32.33/8.62 |-Branch two:
% 32.33/8.62 | (365) all_34_0_24 = 0
% 32.33/8.62 | (778) ~ (all_34_1_25 = 0)
% 32.33/8.62 |
% 32.33/8.62 | Equations (226) can reduce 778 to:
% 32.33/8.62 | (109) $false
% 32.33/8.62 |
% 32.33/8.62 |-The branch is then unsatisfiable
% 32.33/8.62 |-Branch two:
% 32.33/8.62 | (780) all_28_0_18 = 0
% 32.33/8.62 | (781) ~ (all_28_1_19 = 0)
% 32.33/8.62 |
% 32.33/8.62 | Equations (131) can reduce 781 to:
% 32.33/8.62 | (109) $false
% 32.33/8.62 |
% 32.33/8.62 |-The branch is then unsatisfiable
% 32.33/8.62 |-Branch two:
% 32.33/8.62 | (783) all_30_0_20 = 0
% 32.33/8.62 | (784) ~ (all_30_1_21 = 0)
% 32.33/8.62 |
% 32.33/8.62 | Equations (127) can reduce 784 to:
% 32.33/8.62 | (109) $false
% 32.33/8.62 |
% 32.33/8.62 |-The branch is then unsatisfiable
% 32.33/8.62 |-Branch two:
% 32.33/8.62 | (786) ~ (distinct_points(all_1_0_0, all_1_2_2) = 0)
% 32.33/8.62 | (108) all_1_1_1 = 0
% 32.33/8.62 |
% 32.33/8.62 | Equations (108) can reduce 48 to:
% 32.33/8.62 | (109) $false
% 32.33/8.62 |
% 32.33/8.62 |-The branch is then unsatisfiable
% 32.33/8.62 % SZS output end Proof for theBenchmark
% 32.33/8.62
% 32.33/8.62 7935ms
%------------------------------------------------------------------------------