TSTP Solution File: GEO180+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO180+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 03:48:17 EDT 2022
% Result : Theorem 13.44s 3.90s
% Output : Proof 32.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO180+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 06:20:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.58 ____ _
% 0.20/0.58 ___ / __ \_____(_)___ ________ __________
% 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic
% 0.20/0.58 (ePrincess v.1.0)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2015
% 0.20/0.58 (c) Peter Backeman, 2014-2015
% 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59 Bug reports to peter@backeman.se
% 0.20/0.59
% 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.68/0.94 Prover 0: Preprocessing ...
% 1.90/1.07 Prover 0: Warning: ignoring some quantifiers
% 2.05/1.09 Prover 0: Constructing countermodel ...
% 2.80/1.31 Prover 0: gave up
% 2.80/1.31 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.80/1.33 Prover 1: Preprocessing ...
% 3.05/1.42 Prover 1: Constructing countermodel ...
% 3.35/1.48 Prover 1: gave up
% 3.35/1.48 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.46/1.50 Prover 2: Preprocessing ...
% 3.67/1.60 Prover 2: Warning: ignoring some quantifiers
% 4.02/1.61 Prover 2: Constructing countermodel ...
% 4.39/1.74 Prover 2: gave up
% 4.39/1.74 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.39/1.76 Prover 3: Preprocessing ...
% 4.39/1.78 Prover 3: Warning: ignoring some quantifiers
% 4.83/1.78 Prover 3: Constructing countermodel ...
% 5.06/1.84 Prover 3: gave up
% 5.06/1.84 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.06/1.85 Prover 4: Preprocessing ...
% 5.49/1.92 Prover 4: Warning: ignoring some quantifiers
% 5.49/1.93 Prover 4: Constructing countermodel ...
% 10.00/3.05 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.00/3.09 Prover 5: Preprocessing ...
% 10.37/3.17 Prover 5: Constructing countermodel ...
% 13.44/3.90 Prover 5: proved (847ms)
% 13.44/3.90 Prover 4: stopped
% 13.44/3.90
% 13.44/3.90 No countermodel exists, formula is valid
% 13.44/3.90 % SZS status Theorem for theBenchmark
% 13.44/3.90
% 13.44/3.90 Generating proof ... found it (size 779)
% 31.63/9.44
% 31.63/9.44 % SZS output start Proof for theBenchmark
% 31.63/9.44 Assumed formulas after preprocessing and simplification:
% 31.63/9.44 | (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 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) & ~ (v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v2, v1) = v4) | ~ (distinct_points(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0))) | (v4 = 0 & v3 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (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] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v1) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v0) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v1) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v0, v4) = v5 & distinct_points(v0, v1) = 0)
% 31.95/9.49 | Applying alpha-rule on (0) yields:
% 31.95/9.49 | (1) ! [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)))
% 31.95/9.50 | (2) ! [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))
% 31.95/9.50 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 31.95/9.50 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 31.95/9.50 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 31.95/9.50 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 31.95/9.50 | (7) ! [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)))
% 31.95/9.50 | (8) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 31.95/9.50 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0)))))
% 31.95/9.50 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 31.95/9.50 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 31.95/9.50 | (12) ! [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)
% 31.95/9.50 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 31.95/9.50 | (14) ! [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)))
% 31.95/9.50 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 31.95/9.50 | (16) ! [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))
% 31.95/9.50 | (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)
% 31.95/9.50 | (18) ! [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)
% 31.95/9.50 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) & ~ (v3 = 0)))
% 32.08/9.51 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 32.08/9.51 | (21) ! [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))
% 32.08/9.51 | (22) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v1) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v0, v4) = v5 & distinct_points(v0, v1) = 0)
% 32.08/9.51 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 32.08/9.51 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 32.08/9.51 | (25) ! [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))
% 32.08/9.51 | (26) ! [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))
% 32.08/9.51 | (27) ! [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)
% 32.08/9.51 | (28) ! [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)))
% 32.08/9.51 | (29) ! [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)))
% 32.08/9.51 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 32.08/9.51 | (31) ! [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)))
% 32.08/9.51 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 32.08/9.51 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 32.08/9.51 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0)))))
% 32.08/9.51 | (35) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 32.08/9.51 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0)))))
% 32.08/9.51 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v0) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 32.08/9.51 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v2, v1) = v4) | ~ (distinct_points(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0))) | (v4 = 0 & v3 = 0))
% 32.08/9.52 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v1) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 32.08/9.52 | (40) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 32.08/9.52 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0)))))
% 32.08/9.52 | (42) ! [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)))
% 32.08/9.52 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 32.08/9.52 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0)))))
% 32.08/9.52 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 32.08/9.52 | (46) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 32.08/9.52 |
% 32.08/9.52 | Instantiating (22) 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:
% 32.08/9.52 | (47) ~ (all_1_0_0 = 0) & line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1 & line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2 & apart_point_and_line(all_1_3_3, all_1_2_2) = 0 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0 & distinct_points(all_1_5_5, all_1_4_4) = 0
% 32.08/9.52 |
% 32.08/9.52 | Applying alpha-rule on (47) yields:
% 32.08/9.52 | (48) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2
% 32.08/9.52 | (49) line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1
% 32.08/9.52 | (50) apart_point_and_line(all_1_3_3, all_1_2_2) = 0
% 32.08/9.52 | (51) apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0
% 32.08/9.52 | (52) distinct_points(all_1_5_5, all_1_4_4) = 0
% 32.08/9.52 | (53) ~ (all_1_0_0 = 0)
% 32.08/9.52 |
% 32.08/9.52 | Instantiating formula (46) with all_1_5_5 yields:
% 32.08/9.52 | (54) ~ (distinct_points(all_1_5_5, all_1_5_5) = 0)
% 32.08/9.52 |
% 32.08/9.52 | Instantiating formula (19) with 0, 0, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = 0, yields:
% 32.08/9.52 | (55) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_2_2, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_2_2) = v0 & distinct_points(all_1_3_3, v1) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 32.08/9.52 |
% 32.08/9.52 | Instantiating formula (32) with all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, apart_point_and_line(all_1_3_3, all_1_2_2) = 0, yields:
% 32.08/9.52 | (56) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_3_3, all_1_4_4) = v2 & distinct_points(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 32.08/9.52 |
% 32.08/9.52 | Instantiating formula (1) with all_1_0_0, all_1_0_0, all_1_1_1, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.08/9.52 | (57) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.08/9.52 |
% 32.08/9.52 | Instantiating formula (39) with 0, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.08/9.52 | (58) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.17/9.52 |
% 32.17/9.52 | Instantiating formula (6) with 0, all_1_1_1, all_1_5_5, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.17/9.52 | (59) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.17/9.53 |
% 32.17/9.53 | Instantiating formula (6) with 0, all_1_2_2, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.17/9.53 | (60) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.17/9.53 |
% 32.17/9.53 | Instantiating formula (42) with all_1_0_0, all_1_0_0, all_1_1_1, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.17/9.53 | (61) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.53 |
% 32.17/9.53 | Instantiating (60) with all_16_0_6, all_16_1_7, all_16_2_8 yields:
% 32.17/9.53 | (62) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7 & distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8 & distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6 & ( ~ (all_16_1_7 = 0) | ~ (all_16_2_8 = 0) | all_16_0_6 = 0)
% 32.17/9.53 |
% 32.17/9.53 | Applying alpha-rule on (62) yields:
% 32.17/9.53 | (63) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7
% 32.17/9.53 | (64) distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8
% 32.17/9.53 | (65) distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6
% 32.17/9.53 | (66) ~ (all_16_1_7 = 0) | ~ (all_16_2_8 = 0) | all_16_0_6 = 0
% 32.17/9.53 |
% 32.17/9.53 | Instantiating (56) with all_18_0_9, all_18_1_10, all_18_2_11 yields:
% 32.17/9.53 | (67) distinct_points(all_1_3_3, all_1_4_4) = all_18_0_9 & distinct_points(all_1_3_3, all_1_5_5) = all_18_1_10 & distinct_points(all_1_5_5, all_1_4_4) = all_18_2_11 & ( ~ (all_18_2_11 = 0) | (all_18_0_9 = 0 & all_18_1_10 = 0))
% 32.17/9.53 |
% 32.17/9.53 | Applying alpha-rule on (67) yields:
% 32.17/9.53 | (68) distinct_points(all_1_3_3, all_1_4_4) = all_18_0_9
% 32.17/9.53 | (69) distinct_points(all_1_3_3, all_1_5_5) = all_18_1_10
% 32.17/9.53 | (70) distinct_points(all_1_5_5, all_1_4_4) = all_18_2_11
% 32.17/9.53 | (71) ~ (all_18_2_11 = 0) | (all_18_0_9 = 0 & all_18_1_10 = 0)
% 32.17/9.53 |
% 32.17/9.53 | Instantiating (59) with all_20_0_12, all_20_1_13, all_20_2_14 yields:
% 32.17/9.53 | (72) apart_point_and_line(all_1_5_5, all_1_1_1) = all_20_1_13 & distinct_points(all_1_3_3, all_1_4_4) = all_20_2_14 & distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12 & ( ~ (all_20_1_13 = 0) | ~ (all_20_2_14 = 0) | all_20_0_12 = 0)
% 32.17/9.53 |
% 32.17/9.53 | Applying alpha-rule on (72) yields:
% 32.17/9.53 | (73) apart_point_and_line(all_1_5_5, all_1_1_1) = all_20_1_13
% 32.17/9.53 | (74) distinct_points(all_1_3_3, all_1_4_4) = all_20_2_14
% 32.17/9.53 | (75) distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12
% 32.17/9.53 | (76) ~ (all_20_1_13 = 0) | ~ (all_20_2_14 = 0) | all_20_0_12 = 0
% 32.17/9.53 |
% 32.17/9.53 | Instantiating (58) with all_22_0_15, all_22_1_16, all_22_2_17 yields:
% 32.17/9.53 | (77) line_connecting(all_1_5_5, all_1_4_4) = all_22_2_17 & apart_point_and_line(all_1_5_5, all_22_2_17) = all_22_1_16 & distinct_points(all_1_5_5, all_1_5_5) = all_22_0_15 & ( ~ (all_22_1_16 = 0) | all_22_0_15 = 0)
% 32.17/9.53 |
% 32.17/9.53 | Applying alpha-rule on (77) yields:
% 32.17/9.53 | (78) line_connecting(all_1_5_5, all_1_4_4) = all_22_2_17
% 32.17/9.53 | (79) apart_point_and_line(all_1_5_5, all_22_2_17) = all_22_1_16
% 32.17/9.53 | (80) distinct_points(all_1_5_5, all_1_5_5) = all_22_0_15
% 32.17/9.53 | (81) ~ (all_22_1_16 = 0) | all_22_0_15 = 0
% 32.17/9.53 |
% 32.17/9.53 | Instantiating (55) with all_24_0_18, all_24_1_19, all_24_2_20 yields:
% 32.17/9.53 | (82) intersection_point(all_1_2_2, all_1_2_2) = all_24_1_19 & convergent_lines(all_1_2_2, all_1_2_2) = all_24_2_20 & distinct_points(all_1_3_3, all_24_1_19) = all_24_0_18 & ( ~ (all_24_2_20 = 0) | all_24_0_18 = 0)
% 32.17/9.53 |
% 32.17/9.53 | Applying alpha-rule on (82) yields:
% 32.17/9.53 | (83) intersection_point(all_1_2_2, all_1_2_2) = all_24_1_19
% 32.17/9.53 | (84) convergent_lines(all_1_2_2, all_1_2_2) = all_24_2_20
% 32.17/9.53 | (85) distinct_points(all_1_3_3, all_24_1_19) = all_24_0_18
% 32.17/9.53 | (86) ~ (all_24_2_20 = 0) | all_24_0_18 = 0
% 32.17/9.53 |
% 32.17/9.53 +-Applying beta-rule and splitting (57), into two cases.
% 32.17/9.53 |-Branch one:
% 32.17/9.53 | (87) all_1_0_0 = 0
% 32.17/9.53 |
% 32.17/9.53 | Equations (87) can reduce 53 to:
% 32.17/9.53 | (88) $false
% 32.17/9.53 |
% 32.17/9.53 |-The branch is then unsatisfiable
% 32.17/9.53 |-Branch two:
% 32.17/9.53 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.53 | (90) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.53 |
% 32.17/9.53 | Instantiating (90) with all_30_0_21, all_30_1_22, all_30_2_23, all_30_3_24 yields:
% 32.17/9.53 | (91) apart_point_and_line(all_1_5_5, all_1_1_1) = all_30_0_21 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_30_1_22 & distinct_lines(all_1_1_1, all_1_1_1) = all_30_2_23 & distinct_points(all_1_5_5, all_1_5_5) = all_30_3_24 & ( ~ (all_30_2_23 = 0) | ~ (all_30_3_24 = 0) | all_30_0_21 = 0 | all_30_1_22 = 0)
% 32.17/9.53 |
% 32.17/9.53 | Applying alpha-rule on (91) yields:
% 32.17/9.53 | (92) apart_point_and_line(all_1_5_5, all_1_1_1) = all_30_1_22
% 32.17/9.53 | (93) distinct_points(all_1_5_5, all_1_5_5) = all_30_3_24
% 32.17/9.53 | (94) ~ (all_30_2_23 = 0) | ~ (all_30_3_24 = 0) | all_30_0_21 = 0 | all_30_1_22 = 0
% 32.17/9.53 | (95) apart_point_and_line(all_1_5_5, all_1_1_1) = all_30_0_21
% 32.17/9.53 | (96) distinct_lines(all_1_1_1, all_1_1_1) = all_30_2_23
% 32.17/9.53 |
% 32.17/9.53 +-Applying beta-rule and splitting (61), into two cases.
% 32.17/9.53 |-Branch one:
% 32.17/9.53 | (87) all_1_0_0 = 0
% 32.17/9.53 |
% 32.17/9.53 | Equations (87) can reduce 53 to:
% 32.17/9.53 | (88) $false
% 32.17/9.53 |
% 32.17/9.53 |-The branch is then unsatisfiable
% 32.17/9.53 |-Branch two:
% 32.17/9.53 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.54 | (100) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (5) with all_1_5_5, all_1_4_4, all_22_2_17, all_1_2_2 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_22_2_17, line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 32.17/9.54 | (101) all_22_2_17 = all_1_2_2
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_30_0_21, all_1_0_0 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_30_0_21, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.17/9.54 | (102) all_30_0_21 = all_1_0_0
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_30_1_22, all_30_0_21 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_30_0_21, apart_point_and_line(all_1_5_5, all_1_1_1) = all_30_1_22, yields:
% 32.17/9.54 | (103) all_30_0_21 = all_30_1_22
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_20_1_13, all_30_1_22 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_30_1_22, apart_point_and_line(all_1_5_5, all_1_1_1) = all_20_1_13, yields:
% 32.17/9.54 | (104) all_30_1_22 = all_20_1_13
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_16_1_7, all_22_1_16 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.17/9.54 | (105) all_22_1_16 = all_16_1_7 | ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_22_1_16)
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (33) with all_1_3_3, all_1_4_4, all_18_0_9, all_20_2_14 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_20_2_14, distinct_points(all_1_3_3, all_1_4_4) = all_18_0_9, yields:
% 32.17/9.54 | (106) all_20_2_14 = all_18_0_9
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (33) with all_1_5_5, all_1_4_4, all_18_2_11, 0 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_18_2_11, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.17/9.54 | (107) all_18_2_11 = 0
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (33) with all_1_5_5, all_1_4_4, all_16_2_8, all_18_2_11 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_18_2_11, distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8, yields:
% 32.17/9.54 | (108) all_18_2_11 = all_16_2_8
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (33) with all_1_5_5, all_1_5_5, all_22_0_15, all_30_3_24 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_30_3_24, distinct_points(all_1_5_5, all_1_5_5) = all_22_0_15, yields:
% 32.17/9.54 | (109) all_30_3_24 = all_22_0_15
% 32.17/9.54 |
% 32.17/9.54 | Using (80) and (54) yields:
% 32.17/9.54 | (110) ~ (all_22_0_15 = 0)
% 32.17/9.54 |
% 32.17/9.54 | Instantiating formula (33) with all_1_5_5, all_1_5_5, all_16_0_6, all_30_3_24 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_30_3_24, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 32.17/9.54 | (111) all_30_3_24 = all_16_0_6
% 32.17/9.54 |
% 32.17/9.54 | Combining equations (103,102) yields a new equation:
% 32.17/9.54 | (112) all_30_1_22 = all_1_0_0
% 32.17/9.54 |
% 32.17/9.54 | Simplifying 112 yields:
% 32.17/9.54 | (113) all_30_1_22 = all_1_0_0
% 32.17/9.54 |
% 32.17/9.54 | Combining equations (113,104) yields a new equation:
% 32.17/9.54 | (114) all_20_1_13 = all_1_0_0
% 32.17/9.54 |
% 32.17/9.54 | Combining equations (109,111) yields a new equation:
% 32.17/9.54 | (115) all_22_0_15 = all_16_0_6
% 32.17/9.54 |
% 32.17/9.54 | Simplifying 115 yields:
% 32.17/9.54 | (116) all_22_0_15 = all_16_0_6
% 32.17/9.54 |
% 32.17/9.54 | Combining equations (107,108) yields a new equation:
% 32.17/9.54 | (117) all_16_2_8 = 0
% 32.17/9.54 |
% 32.17/9.54 | Combining equations (117,108) yields a new equation:
% 32.17/9.54 | (107) all_18_2_11 = 0
% 32.17/9.54 |
% 32.17/9.54 | Equations (116) can reduce 110 to:
% 32.17/9.54 | (119) ~ (all_16_0_6 = 0)
% 32.17/9.54 |
% 32.17/9.54 | From (101) and (78) follows:
% 32.17/9.54 | (48) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2
% 32.17/9.54 |
% 32.17/9.54 | From (101) and (79) follows:
% 32.17/9.54 | (121) apart_point_and_line(all_1_5_5, all_1_2_2) = all_22_1_16
% 32.17/9.54 |
% 32.17/9.54 | From (114) and (73) follows:
% 32.17/9.54 | (51) apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0
% 32.17/9.54 |
% 32.17/9.54 | From (106) and (74) follows:
% 32.17/9.54 | (68) distinct_points(all_1_3_3, all_1_4_4) = all_18_0_9
% 32.17/9.54 |
% 32.17/9.54 | From (117) and (64) follows:
% 32.17/9.54 | (52) distinct_points(all_1_5_5, all_1_4_4) = 0
% 32.17/9.54 |
% 32.17/9.54 | From (116) and (80) follows:
% 32.17/9.54 | (65) distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6
% 32.17/9.54 |
% 32.17/9.54 +-Applying beta-rule and splitting (81), into two cases.
% 32.17/9.54 |-Branch one:
% 32.17/9.54 | (126) ~ (all_22_1_16 = 0)
% 32.17/9.54 |
% 32.17/9.54 +-Applying beta-rule and splitting (71), into two cases.
% 32.17/9.54 |-Branch one:
% 32.17/9.54 | (127) ~ (all_18_2_11 = 0)
% 32.17/9.54 |
% 32.17/9.54 | Equations (107) can reduce 127 to:
% 32.17/9.54 | (88) $false
% 32.17/9.54 |
% 32.17/9.54 |-The branch is then unsatisfiable
% 32.17/9.54 |-Branch two:
% 32.17/9.54 | (107) all_18_2_11 = 0
% 32.17/9.54 | (130) all_18_0_9 = 0 & all_18_1_10 = 0
% 32.17/9.54 |
% 32.17/9.54 | Applying alpha-rule on (130) yields:
% 32.17/9.54 | (131) all_18_0_9 = 0
% 32.17/9.54 | (132) all_18_1_10 = 0
% 32.17/9.54 |
% 32.17/9.54 | From (131) and (68) follows:
% 32.17/9.54 | (133) distinct_points(all_1_3_3, all_1_4_4) = 0
% 32.17/9.54 |
% 32.17/9.54 | From (132) and (69) follows:
% 32.17/9.54 | (134) distinct_points(all_1_3_3, all_1_5_5) = 0
% 32.17/9.54 |
% 32.17/9.54 +-Applying beta-rule and splitting (105), into two cases.
% 32.17/9.54 |-Branch one:
% 32.17/9.54 | (135) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_22_1_16)
% 32.17/9.55 |
% 32.17/9.55 | Using (121) and (135) yields:
% 32.17/9.55 | (136) $false
% 32.17/9.55 |
% 32.17/9.55 |-The branch is then unsatisfiable
% 32.17/9.55 |-Branch two:
% 32.17/9.55 | (121) apart_point_and_line(all_1_5_5, all_1_2_2) = all_22_1_16
% 32.17/9.55 | (138) all_22_1_16 = all_16_1_7
% 32.17/9.55 |
% 32.17/9.55 | Equations (138) can reduce 126 to:
% 32.17/9.55 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.55 |
% 32.17/9.55 | From (138) and (121) follows:
% 32.17/9.55 | (63) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (46) with all_1_4_4 yields:
% 32.17/9.55 | (141) ~ (distinct_points(all_1_4_4, all_1_4_4) = 0)
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (42) with all_16_1_7, all_1_0_0, all_1_2_2, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.17/9.55 | (142) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (42) with all_1_0_0, all_16_1_7, all_1_1_1, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.17/9.55 | (143) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (1) with all_16_1_7, all_1_0_0, all_1_2_2, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.17/9.55 | (144) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (1) with all_1_0_0, all_16_1_7, all_1_1_1, all_1_2_2, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.17/9.55 | (145) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (29) with all_16_1_7, all_1_0_0, all_1_1_1, all_1_2_2, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.17/9.55 | (146) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (29) with all_1_0_0, all_16_1_7, all_1_2_2, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.17/9.55 | (147) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (42) with all_16_1_7, all_16_1_7, all_1_2_2, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.17/9.55 | (148) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (34) with all_24_1_19, all_16_1_7, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_2_2) = all_24_1_19, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.17/9.55 | (149) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_2_2) = v0 & distinct_points(all_1_5_5, all_24_1_19) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_16_1_7 = 0))))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (39) with 0, all_1_3_3, all_1_4_4, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 32.17/9.55 | (150) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (6) with 0, all_1_1_1, all_1_3_3, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 32.17/9.55 | (151) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (39) with 0, all_1_3_3, all_1_5_5, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, yields:
% 32.17/9.55 | (152) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_5_5) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (7) with all_1_0_0, all_16_1_7, all_1_1_1, all_1_2_2, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_3_3, all_1_5_5) = 0, yields:
% 32.17/9.55 | (153) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.55 |
% 32.17/9.55 | Instantiating formula (7) with all_16_1_7, all_1_0_0, all_1_2_2, all_1_1_1, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_3_3, all_1_5_5) = 0, yields:
% 32.17/9.56 | (154) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (10) with all_20_0_12, all_1_3_3, all_1_5_5, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12, yields:
% 32.17/9.56 | (155) all_20_0_12 = 0 | distinct_points(all_1_3_3, all_1_3_3) = 0
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (37) with all_20_0_12, all_1_5_5, all_1_5_5, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12, yields:
% 32.17/9.56 | (156) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_20_0_12 = 0)))
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (39) with 0, all_1_5_5, all_1_3_3, all_1_5_5 yields:
% 32.17/9.56 | (157) ~ (distinct_points(all_1_5_5, all_1_3_3) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (37) with 0, all_1_3_3, all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, yields:
% 32.17/9.56 | (158) ~ (distinct_points(all_1_5_5, all_1_3_3) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (3) with all_16_0_6, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 32.17/9.56 | (159) all_16_0_6 = 0 | distinct_points(all_1_4_4, all_1_5_5) = 0
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (38) with all_16_0_6, 0, all_1_5_5, all_1_5_5, all_1_4_4 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 32.17/9.56 | (160) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (39) with all_16_0_6, all_1_5_5, all_1_5_5, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 32.17/9.56 | (161) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_16_0_6 = 0)))
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (37) with all_16_0_6, all_1_5_5, all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 32.17/9.56 | (162) ~ (distinct_points(all_1_5_5, all_1_3_3) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_16_0_6 = 0)))
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (38) with all_16_0_6, all_20_0_12, all_1_5_5, all_1_5_5, all_1_3_3 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 32.17/9.56 | (163) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0))) | (all_20_0_12 = 0 & all_16_0_6 = 0)
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (38) with all_20_0_12, all_16_0_6, all_1_5_5, all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 32.17/9.56 | (164) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0))) | (all_20_0_12 = 0 & all_16_0_6 = 0)
% 32.17/9.56 |
% 32.17/9.56 | Instantiating formula (38) with all_16_0_6, all_16_0_6, all_1_5_5, all_1_5_5, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 32.17/9.56 | (165) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 32.17/9.56 |
% 32.17/9.56 | Instantiating (161) with all_70_0_28, all_70_1_29, all_70_2_30 yields:
% 32.17/9.56 | (166) line_connecting(all_1_3_3, all_1_5_5) = all_70_2_30 & apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29 & distinct_points(all_1_5_5, all_1_3_3) = all_70_0_28 & ( ~ (all_70_1_29 = 0) | (all_70_0_28 = 0 & all_16_0_6 = 0))
% 32.17/9.56 |
% 32.17/9.56 | Applying alpha-rule on (166) yields:
% 32.17/9.56 | (167) line_connecting(all_1_3_3, all_1_5_5) = all_70_2_30
% 32.17/9.56 | (168) apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29
% 32.17/9.56 | (169) distinct_points(all_1_5_5, all_1_3_3) = all_70_0_28
% 32.17/9.56 | (170) ~ (all_70_1_29 = 0) | (all_70_0_28 = 0 & all_16_0_6 = 0)
% 32.17/9.56 |
% 32.17/9.56 | Instantiating (151) with all_72_0_31, all_72_1_32, all_72_2_33 yields:
% 32.17/9.56 | (171) apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32 & distinct_points(all_1_3_3, all_1_3_3) = all_72_0_31 & distinct_points(all_1_3_3, all_1_4_4) = all_72_2_33 & ( ~ (all_72_1_32 = 0) | ~ (all_72_2_33 = 0) | all_72_0_31 = 0)
% 32.17/9.56 |
% 32.17/9.56 | Applying alpha-rule on (171) yields:
% 32.17/9.56 | (172) apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32
% 32.17/9.56 | (173) distinct_points(all_1_3_3, all_1_3_3) = all_72_0_31
% 32.17/9.56 | (174) distinct_points(all_1_3_3, all_1_4_4) = all_72_2_33
% 32.17/9.56 | (175) ~ (all_72_1_32 = 0) | ~ (all_72_2_33 = 0) | all_72_0_31 = 0
% 32.17/9.56 |
% 32.17/9.56 | Instantiating (149) with all_74_0_34, all_74_1_35, all_74_2_36 yields:
% 32.17/9.56 | (176) apart_point_and_line(all_1_5_5, all_1_2_2) = all_74_1_35 & convergent_lines(all_1_2_2, all_1_2_2) = all_74_2_36 & distinct_points(all_1_5_5, all_24_1_19) = all_74_0_34 & ( ~ (all_74_2_36 = 0) | all_74_0_34 = 0 | ( ~ (all_74_1_35 = 0) & ~ (all_16_1_7 = 0)))
% 32.17/9.56 |
% 32.17/9.56 | Applying alpha-rule on (176) yields:
% 32.17/9.56 | (177) apart_point_and_line(all_1_5_5, all_1_2_2) = all_74_1_35
% 32.17/9.56 | (178) convergent_lines(all_1_2_2, all_1_2_2) = all_74_2_36
% 32.17/9.56 | (179) distinct_points(all_1_5_5, all_24_1_19) = all_74_0_34
% 32.17/9.57 | (180) ~ (all_74_2_36 = 0) | all_74_0_34 = 0 | ( ~ (all_74_1_35 = 0) & ~ (all_16_1_7 = 0))
% 32.17/9.57 |
% 32.17/9.57 | Instantiating (150) with all_76_0_37, all_76_1_38, all_76_2_39 yields:
% 32.17/9.57 | (181) line_connecting(all_1_3_3, all_1_4_4) = all_76_2_39 & apart_point_and_line(all_1_3_3, all_76_2_39) = all_76_1_38 & distinct_points(all_1_3_3, all_1_3_3) = all_76_0_37 & ( ~ (all_76_1_38 = 0) | all_76_0_37 = 0)
% 32.17/9.57 |
% 32.17/9.57 | Applying alpha-rule on (181) yields:
% 32.17/9.57 | (182) line_connecting(all_1_3_3, all_1_4_4) = all_76_2_39
% 32.17/9.57 | (183) apart_point_and_line(all_1_3_3, all_76_2_39) = all_76_1_38
% 32.17/9.57 | (184) distinct_points(all_1_3_3, all_1_3_3) = all_76_0_37
% 32.17/9.57 | (185) ~ (all_76_1_38 = 0) | all_76_0_37 = 0
% 32.17/9.57 |
% 32.17/9.57 | Instantiating (156) with all_78_0_40, all_78_1_41, all_78_2_42 yields:
% 32.17/9.57 | (186) line_connecting(all_1_3_3, all_1_5_5) = all_78_2_42 & apart_point_and_line(all_1_5_5, all_78_2_42) = all_78_1_41 & distinct_points(all_1_5_5, all_1_5_5) = all_78_0_40 & ( ~ (all_78_1_41 = 0) | (all_78_0_40 = 0 & all_20_0_12 = 0))
% 32.17/9.57 |
% 32.17/9.57 | Applying alpha-rule on (186) yields:
% 32.17/9.57 | (187) line_connecting(all_1_3_3, all_1_5_5) = all_78_2_42
% 32.17/9.57 | (188) apart_point_and_line(all_1_5_5, all_78_2_42) = all_78_1_41
% 32.17/9.57 | (189) distinct_points(all_1_5_5, all_1_5_5) = all_78_0_40
% 32.17/9.57 | (190) ~ (all_78_1_41 = 0) | (all_78_0_40 = 0 & all_20_0_12 = 0)
% 32.17/9.57 |
% 32.17/9.57 | Instantiating (152) with all_80_0_43, all_80_1_44, all_80_2_45 yields:
% 32.17/9.57 | (191) line_connecting(all_1_3_3, all_1_5_5) = all_80_2_45 & apart_point_and_line(all_1_3_3, all_80_2_45) = all_80_1_44 & distinct_points(all_1_3_3, all_1_3_3) = all_80_0_43 & ( ~ (all_80_1_44 = 0) | all_80_0_43 = 0)
% 32.17/9.57 |
% 32.17/9.57 | Applying alpha-rule on (191) yields:
% 32.17/9.57 | (192) line_connecting(all_1_3_3, all_1_5_5) = all_80_2_45
% 32.17/9.57 | (193) apart_point_and_line(all_1_3_3, all_80_2_45) = all_80_1_44
% 32.17/9.57 | (194) distinct_points(all_1_3_3, all_1_3_3) = all_80_0_43
% 32.17/9.57 | (195) ~ (all_80_1_44 = 0) | all_80_0_43 = 0
% 32.17/9.57 |
% 32.17/9.57 +-Applying beta-rule and splitting (159), into two cases.
% 32.17/9.57 |-Branch one:
% 32.17/9.57 | (196) distinct_points(all_1_4_4, all_1_5_5) = 0
% 32.17/9.57 |
% 32.17/9.57 +-Applying beta-rule and splitting (163), into two cases.
% 32.17/9.57 |-Branch one:
% 32.17/9.57 | (197) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 32.17/9.57 |
% 32.17/9.57 | Instantiating (197) with all_88_0_46, all_88_1_47, all_88_2_48 yields:
% 32.17/9.57 | (198) line_connecting(all_1_3_3, all_1_5_5) = all_88_1_47 & apart_point_and_line(all_1_5_5, all_88_1_47) = all_88_0_46 & distinct_points(all_1_3_3, all_1_5_5) = all_88_2_48 & ( ~ (all_88_0_46 = 0) | ~ (all_88_2_48 = 0))
% 32.17/9.57 |
% 32.17/9.57 | Applying alpha-rule on (198) yields:
% 32.17/9.57 | (199) line_connecting(all_1_3_3, all_1_5_5) = all_88_1_47
% 32.17/9.57 | (200) apart_point_and_line(all_1_5_5, all_88_1_47) = all_88_0_46
% 32.17/9.57 | (201) distinct_points(all_1_3_3, all_1_5_5) = all_88_2_48
% 32.17/9.57 | (202) ~ (all_88_0_46 = 0) | ~ (all_88_2_48 = 0)
% 32.17/9.57 |
% 32.17/9.57 +-Applying beta-rule and splitting (164), into two cases.
% 32.17/9.57 |-Branch one:
% 32.17/9.57 | (203) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 32.17/9.57 |
% 32.17/9.57 | Instantiating (203) with all_92_0_49, all_92_1_50, all_92_2_51 yields:
% 32.17/9.57 | (204) line_connecting(all_1_5_5, all_1_3_3) = all_92_1_50 & apart_point_and_line(all_1_5_5, all_92_1_50) = all_92_0_49 & distinct_points(all_1_5_5, all_1_3_3) = all_92_2_51 & ( ~ (all_92_0_49 = 0) | ~ (all_92_2_51 = 0))
% 32.17/9.57 |
% 32.17/9.57 | Applying alpha-rule on (204) yields:
% 32.17/9.57 | (205) line_connecting(all_1_5_5, all_1_3_3) = all_92_1_50
% 32.17/9.57 | (206) apart_point_and_line(all_1_5_5, all_92_1_50) = all_92_0_49
% 32.17/9.57 | (207) distinct_points(all_1_5_5, all_1_3_3) = all_92_2_51
% 32.17/9.57 | (208) ~ (all_92_0_49 = 0) | ~ (all_92_2_51 = 0)
% 32.17/9.57 |
% 32.17/9.57 +-Applying beta-rule and splitting (165), into two cases.
% 32.17/9.57 |-Branch one:
% 32.17/9.57 | (209) all_16_0_6 = 0
% 32.17/9.57 |
% 32.17/9.57 | Equations (209) can reduce 119 to:
% 32.17/9.57 | (88) $false
% 32.17/9.57 |
% 32.17/9.57 |-The branch is then unsatisfiable
% 32.17/9.57 |-Branch two:
% 32.17/9.57 | (119) ~ (all_16_0_6 = 0)
% 32.17/9.57 | (212) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 32.17/9.57 |
% 32.17/9.57 +-Applying beta-rule and splitting (160), into two cases.
% 32.17/9.57 |-Branch one:
% 32.17/9.57 | (209) all_16_0_6 = 0
% 32.17/9.57 |
% 32.17/9.57 | Equations (209) can reduce 119 to:
% 32.17/9.57 | (88) $false
% 32.17/9.57 |
% 32.17/9.57 |-The branch is then unsatisfiable
% 32.17/9.57 |-Branch two:
% 32.17/9.57 | (119) ~ (all_16_0_6 = 0)
% 32.17/9.57 | (216) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 32.17/9.57 |
% 32.17/9.57 | Instantiating (216) with all_106_0_55, all_106_1_56, all_106_2_57 yields:
% 32.17/9.57 | (217) line_connecting(all_1_4_4, all_1_5_5) = all_106_1_56 & apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55 & distinct_points(all_1_4_4, all_1_5_5) = all_106_2_57 & ( ~ (all_106_0_55 = 0) | ~ (all_106_2_57 = 0))
% 32.17/9.57 |
% 32.17/9.57 | Applying alpha-rule on (217) yields:
% 32.17/9.57 | (218) line_connecting(all_1_4_4, all_1_5_5) = all_106_1_56
% 32.17/9.57 | (219) apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55
% 32.17/9.57 | (220) distinct_points(all_1_4_4, all_1_5_5) = all_106_2_57
% 32.17/9.57 | (221) ~ (all_106_0_55 = 0) | ~ (all_106_2_57 = 0)
% 32.17/9.57 |
% 32.17/9.57 +-Applying beta-rule and splitting (148), into two cases.
% 32.17/9.57 |-Branch one:
% 32.17/9.57 | (222) all_16_1_7 = 0
% 32.17/9.57 |
% 32.17/9.57 | Equations (222) can reduce 139 to:
% 32.17/9.57 | (88) $false
% 32.17/9.57 |
% 32.17/9.57 |-The branch is then unsatisfiable
% 32.17/9.57 |-Branch two:
% 32.17/9.57 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (225) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.58 |
% 32.17/9.58 | Instantiating (225) with all_111_0_58, all_111_1_59, all_111_2_60 yields:
% 32.17/9.58 | (226) apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_0_58 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59 & distinct_lines(all_1_2_2, all_1_2_2) = all_111_2_60 & ( ~ (all_111_2_60 = 0) | all_111_0_58 = 0 | all_111_1_59 = 0)
% 32.17/9.58 |
% 32.17/9.58 | Applying alpha-rule on (226) yields:
% 32.17/9.58 | (227) apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_0_58
% 32.17/9.58 | (228) apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59
% 32.17/9.58 | (229) distinct_lines(all_1_2_2, all_1_2_2) = all_111_2_60
% 32.17/9.58 | (230) ~ (all_111_2_60 = 0) | all_111_0_58 = 0 | all_111_1_59 = 0
% 32.17/9.58 |
% 32.17/9.58 +-Applying beta-rule and splitting (153), into two cases.
% 32.17/9.58 |-Branch one:
% 32.17/9.58 | (222) all_16_1_7 = 0
% 32.17/9.58 |
% 32.17/9.58 | Equations (222) can reduce 139 to:
% 32.17/9.58 | (88) $false
% 32.17/9.58 |
% 32.17/9.58 |-The branch is then unsatisfiable
% 32.17/9.58 |-Branch two:
% 32.17/9.58 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (234) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.58 |
% 32.17/9.58 +-Applying beta-rule and splitting (143), into two cases.
% 32.17/9.58 |-Branch one:
% 32.17/9.58 | (222) all_16_1_7 = 0
% 32.17/9.58 |
% 32.17/9.58 | Equations (222) can reduce 139 to:
% 32.17/9.58 | (88) $false
% 32.17/9.58 |
% 32.17/9.58 |-The branch is then unsatisfiable
% 32.17/9.58 |-Branch two:
% 32.17/9.58 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (238) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.58 |
% 32.17/9.58 +-Applying beta-rule and splitting (144), into two cases.
% 32.17/9.58 |-Branch one:
% 32.17/9.58 | (222) all_16_1_7 = 0
% 32.17/9.58 |
% 32.17/9.58 | Equations (222) can reduce 139 to:
% 32.17/9.58 | (88) $false
% 32.17/9.58 |
% 32.17/9.58 |-The branch is then unsatisfiable
% 32.17/9.58 |-Branch two:
% 32.17/9.58 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (242) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.58 |
% 32.17/9.58 +-Applying beta-rule and splitting (154), into two cases.
% 32.17/9.58 |-Branch one:
% 32.17/9.58 | (222) all_16_1_7 = 0
% 32.17/9.58 |
% 32.17/9.58 | Equations (222) can reduce 139 to:
% 32.17/9.58 | (88) $false
% 32.17/9.58 |
% 32.17/9.58 |-The branch is then unsatisfiable
% 32.17/9.58 |-Branch two:
% 32.17/9.58 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (246) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.58 |
% 32.17/9.58 +-Applying beta-rule and splitting (145), into two cases.
% 32.17/9.58 |-Branch one:
% 32.17/9.58 | (222) all_16_1_7 = 0
% 32.17/9.58 |
% 32.17/9.58 | Equations (222) can reduce 139 to:
% 32.17/9.58 | (88) $false
% 32.17/9.58 |
% 32.17/9.58 |-The branch is then unsatisfiable
% 32.17/9.58 |-Branch two:
% 32.17/9.58 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (250) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.58 |
% 32.17/9.58 +-Applying beta-rule and splitting (146), into two cases.
% 32.17/9.58 |-Branch one:
% 32.17/9.58 | (222) all_16_1_7 = 0
% 32.17/9.58 |
% 32.17/9.58 | Equations (222) can reduce 139 to:
% 32.17/9.58 | (88) $false
% 32.17/9.58 |
% 32.17/9.58 |-The branch is then unsatisfiable
% 32.17/9.58 |-Branch two:
% 32.17/9.58 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (254) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.58 |
% 32.17/9.58 +-Applying beta-rule and splitting (142), into two cases.
% 32.17/9.58 |-Branch one:
% 32.17/9.58 | (222) all_16_1_7 = 0
% 32.17/9.58 |
% 32.17/9.58 | Equations (222) can reduce 139 to:
% 32.17/9.58 | (88) $false
% 32.17/9.58 |
% 32.17/9.58 |-The branch is then unsatisfiable
% 32.17/9.58 |-Branch two:
% 32.17/9.58 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (258) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.58 |
% 32.17/9.58 +-Applying beta-rule and splitting (147), into two cases.
% 32.17/9.58 |-Branch one:
% 32.17/9.58 | (222) all_16_1_7 = 0
% 32.17/9.58 |
% 32.17/9.58 | Equations (222) can reduce 139 to:
% 32.17/9.58 | (88) $false
% 32.17/9.58 |
% 32.17/9.58 |-The branch is then unsatisfiable
% 32.17/9.58 |-Branch two:
% 32.17/9.58 | (139) ~ (all_16_1_7 = 0)
% 32.17/9.58 | (262) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.59 |
% 32.17/9.59 +-Applying beta-rule and splitting (234), into two cases.
% 32.17/9.59 |-Branch one:
% 32.17/9.59 | (87) all_1_0_0 = 0
% 32.17/9.59 |
% 32.17/9.59 | Equations (87) can reduce 53 to:
% 32.17/9.59 | (88) $false
% 32.17/9.59 |
% 32.17/9.59 |-The branch is then unsatisfiable
% 32.17/9.59 |-Branch two:
% 32.17/9.59 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.59 | (266) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.59 |
% 32.17/9.59 | Instantiating (266) with all_146_0_62, all_146_1_63, all_146_2_64 yields:
% 32.17/9.59 | (267) apart_point_and_line(all_1_3_3, all_1_1_1) = all_146_0_62 & apart_point_and_line(all_1_3_3, all_1_2_2) = all_146_1_63 & distinct_lines(all_1_2_2, all_1_1_1) = all_146_2_64 & ( ~ (all_146_2_64 = 0) | all_146_0_62 = 0 | all_146_1_63 = 0)
% 32.17/9.59 |
% 32.17/9.59 | Applying alpha-rule on (267) yields:
% 32.17/9.59 | (268) apart_point_and_line(all_1_3_3, all_1_1_1) = all_146_0_62
% 32.17/9.59 | (269) apart_point_and_line(all_1_3_3, all_1_2_2) = all_146_1_63
% 32.17/9.59 | (270) distinct_lines(all_1_2_2, all_1_1_1) = all_146_2_64
% 32.17/9.59 | (271) ~ (all_146_2_64 = 0) | all_146_0_62 = 0 | all_146_1_63 = 0
% 32.17/9.59 |
% 32.17/9.59 +-Applying beta-rule and splitting (238), into two cases.
% 32.17/9.59 |-Branch one:
% 32.17/9.59 | (87) all_1_0_0 = 0
% 32.17/9.59 |
% 32.17/9.59 | Equations (87) can reduce 53 to:
% 32.17/9.59 | (88) $false
% 32.17/9.59 |
% 32.17/9.59 |-The branch is then unsatisfiable
% 32.17/9.59 |-Branch two:
% 32.17/9.59 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.59 | (275) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.59 |
% 32.17/9.59 | Instantiating (275) with all_151_0_65, all_151_1_66, all_151_2_67 yields:
% 32.17/9.59 | (276) apart_point_and_line(all_1_4_4, all_1_1_1) = all_151_0_65 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_151_1_66 & distinct_lines(all_1_2_2, all_1_1_1) = all_151_2_67 & ( ~ (all_151_2_67 = 0) | all_151_0_65 = 0 | all_151_1_66 = 0)
% 32.17/9.59 |
% 32.17/9.59 | Applying alpha-rule on (276) yields:
% 32.17/9.59 | (277) apart_point_and_line(all_1_4_4, all_1_1_1) = all_151_0_65
% 32.17/9.59 | (278) apart_point_and_line(all_1_4_4, all_1_2_2) = all_151_1_66
% 32.17/9.59 | (279) distinct_lines(all_1_2_2, all_1_1_1) = all_151_2_67
% 32.17/9.59 | (280) ~ (all_151_2_67 = 0) | all_151_0_65 = 0 | all_151_1_66 = 0
% 32.17/9.59 |
% 32.17/9.59 +-Applying beta-rule and splitting (242), into two cases.
% 32.17/9.59 |-Branch one:
% 32.17/9.59 | (87) all_1_0_0 = 0
% 32.17/9.59 |
% 32.17/9.59 | Equations (87) can reduce 53 to:
% 32.17/9.59 | (88) $false
% 32.17/9.59 |
% 32.17/9.59 |-The branch is then unsatisfiable
% 32.17/9.59 |-Branch two:
% 32.17/9.59 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.59 | (284) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.59 |
% 32.17/9.59 | Instantiating (284) with all_156_0_68, all_156_1_69, all_156_2_70, all_156_3_71 yields:
% 32.17/9.59 | (285) apart_point_and_line(all_1_5_5, all_1_1_1) = all_156_0_68 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_156_1_69 & distinct_lines(all_1_1_1, all_1_2_2) = all_156_2_70 & distinct_points(all_1_5_5, all_1_5_5) = all_156_3_71 & ( ~ (all_156_2_70 = 0) | ~ (all_156_3_71 = 0) | all_156_0_68 = 0 | all_156_1_69 = 0)
% 32.17/9.59 |
% 32.17/9.59 | Applying alpha-rule on (285) yields:
% 32.17/9.59 | (286) ~ (all_156_2_70 = 0) | ~ (all_156_3_71 = 0) | all_156_0_68 = 0 | all_156_1_69 = 0
% 32.17/9.59 | (287) distinct_lines(all_1_1_1, all_1_2_2) = all_156_2_70
% 32.17/9.59 | (288) apart_point_and_line(all_1_5_5, all_1_2_2) = all_156_1_69
% 32.17/9.59 | (289) distinct_points(all_1_5_5, all_1_5_5) = all_156_3_71
% 32.17/9.59 | (290) apart_point_and_line(all_1_5_5, all_1_1_1) = all_156_0_68
% 32.17/9.59 |
% 32.17/9.59 +-Applying beta-rule and splitting (246), into two cases.
% 32.17/9.59 |-Branch one:
% 32.17/9.59 | (87) all_1_0_0 = 0
% 32.17/9.59 |
% 32.17/9.59 | Equations (87) can reduce 53 to:
% 32.17/9.59 | (88) $false
% 32.17/9.59 |
% 32.17/9.59 |-The branch is then unsatisfiable
% 32.17/9.59 |-Branch two:
% 32.17/9.59 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.59 | (294) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.59 |
% 32.17/9.59 | Instantiating (294) with all_161_0_72, all_161_1_73, all_161_2_74 yields:
% 32.17/9.59 | (295) apart_point_and_line(all_1_3_3, all_1_1_1) = all_161_1_73 & apart_point_and_line(all_1_3_3, all_1_2_2) = all_161_0_72 & distinct_lines(all_1_1_1, all_1_2_2) = all_161_2_74 & ( ~ (all_161_2_74 = 0) | all_161_0_72 = 0 | all_161_1_73 = 0)
% 32.17/9.59 |
% 32.17/9.59 | Applying alpha-rule on (295) yields:
% 32.17/9.59 | (296) apart_point_and_line(all_1_3_3, all_1_1_1) = all_161_1_73
% 32.17/9.59 | (297) apart_point_and_line(all_1_3_3, all_1_2_2) = all_161_0_72
% 32.17/9.59 | (298) distinct_lines(all_1_1_1, all_1_2_2) = all_161_2_74
% 32.17/9.59 | (299) ~ (all_161_2_74 = 0) | all_161_0_72 = 0 | all_161_1_73 = 0
% 32.17/9.59 |
% 32.17/9.59 +-Applying beta-rule and splitting (250), into two cases.
% 32.17/9.59 |-Branch one:
% 32.17/9.59 | (87) all_1_0_0 = 0
% 32.17/9.59 |
% 32.17/9.59 | Equations (87) can reduce 53 to:
% 32.17/9.59 | (88) $false
% 32.17/9.59 |
% 32.17/9.59 |-The branch is then unsatisfiable
% 32.17/9.59 |-Branch two:
% 32.17/9.59 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.59 | (303) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.59 |
% 32.17/9.59 | Instantiating (303) with all_166_0_75, all_166_1_76, all_166_2_77, all_166_3_78 yields:
% 32.17/9.59 | (304) apart_point_and_line(all_1_5_5, all_1_1_1) = all_166_1_76 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_166_0_75 & distinct_lines(all_1_2_2, all_1_1_1) = all_166_2_77 & distinct_points(all_1_5_5, all_1_5_5) = all_166_3_78 & ( ~ (all_166_2_77 = 0) | ~ (all_166_3_78 = 0) | all_166_0_75 = 0 | all_166_1_76 = 0)
% 32.17/9.59 |
% 32.17/9.59 | Applying alpha-rule on (304) yields:
% 32.17/9.59 | (305) ~ (all_166_2_77 = 0) | ~ (all_166_3_78 = 0) | all_166_0_75 = 0 | all_166_1_76 = 0
% 32.17/9.59 | (306) distinct_points(all_1_5_5, all_1_5_5) = all_166_3_78
% 32.17/9.59 | (307) apart_point_and_line(all_1_5_5, all_1_1_1) = all_166_1_76
% 32.17/9.60 | (308) apart_point_and_line(all_1_5_5, all_1_2_2) = all_166_0_75
% 32.17/9.60 | (309) distinct_lines(all_1_2_2, all_1_1_1) = all_166_2_77
% 32.17/9.60 |
% 32.17/9.60 +-Applying beta-rule and splitting (254), into two cases.
% 32.17/9.60 |-Branch one:
% 32.17/9.60 | (87) all_1_0_0 = 0
% 32.17/9.60 |
% 32.17/9.60 | Equations (87) can reduce 53 to:
% 32.17/9.60 | (88) $false
% 32.17/9.60 |
% 32.17/9.60 |-The branch is then unsatisfiable
% 32.17/9.60 |-Branch two:
% 32.17/9.60 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.60 | (313) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.60 |
% 32.17/9.60 | Instantiating (313) with all_171_0_79, all_171_1_80, all_171_2_81, all_171_3_82 yields:
% 32.17/9.60 | (314) apart_point_and_line(all_1_5_5, all_1_1_1) = all_171_0_79 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_171_1_80 & distinct_lines(all_1_2_2, all_1_1_1) = all_171_2_81 & distinct_points(all_1_5_5, all_1_5_5) = all_171_3_82 & ( ~ (all_171_2_81 = 0) | ~ (all_171_3_82 = 0) | all_171_0_79 = 0 | all_171_1_80 = 0)
% 32.17/9.60 |
% 32.17/9.60 | Applying alpha-rule on (314) yields:
% 32.17/9.60 | (315) apart_point_and_line(all_1_5_5, all_1_2_2) = all_171_1_80
% 32.17/9.60 | (316) distinct_points(all_1_5_5, all_1_5_5) = all_171_3_82
% 32.17/9.60 | (317) distinct_lines(all_1_2_2, all_1_1_1) = all_171_2_81
% 32.17/9.60 | (318) ~ (all_171_2_81 = 0) | ~ (all_171_3_82 = 0) | all_171_0_79 = 0 | all_171_1_80 = 0
% 32.17/9.60 | (319) apart_point_and_line(all_1_5_5, all_1_1_1) = all_171_0_79
% 32.17/9.60 |
% 32.17/9.60 +-Applying beta-rule and splitting (258), into two cases.
% 32.17/9.60 |-Branch one:
% 32.17/9.60 | (87) all_1_0_0 = 0
% 32.17/9.60 |
% 32.17/9.60 | Equations (87) can reduce 53 to:
% 32.17/9.60 | (88) $false
% 32.17/9.60 |
% 32.17/9.60 |-The branch is then unsatisfiable
% 32.17/9.60 |-Branch two:
% 32.17/9.60 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.60 | (323) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.17/9.60 |
% 32.17/9.60 | Instantiating (323) with all_176_0_83, all_176_1_84, all_176_2_85 yields:
% 32.17/9.60 | (324) apart_point_and_line(all_1_4_4, all_1_1_1) = all_176_1_84 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_176_0_83 & distinct_lines(all_1_1_1, all_1_2_2) = all_176_2_85 & ( ~ (all_176_2_85 = 0) | all_176_0_83 = 0 | all_176_1_84 = 0)
% 32.17/9.60 |
% 32.17/9.60 | Applying alpha-rule on (324) yields:
% 32.17/9.60 | (325) apart_point_and_line(all_1_4_4, all_1_1_1) = all_176_1_84
% 32.17/9.60 | (326) apart_point_and_line(all_1_4_4, all_1_2_2) = all_176_0_83
% 32.17/9.60 | (327) distinct_lines(all_1_1_1, all_1_2_2) = all_176_2_85
% 32.17/9.60 | (328) ~ (all_176_2_85 = 0) | all_176_0_83 = 0 | all_176_1_84 = 0
% 32.17/9.60 |
% 32.17/9.60 +-Applying beta-rule and splitting (262), into two cases.
% 32.17/9.60 |-Branch one:
% 32.17/9.60 | (87) all_1_0_0 = 0
% 32.17/9.60 |
% 32.17/9.60 | Equations (87) can reduce 53 to:
% 32.17/9.60 | (88) $false
% 32.17/9.60 |
% 32.17/9.60 |-The branch is then unsatisfiable
% 32.17/9.60 |-Branch two:
% 32.17/9.60 | (53) ~ (all_1_0_0 = 0)
% 32.17/9.60 | (332) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.17/9.60 |
% 32.17/9.60 | Instantiating (332) with all_181_0_86, all_181_1_87, all_181_2_88, all_181_3_89 yields:
% 32.17/9.60 | (333) apart_point_and_line(all_1_5_5, all_1_1_1) = all_181_1_87 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_181_0_86 & distinct_lines(all_1_1_1, all_1_2_2) = all_181_2_88 & distinct_points(all_1_5_5, all_1_5_5) = all_181_3_89 & ( ~ (all_181_2_88 = 0) | ~ (all_181_3_89 = 0) | all_181_0_86 = 0 | all_181_1_87 = 0)
% 32.17/9.60 |
% 32.17/9.60 | Applying alpha-rule on (333) yields:
% 32.17/9.60 | (334) distinct_points(all_1_5_5, all_1_5_5) = all_181_3_89
% 32.17/9.60 | (335) distinct_lines(all_1_1_1, all_1_2_2) = all_181_2_88
% 32.17/9.60 | (336) apart_point_and_line(all_1_5_5, all_1_2_2) = all_181_0_86
% 32.17/9.60 | (337) apart_point_and_line(all_1_5_5, all_1_1_1) = all_181_1_87
% 32.17/9.60 | (338) ~ (all_181_2_88 = 0) | ~ (all_181_3_89 = 0) | all_181_0_86 = 0 | all_181_1_87 = 0
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (5) with all_1_3_3, all_1_4_4, all_76_2_39, all_1_1_1 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_76_2_39, line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1, yields:
% 32.17/9.60 | (339) all_76_2_39 = all_1_1_1
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (5) with all_1_3_3, all_1_5_5, all_80_2_45, all_88_1_47 and discharging atoms line_connecting(all_1_3_3, all_1_5_5) = all_88_1_47, line_connecting(all_1_3_3, all_1_5_5) = all_80_2_45, yields:
% 32.17/9.60 | (340) all_88_1_47 = all_80_2_45
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (5) with all_1_3_3, all_1_5_5, all_78_2_42, all_80_2_45 and discharging atoms line_connecting(all_1_3_3, all_1_5_5) = all_80_2_45, line_connecting(all_1_3_3, all_1_5_5) = all_78_2_42, yields:
% 32.17/9.60 | (341) all_80_2_45 = all_78_2_42
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (5) with all_1_3_3, all_1_5_5, all_70_2_30, all_88_1_47 and discharging atoms line_connecting(all_1_3_3, all_1_5_5) = all_88_1_47, line_connecting(all_1_3_3, all_1_5_5) = all_70_2_30, yields:
% 32.17/9.60 | (342) all_88_1_47 = all_70_2_30
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_3_3, all_1_1_1, all_72_1_32, all_76_1_38 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32, yields:
% 32.17/9.60 | (343) all_76_1_38 = all_72_1_32 | ~ (apart_point_and_line(all_1_3_3, all_1_1_1) = all_76_1_38)
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_3_3, all_1_2_2, all_161_0_72, 0 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_161_0_72, apart_point_and_line(all_1_3_3, all_1_2_2) = 0, yields:
% 32.17/9.60 | (344) all_161_0_72 = 0
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_3_3, all_1_2_2, all_146_1_63, all_161_0_72 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_161_0_72, apart_point_and_line(all_1_3_3, all_1_2_2) = all_146_1_63, yields:
% 32.17/9.60 | (345) all_161_0_72 = all_146_1_63
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_4_4, all_1_1_1, all_151_0_65, all_176_1_84 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_176_1_84, apart_point_and_line(all_1_4_4, all_1_1_1) = all_151_0_65, yields:
% 32.17/9.60 | (346) all_176_1_84 = all_151_0_65
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_151_1_66, all_176_0_83 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_176_0_83, apart_point_and_line(all_1_4_4, all_1_2_2) = all_151_1_66, yields:
% 32.17/9.60 | (347) all_176_0_83 = all_151_1_66
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_111_0_58, all_151_1_66 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_151_1_66, apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_0_58, yields:
% 32.17/9.60 | (348) all_151_1_66 = all_111_0_58
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_111_1_59, all_176_0_83 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_176_0_83, apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59, yields:
% 32.17/9.60 | (349) all_176_0_83 = all_111_1_59
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_78_2_42, all_78_1_41, all_88_0_46 and discharging atoms apart_point_and_line(all_1_5_5, all_78_2_42) = all_78_1_41, yields:
% 32.17/9.60 | (350) all_88_0_46 = all_78_1_41 | ~ (apart_point_and_line(all_1_5_5, all_78_2_42) = all_88_0_46)
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_70_2_30, all_70_1_29, all_78_1_41 and discharging atoms apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, yields:
% 32.17/9.60 | (351) all_78_1_41 = all_70_1_29 | ~ (apart_point_and_line(all_1_5_5, all_70_2_30) = all_78_1_41)
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_171_0_79, all_181_1_87 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_181_1_87, apart_point_and_line(all_1_5_5, all_1_1_1) = all_171_0_79, yields:
% 32.17/9.60 | (352) all_181_1_87 = all_171_0_79
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_166_1_76, all_1_0_0 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_166_1_76, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.17/9.60 | (353) all_166_1_76 = all_1_0_0
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_166_1_76, all_171_0_79 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_171_0_79, apart_point_and_line(all_1_5_5, all_1_1_1) = all_166_1_76, yields:
% 32.17/9.60 | (354) all_171_0_79 = all_166_1_76
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_156_0_68, all_181_1_87 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_181_1_87, apart_point_and_line(all_1_5_5, all_1_1_1) = all_156_0_68, yields:
% 32.17/9.60 | (355) all_181_1_87 = all_156_0_68
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_181_0_86, all_16_1_7 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_181_0_86, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.17/9.60 | (356) all_181_0_86 = all_16_1_7
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_166_0_75, all_171_1_80 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_171_1_80, apart_point_and_line(all_1_5_5, all_1_2_2) = all_166_0_75, yields:
% 32.17/9.60 | (357) all_171_1_80 = all_166_0_75
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_156_1_69, all_181_0_86 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_181_0_86, apart_point_and_line(all_1_5_5, all_1_2_2) = all_156_1_69, yields:
% 32.17/9.60 | (358) all_181_0_86 = all_156_1_69
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_156_1_69, all_166_0_75 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_166_0_75, apart_point_and_line(all_1_5_5, all_1_2_2) = all_156_1_69, yields:
% 32.17/9.60 | (359) all_166_0_75 = all_156_1_69
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_74_1_35, all_171_1_80 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_171_1_80, apart_point_and_line(all_1_5_5, all_1_2_2) = all_74_1_35, yields:
% 32.17/9.60 | (360) all_171_1_80 = all_74_1_35
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (13) with all_1_1_1, all_1_2_2, all_176_2_85, all_181_2_88 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_181_2_88, distinct_lines(all_1_1_1, all_1_2_2) = all_176_2_85, yields:
% 32.17/9.60 | (361) all_181_2_88 = all_176_2_85
% 32.17/9.60 |
% 32.17/9.60 | Instantiating formula (13) with all_1_1_1, all_1_2_2, all_161_2_74, all_181_2_88 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_181_2_88, distinct_lines(all_1_1_1, all_1_2_2) = all_161_2_74, yields:
% 32.17/9.61 | (362) all_181_2_88 = all_161_2_74
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (13) with all_1_1_1, all_1_2_2, all_156_2_70, all_176_2_85 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_176_2_85, distinct_lines(all_1_1_1, all_1_2_2) = all_156_2_70, yields:
% 32.17/9.61 | (363) all_176_2_85 = all_156_2_70
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (13) with all_1_2_2, all_1_1_1, all_166_2_77, all_171_2_81 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = all_171_2_81, distinct_lines(all_1_2_2, all_1_1_1) = all_166_2_77, yields:
% 32.17/9.61 | (364) all_171_2_81 = all_166_2_77
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (13) with all_1_2_2, all_1_1_1, all_151_2_67, all_171_2_81 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = all_171_2_81, distinct_lines(all_1_2_2, all_1_1_1) = all_151_2_67, yields:
% 32.17/9.61 | (365) all_171_2_81 = all_151_2_67
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (13) with all_1_2_2, all_1_1_1, all_146_2_64, all_166_2_77 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = all_166_2_77, distinct_lines(all_1_2_2, all_1_1_1) = all_146_2_64, yields:
% 32.17/9.61 | (366) all_166_2_77 = all_146_2_64
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (35) with all_1_2_2 yields:
% 32.17/9.61 | (367) ~ (distinct_lines(all_1_2_2, all_1_2_2) = 0)
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (46) with all_1_3_3 yields:
% 32.17/9.61 | (368) ~ (distinct_points(all_1_3_3, all_1_3_3) = 0)
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (33) with all_1_3_3, all_1_3_3, all_76_0_37, all_80_0_43 and discharging atoms distinct_points(all_1_3_3, all_1_3_3) = all_80_0_43, distinct_points(all_1_3_3, all_1_3_3) = all_76_0_37, yields:
% 32.17/9.61 | (369) all_80_0_43 = all_76_0_37
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (33) with all_1_3_3, all_1_3_3, all_72_0_31, all_80_0_43 and discharging atoms distinct_points(all_1_3_3, all_1_3_3) = all_80_0_43, distinct_points(all_1_3_3, all_1_3_3) = all_72_0_31, yields:
% 32.17/9.61 | (370) all_80_0_43 = all_72_0_31
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (33) with all_1_3_3, all_1_4_4, all_72_2_33, 0 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_72_2_33, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 32.17/9.61 | (371) all_72_2_33 = 0
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (33) with all_1_3_3, all_1_5_5, all_88_2_48, 0 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = all_88_2_48, distinct_points(all_1_3_3, all_1_5_5) = 0, yields:
% 32.17/9.61 | (372) all_88_2_48 = 0
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (33) with all_1_4_4, all_1_5_5, 0, all_106_2_57 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_106_2_57, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.17/9.61 | (373) all_106_2_57 = 0
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (33) with all_1_5_5, all_1_3_3, all_92_2_51, all_20_0_12 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_92_2_51, distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12, yields:
% 32.17/9.61 | (374) all_92_2_51 = all_20_0_12
% 32.17/9.61 |
% 32.17/9.61 | Instantiating formula (33) with all_1_5_5, all_1_3_3, all_70_0_28, all_92_2_51 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_92_2_51, distinct_points(all_1_5_5, all_1_3_3) = all_70_0_28, yields:
% 32.17/9.61 | (375) all_92_2_51 = all_70_0_28
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (358,356) yields a new equation:
% 32.17/9.61 | (376) all_156_1_69 = all_16_1_7
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 376 yields:
% 32.17/9.61 | (377) all_156_1_69 = all_16_1_7
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (352,355) yields a new equation:
% 32.17/9.61 | (378) all_171_0_79 = all_156_0_68
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 378 yields:
% 32.17/9.61 | (379) all_171_0_79 = all_156_0_68
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (361,362) yields a new equation:
% 32.17/9.61 | (380) all_176_2_85 = all_161_2_74
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 380 yields:
% 32.17/9.61 | (381) all_176_2_85 = all_161_2_74
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (347,349) yields a new equation:
% 32.17/9.61 | (382) all_151_1_66 = all_111_1_59
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 382 yields:
% 32.17/9.61 | (383) all_151_1_66 = all_111_1_59
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (381,363) yields a new equation:
% 32.17/9.61 | (384) all_161_2_74 = all_156_2_70
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 384 yields:
% 32.17/9.61 | (385) all_161_2_74 = all_156_2_70
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (354,379) yields a new equation:
% 32.17/9.61 | (386) all_166_1_76 = all_156_0_68
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 386 yields:
% 32.17/9.61 | (387) all_166_1_76 = all_156_0_68
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (357,360) yields a new equation:
% 32.17/9.61 | (388) all_166_0_75 = all_74_1_35
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 388 yields:
% 32.17/9.61 | (389) all_166_0_75 = all_74_1_35
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (364,365) yields a new equation:
% 32.17/9.61 | (390) all_166_2_77 = all_151_2_67
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 390 yields:
% 32.17/9.61 | (391) all_166_2_77 = all_151_2_67
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (359,389) yields a new equation:
% 32.17/9.61 | (392) all_156_1_69 = all_74_1_35
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 392 yields:
% 32.17/9.61 | (393) all_156_1_69 = all_74_1_35
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (353,387) yields a new equation:
% 32.17/9.61 | (394) all_156_0_68 = all_1_0_0
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (366,391) yields a new equation:
% 32.17/9.61 | (395) all_151_2_67 = all_146_2_64
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (345,344) yields a new equation:
% 32.17/9.61 | (396) all_146_1_63 = 0
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 396 yields:
% 32.17/9.61 | (397) all_146_1_63 = 0
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (393,377) yields a new equation:
% 32.17/9.61 | (398) all_74_1_35 = all_16_1_7
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 398 yields:
% 32.17/9.61 | (399) all_74_1_35 = all_16_1_7
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (383,348) yields a new equation:
% 32.17/9.61 | (400) all_111_0_58 = all_111_1_59
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (375,374) yields a new equation:
% 32.17/9.61 | (401) all_70_0_28 = all_20_0_12
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 401 yields:
% 32.17/9.61 | (402) all_70_0_28 = all_20_0_12
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (340,342) yields a new equation:
% 32.17/9.61 | (403) all_80_2_45 = all_70_2_30
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 403 yields:
% 32.17/9.61 | (404) all_80_2_45 = all_70_2_30
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (369,370) yields a new equation:
% 32.17/9.61 | (405) all_76_0_37 = all_72_0_31
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 405 yields:
% 32.17/9.61 | (406) all_76_0_37 = all_72_0_31
% 32.17/9.61 |
% 32.17/9.61 | Combining equations (341,404) yields a new equation:
% 32.17/9.61 | (407) all_78_2_42 = all_70_2_30
% 32.17/9.61 |
% 32.17/9.61 | Simplifying 407 yields:
% 32.17/9.61 | (408) all_78_2_42 = all_70_2_30
% 32.17/9.61 |
% 32.17/9.61 | From (339) and (182) follows:
% 32.17/9.61 | (49) line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1
% 32.17/9.61 |
% 32.17/9.61 | From (404) and (193) follows:
% 32.17/9.61 | (410) apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44
% 32.17/9.61 |
% 32.17/9.61 | From (339) and (183) follows:
% 32.17/9.61 | (411) apart_point_and_line(all_1_3_3, all_1_1_1) = all_76_1_38
% 32.17/9.61 |
% 32.17/9.61 | From (397) and (269) follows:
% 32.17/9.61 | (50) apart_point_and_line(all_1_3_3, all_1_2_2) = 0
% 32.17/9.61 |
% 32.17/9.61 | From (346) and (325) follows:
% 32.17/9.61 | (277) apart_point_and_line(all_1_4_4, all_1_1_1) = all_151_0_65
% 32.17/9.61 |
% 32.17/9.61 | From (400) and (227) follows:
% 32.17/9.61 | (228) apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59
% 32.17/9.61 |
% 32.17/9.61 | From (342) and (200) follows:
% 32.17/9.61 | (415) apart_point_and_line(all_1_5_5, all_70_2_30) = all_88_0_46
% 32.17/9.61 |
% 32.17/9.61 | From (394) and (290) follows:
% 32.17/9.61 | (51) apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0
% 32.17/9.61 |
% 32.17/9.61 | From (399) and (177) follows:
% 32.17/9.61 | (63) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7
% 32.17/9.61 |
% 32.17/9.61 | From (385) and (298) follows:
% 32.17/9.61 | (287) distinct_lines(all_1_1_1, all_1_2_2) = all_156_2_70
% 32.17/9.61 |
% 32.17/9.61 | From (395) and (279) follows:
% 32.17/9.61 | (270) distinct_lines(all_1_2_2, all_1_1_1) = all_146_2_64
% 32.17/9.61 |
% 32.17/9.61 | From (406) and (184) follows:
% 32.17/9.61 | (173) distinct_points(all_1_3_3, all_1_3_3) = all_72_0_31
% 32.17/9.61 |
% 32.17/9.61 | From (371) and (174) follows:
% 32.17/9.61 | (133) distinct_points(all_1_3_3, all_1_4_4) = 0
% 32.17/9.61 |
% 32.17/9.61 | From (372) and (201) follows:
% 32.17/9.61 | (134) distinct_points(all_1_3_3, all_1_5_5) = 0
% 32.17/9.61 |
% 32.17/9.61 | From (373) and (220) follows:
% 32.17/9.61 | (196) distinct_points(all_1_4_4, all_1_5_5) = 0
% 32.17/9.61 |
% 32.17/9.61 | From (402) and (169) follows:
% 32.17/9.61 | (75) distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12
% 32.17/9.61 |
% 32.17/9.61 +-Applying beta-rule and splitting (221), into two cases.
% 32.17/9.61 |-Branch one:
% 32.17/9.61 | (425) ~ (all_106_0_55 = 0)
% 32.17/9.61 |
% 32.17/9.61 +-Applying beta-rule and splitting (350), into two cases.
% 32.17/9.61 |-Branch one:
% 32.17/9.61 | (426) ~ (apart_point_and_line(all_1_5_5, all_78_2_42) = all_88_0_46)
% 32.17/9.61 |
% 32.17/9.61 | From (408) and (426) follows:
% 32.17/9.61 | (427) ~ (apart_point_and_line(all_1_5_5, all_70_2_30) = all_88_0_46)
% 32.17/9.61 |
% 32.17/9.61 | Using (415) and (427) yields:
% 32.17/9.61 | (136) $false
% 32.17/9.61 |
% 32.17/9.61 |-The branch is then unsatisfiable
% 32.17/9.61 |-Branch two:
% 32.17/9.61 | (429) apart_point_and_line(all_1_5_5, all_78_2_42) = all_88_0_46
% 32.17/9.61 | (430) all_88_0_46 = all_78_1_41
% 32.17/9.61 |
% 32.17/9.61 | From (430) and (415) follows:
% 32.17/9.61 | (431) apart_point_and_line(all_1_5_5, all_70_2_30) = all_78_1_41
% 32.17/9.62 |
% 32.17/9.62 +-Applying beta-rule and splitting (343), into two cases.
% 32.17/9.62 |-Branch one:
% 32.17/9.62 | (432) ~ (apart_point_and_line(all_1_3_3, all_1_1_1) = all_76_1_38)
% 32.17/9.62 |
% 32.17/9.62 | Using (411) and (432) yields:
% 32.17/9.62 | (136) $false
% 32.17/9.62 |
% 32.17/9.62 |-The branch is then unsatisfiable
% 32.17/9.62 |-Branch two:
% 32.17/9.62 | (411) apart_point_and_line(all_1_3_3, all_1_1_1) = all_76_1_38
% 32.17/9.62 | (435) all_76_1_38 = all_72_1_32
% 32.17/9.62 |
% 32.17/9.62 | From (435) and (411) follows:
% 32.17/9.62 | (172) apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32
% 32.62/9.62 |
% 32.62/9.62 +-Applying beta-rule and splitting (351), into two cases.
% 32.62/9.62 |-Branch one:
% 32.62/9.62 | (437) ~ (apart_point_and_line(all_1_5_5, all_70_2_30) = all_78_1_41)
% 32.62/9.62 |
% 32.62/9.62 | Using (431) and (437) yields:
% 32.62/9.62 | (136) $false
% 32.62/9.62 |
% 32.62/9.62 |-The branch is then unsatisfiable
% 32.62/9.62 |-Branch two:
% 32.62/9.62 | (431) apart_point_and_line(all_1_5_5, all_70_2_30) = all_78_1_41
% 32.62/9.62 | (440) all_78_1_41 = all_70_1_29
% 32.62/9.62 |
% 32.62/9.62 | From (440) and (431) follows:
% 32.62/9.62 | (168) apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29
% 32.62/9.62 |
% 32.62/9.62 +-Applying beta-rule and splitting (155), into two cases.
% 32.62/9.62 |-Branch one:
% 32.62/9.62 | (442) distinct_points(all_1_3_3, all_1_3_3) = 0
% 32.62/9.62 |
% 32.62/9.62 | Using (442) and (368) yields:
% 32.62/9.62 | (136) $false
% 32.62/9.62 |
% 32.62/9.62 |-The branch is then unsatisfiable
% 32.62/9.62 |-Branch two:
% 32.62/9.62 | (368) ~ (distinct_points(all_1_3_3, all_1_3_3) = 0)
% 32.62/9.62 | (445) all_20_0_12 = 0
% 32.62/9.62 |
% 32.62/9.62 | From (445) and (75) follows:
% 32.62/9.62 | (446) distinct_points(all_1_5_5, all_1_3_3) = 0
% 32.62/9.62 |
% 32.62/9.62 +-Applying beta-rule and splitting (157), into two cases.
% 32.62/9.62 |-Branch one:
% 32.62/9.62 | (447) ~ (distinct_points(all_1_5_5, all_1_3_3) = 0)
% 32.62/9.62 |
% 32.62/9.62 | Using (446) and (447) yields:
% 32.62/9.62 | (136) $false
% 32.62/9.62 |
% 32.62/9.62 |-The branch is then unsatisfiable
% 32.62/9.62 |-Branch two:
% 32.62/9.62 | (446) distinct_points(all_1_5_5, all_1_3_3) = 0
% 32.62/9.62 | (450) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.62/9.62 |
% 32.62/9.62 +-Applying beta-rule and splitting (162), into two cases.
% 32.62/9.62 |-Branch one:
% 32.62/9.62 | (447) ~ (distinct_points(all_1_5_5, all_1_3_3) = 0)
% 32.62/9.62 |
% 32.62/9.62 | Using (446) and (447) yields:
% 32.62/9.62 | (136) $false
% 32.62/9.62 |
% 32.62/9.62 |-The branch is then unsatisfiable
% 32.62/9.62 |-Branch two:
% 32.62/9.62 | (446) distinct_points(all_1_5_5, all_1_3_3) = 0
% 32.62/9.62 | (454) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_16_0_6 = 0)))
% 32.62/9.62 |
% 32.62/9.62 | Instantiating (454) with all_217_0_93, all_217_1_94, all_217_2_95 yields:
% 32.62/9.62 | (455) line_connecting(all_1_5_5, all_1_3_3) = all_217_2_95 & apart_point_and_line(all_1_5_5, all_217_2_95) = all_217_1_94 & distinct_points(all_1_5_5, all_1_3_3) = all_217_0_93 & ( ~ (all_217_1_94 = 0) | (all_217_0_93 = 0 & all_16_0_6 = 0))
% 32.62/9.62 |
% 32.62/9.62 | Applying alpha-rule on (455) yields:
% 32.62/9.62 | (456) line_connecting(all_1_5_5, all_1_3_3) = all_217_2_95
% 32.62/9.62 | (457) apart_point_and_line(all_1_5_5, all_217_2_95) = all_217_1_94
% 32.62/9.62 | (458) distinct_points(all_1_5_5, all_1_3_3) = all_217_0_93
% 32.62/9.62 | (459) ~ (all_217_1_94 = 0) | (all_217_0_93 = 0 & all_16_0_6 = 0)
% 32.62/9.62 |
% 32.62/9.62 +-Applying beta-rule and splitting (158), into two cases.
% 32.62/9.62 |-Branch one:
% 32.62/9.62 | (447) ~ (distinct_points(all_1_5_5, all_1_3_3) = 0)
% 32.62/9.62 |
% 32.62/9.62 | Using (446) and (447) yields:
% 32.62/9.62 | (136) $false
% 32.62/9.62 |
% 32.62/9.62 |-The branch is then unsatisfiable
% 32.62/9.62 |-Branch two:
% 32.62/9.62 | (446) distinct_points(all_1_5_5, all_1_3_3) = 0
% 32.62/9.62 | (463) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.62/9.62 |
% 32.62/9.62 | Instantiating (463) with all_226_0_96, all_226_1_97, all_226_2_98 yields:
% 32.62/9.62 | (464) line_connecting(all_1_5_5, all_1_3_3) = all_226_2_98 & apart_point_and_line(all_1_3_3, all_226_2_98) = all_226_1_97 & distinct_points(all_1_3_3, all_1_3_3) = all_226_0_96 & ( ~ (all_226_1_97 = 0) | all_226_0_96 = 0)
% 32.62/9.62 |
% 32.62/9.62 | Applying alpha-rule on (464) yields:
% 32.62/9.62 | (465) line_connecting(all_1_5_5, all_1_3_3) = all_226_2_98
% 32.62/9.62 | (466) apart_point_and_line(all_1_3_3, all_226_2_98) = all_226_1_97
% 32.62/9.62 | (467) distinct_points(all_1_3_3, all_1_3_3) = all_226_0_96
% 32.62/9.62 | (468) ~ (all_226_1_97 = 0) | all_226_0_96 = 0
% 32.62/9.62 |
% 32.62/9.62 | Instantiating formula (5) with all_1_5_5, all_1_3_3, all_226_2_98, all_92_1_50 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_226_2_98, line_connecting(all_1_5_5, all_1_3_3) = all_92_1_50, yields:
% 32.62/9.62 | (469) all_226_2_98 = all_92_1_50
% 32.62/9.62 |
% 32.62/9.62 | Instantiating formula (33) with all_1_3_3, all_1_3_3, all_226_0_96, all_72_0_31 and discharging atoms distinct_points(all_1_3_3, all_1_3_3) = all_226_0_96, distinct_points(all_1_3_3, all_1_3_3) = all_72_0_31, yields:
% 32.62/9.62 | (470) all_226_0_96 = all_72_0_31
% 32.62/9.62 |
% 32.62/9.62 | Instantiating formula (33) with all_1_5_5, all_1_3_3, 0, all_217_0_93 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_217_0_93, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 32.62/9.62 | (471) all_217_0_93 = 0
% 32.62/9.62 |
% 32.62/9.62 | Using (467) and (368) yields:
% 32.62/9.62 | (472) ~ (all_226_0_96 = 0)
% 32.62/9.62 |
% 32.62/9.62 | Equations (470) can reduce 472 to:
% 32.62/9.62 | (473) ~ (all_72_0_31 = 0)
% 32.62/9.62 |
% 32.62/9.62 | From (469) and (466) follows:
% 32.62/9.62 | (474) apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97
% 32.62/9.62 |
% 32.62/9.62 | From (471) and (458) follows:
% 32.62/9.62 | (446) distinct_points(all_1_5_5, all_1_3_3) = 0
% 32.62/9.62 |
% 32.62/9.62 +-Applying beta-rule and splitting (175), into two cases.
% 32.62/9.62 |-Branch one:
% 32.62/9.62 | (476) ~ (all_72_1_32 = 0)
% 32.62/9.62 |
% 32.62/9.62 +-Applying beta-rule and splitting (195), into two cases.
% 32.62/9.62 |-Branch one:
% 32.62/9.62 | (477) ~ (all_80_1_44 = 0)
% 32.62/9.62 |
% 32.62/9.62 +-Applying beta-rule and splitting (468), into two cases.
% 32.62/9.62 |-Branch one:
% 32.62/9.62 | (478) ~ (all_226_1_97 = 0)
% 32.62/9.62 |
% 32.62/9.62 | Instantiating formula (6) with 0, all_106_1_56, all_1_3_3, all_1_5_5, all_1_4_4 and discharging atoms line_connecting(all_1_4_4, all_1_5_5) = all_106_1_56, distinct_points(all_1_3_3, all_1_5_5) = 0, yields:
% 32.62/9.62 | (479) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v2 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.62/9.62 |
% 32.62/9.62 | Instantiating formula (1) with all_226_1_97, all_1_0_0, all_92_1_50, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.62 | (480) all_226_1_97 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_1_1_1, all_92_1_50) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.62 |
% 32.62/9.62 | Instantiating formula (1) with all_1_0_0, all_226_1_97, all_1_1_1, all_92_1_50, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.62 | (481) all_226_1_97 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_92_1_50, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.62 |
% 32.62/9.62 | Instantiating formula (29) with all_226_1_97, all_1_0_0, all_1_1_1, all_92_1_50, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.62 | (482) all_226_1_97 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_92_1_50, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.62 |
% 32.62/9.62 | Instantiating formula (29) with all_1_0_0, all_226_1_97, all_92_1_50, all_1_1_1, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.63 | (483) all_226_1_97 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_1_1_1, all_92_1_50) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_226_1_97, all_16_1_7, all_92_1_50, all_1_2_2, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (484) all_226_1_97 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_1_2_2, all_92_1_50) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_16_1_7, all_226_1_97, all_1_2_2, all_92_1_50, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (485) all_226_1_97 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_92_1_50, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (29) with all_226_1_97, all_16_1_7, all_1_2_2, all_92_1_50, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (486) all_226_1_97 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_92_1_50, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (29) with all_16_1_7, all_226_1_97, all_92_1_50, all_1_2_2, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (487) all_226_1_97 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_1_2_2, all_92_1_50) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (42) with all_226_1_97, all_226_1_97, all_92_1_50, all_92_1_50, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 32.62/9.63 | (488) all_226_1_97 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_92_1_50) = v2 & apart_point_and_line(all_1_4_4, all_92_1_50) = v1 & distinct_lines(all_92_1_50, all_92_1_50) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_226_1_97, all_226_1_97, all_92_1_50, all_92_1_50, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, yields:
% 32.62/9.63 | (489) all_226_1_97 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_92_1_50) = v3 & apart_point_and_line(all_1_3_3, all_92_1_50) = v2 & distinct_lines(all_92_1_50, all_92_1_50) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_80_1_44, all_1_0_0, all_70_2_30, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.63 | (490) all_80_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_1_0_0, all_80_1_44, all_1_1_1, all_70_2_30, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.63 | (491) all_80_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (29) with all_80_1_44, all_1_0_0, all_1_1_1, all_70_2_30, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.63 | (492) all_80_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (29) with all_1_0_0, all_80_1_44, all_70_2_30, all_1_1_1, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.63 | (493) all_80_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_80_1_44, all_16_1_7, all_70_2_30, all_1_2_2, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (494) all_80_1_44 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_1_2_2, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_16_1_7, all_80_1_44, all_1_2_2, all_70_2_30, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (495) all_80_1_44 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (29) with all_80_1_44, all_16_1_7, all_1_2_2, all_70_2_30, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (496) all_80_1_44 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (29) with all_16_1_7, all_80_1_44, all_70_2_30, all_1_2_2, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (497) all_80_1_44 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_1_2_2, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (42) with all_80_1_44, all_80_1_44, all_70_2_30, all_70_2_30, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 32.62/9.63 | (498) all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_70_2_30) = v2 & apart_point_and_line(all_1_4_4, all_70_2_30) = v1 & distinct_lines(all_70_2_30, all_70_2_30) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_80_1_44, all_80_1_44, all_70_2_30, all_70_2_30, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, yields:
% 32.62/9.63 | (499) all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_70_2_30) = v3 & apart_point_and_line(all_1_3_3, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (29) with all_151_0_65, all_16_1_7, all_1_2_2, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_151_0_65, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.63 | (500) all_151_0_65 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (32) with all_1_1_1, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1, yields:
% 32.62/9.63 | (501) ~ (apart_point_and_line(all_1_4_4, all_1_1_1) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_1_0_0, all_111_1_59, all_1_1_1, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.63 | (502) all_111_1_59 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (34) with all_24_1_19, all_111_1_59, all_1_4_4, all_1_2_2, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_2_2) = all_24_1_19, apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59, yields:
% 32.62/9.63 | (503) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_2_2) = v0 & distinct_points(all_1_4_4, all_24_1_19) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_111_1_59 = 0))))
% 32.62/9.63 |
% 32.62/9.63 | Instantiating formula (1) with all_106_0_55, all_1_0_0, all_106_1_56, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.63 | (504) all_106_0_55 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_1_0_0, all_106_0_55, all_1_1_1, all_106_1_56, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.64 | (505) all_106_0_55 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_106_0_55, all_1_0_0, all_1_1_1, all_106_1_56, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.64 | (506) all_106_0_55 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_1_0_0, all_106_0_55, all_106_1_56, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields:
% 32.62/9.64 | (507) all_106_0_55 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_106_0_55, all_16_1_7, all_106_1_56, all_1_2_2, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.64 | (508) all_106_0_55 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_16_1_7, all_106_0_55, all_1_2_2, all_106_1_56, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.64 | (509) all_106_0_55 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_106_1_56, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_106_0_55, all_16_1_7, all_1_2_2, all_106_1_56, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.64 | (510) all_106_0_55 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_106_1_56, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_16_1_7, all_106_0_55, all_106_1_56, all_1_2_2, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.64 | (511) all_106_0_55 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_106_0_55, all_80_1_44, all_106_1_56, all_70_2_30, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (512) all_106_0_55 = 0 | all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_106_1_56) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_80_1_44, all_106_0_55, all_70_2_30, all_106_1_56, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (513) all_106_0_55 = 0 | all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_106_1_56, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_106_0_55, all_80_1_44, all_70_2_30, all_106_1_56, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (514) all_106_0_55 = 0 | all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_106_1_56, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_80_1_44, all_106_0_55, all_106_1_56, all_70_2_30, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (515) all_106_0_55 = 0 | all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_106_0_55, all_72_1_32, all_106_1_56, all_1_1_1, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32, apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (516) all_106_0_55 = 0 | all_72_1_32 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_72_1_32, all_106_0_55, all_1_1_1, all_106_1_56, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32, apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (517) all_106_0_55 = 0 | all_72_1_32 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_106_0_55, all_72_1_32, all_1_1_1, all_106_1_56, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32, apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (518) all_106_0_55 = 0 | all_72_1_32 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_72_1_32, all_106_0_55, all_106_1_56, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32, apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (519) all_106_0_55 = 0 | all_72_1_32 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_106_0_55, all_106_0_55, all_106_1_56, all_106_1_56, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, yields:
% 32.62/9.64 | (520) all_106_0_55 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & distinct_lines(all_106_1_56, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_70_1_29, all_72_1_32, all_70_2_30, all_1_1_1, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, yields:
% 32.62/9.64 | (521) all_72_1_32 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_70_2_30) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_72_1_32, all_70_1_29, all_70_2_30, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, yields:
% 32.62/9.64 | (522) all_72_1_32 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_70_2_30) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_70_1_29, all_111_1_59, all_70_2_30, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, yields:
% 32.62/9.64 | (523) all_111_1_59 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_70_2_30) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_70_2_30) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_70_1_29, all_106_0_55, all_70_2_30, all_106_1_56, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, yields:
% 32.62/9.64 | (524) all_106_0_55 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_106_1_56, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (1) with all_106_0_55, all_70_1_29, all_106_1_56, all_70_2_30, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, yields:
% 32.62/9.64 | (525) all_106_0_55 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.64 |
% 32.62/9.64 | Instantiating formula (29) with all_70_1_29, all_106_0_55, all_106_1_56, all_70_2_30, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, yields:
% 32.62/9.64 | (526) all_106_0_55 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (29) with all_106_0_55, all_70_1_29, all_70_2_30, all_106_1_56, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, yields:
% 32.62/9.65 | (527) all_106_0_55 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_106_1_56, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (31) with all_111_1_59, all_16_1_7, all_1_2_2, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 32.62/9.65 | (528) all_111_1_59 = 0 | all_16_1_7 = 0 | ~ (distinct_lines(all_1_1_1, all_1_2_2) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (27) with all_146_2_64, all_1_1_1, all_1_2_2, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = 0, distinct_lines(all_1_2_2, all_1_1_1) = all_146_2_64, yields:
% 32.62/9.65 | (529) all_146_2_64 = 0 | apart_point_and_line(all_1_3_3, all_1_1_1) = 0
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (30) with all_156_2_70, all_1_2_2, all_1_1_1, all_1_2_2 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_156_2_70, ~ (distinct_lines(all_1_2_2, all_1_2_2) = 0), yields:
% 32.62/9.65 | (530) all_156_2_70 = 0 | ~ (distinct_lines(all_1_2_2, all_1_1_1) = 0)
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (37) with 0, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = 0, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.62/9.65 | (531) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (39) with 0, all_1_4_4, all_1_5_5, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (532) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (43) with 0, all_1_2_2, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (533) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (6) with 0, all_106_1_56, all_1_4_4, all_1_5_5, all_1_4_4 and discharging atoms line_connecting(all_1_4_4, all_1_5_5) = all_106_1_56, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (534) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (7) with all_16_1_7, all_106_0_55, all_1_2_2, all_106_1_56, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (535) all_106_0_55 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_106_1_56, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (7) with all_106_0_55, all_16_1_7, all_106_1_56, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (536) all_106_0_55 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (7) with all_106_0_55, all_106_0_55, all_106_1_56, all_106_1_56, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (537) all_106_0_55 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v2 & apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & distinct_lines(all_106_1_56, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (7) with all_106_0_55, all_70_1_29, all_106_1_56, all_70_2_30, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (538) all_106_0_55 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v2 & apart_point_and_line(all_1_4_4, all_70_2_30) = v1 & distinct_lines(all_70_2_30, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (7) with all_70_1_29, all_106_0_55, all_70_2_30, all_106_1_56, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (539) all_106_0_55 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & apart_point_and_line(all_1_4_4, all_70_2_30) = v2 & distinct_lines(all_106_1_56, all_70_2_30) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (39) with 0, all_1_3_3, all_1_5_5, all_1_4_4 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 32.62/9.65 | (540) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (42) with all_16_1_7, all_106_0_55, all_1_2_2, all_106_1_56, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 32.62/9.65 | (541) all_106_0_55 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_106_1_56, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (7) with all_226_1_97, all_226_1_97, all_92_1_50, all_92_1_50, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_92_1_50) = all_226_1_97, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 32.62/9.65 | (542) all_226_1_97 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v1 & distinct_lines(all_92_1_50, all_92_1_50) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (7) with all_80_1_44, all_80_1_44, all_70_2_30, all_70_2_30, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_70_2_30) = all_80_1_44, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 32.62/9.65 | (543) all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v1 & distinct_lines(all_70_2_30, all_70_2_30) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (42) with all_106_0_55, all_16_1_7, all_106_1_56, all_1_2_2, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 32.62/9.65 | (544) all_106_0_55 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (42) with all_106_0_55, all_106_0_55, all_106_1_56, all_106_1_56, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 32.62/9.65 | (545) all_106_0_55 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & distinct_lines(all_106_1_56, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (42) with all_106_0_55, all_70_1_29, all_106_1_56, all_70_2_30, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 32.62/9.65 | (546) all_106_0_55 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_3_3, all_70_2_30) = v1 & distinct_lines(all_70_2_30, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating formula (42) with all_70_1_29, all_106_0_55, all_70_2_30, all_106_1_56, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_106_1_56) = all_106_0_55, apart_point_and_line(all_1_5_5, all_70_2_30) = all_70_1_29, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 32.62/9.65 | (547) all_106_0_55 = 0 | all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & apart_point_and_line(all_1_3_3, all_70_2_30) = v2 & distinct_lines(all_106_1_56, all_70_2_30) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating (503) with all_271_0_102, all_271_1_103, all_271_2_104 yields:
% 32.62/9.65 | (548) apart_point_and_line(all_1_4_4, all_1_2_2) = all_271_1_103 & convergent_lines(all_1_2_2, all_1_2_2) = all_271_2_104 & distinct_points(all_1_4_4, all_24_1_19) = all_271_0_102 & ( ~ (all_271_2_104 = 0) | all_271_0_102 = 0 | ( ~ (all_271_1_103 = 0) & ~ (all_111_1_59 = 0)))
% 32.62/9.65 |
% 32.62/9.65 | Applying alpha-rule on (548) yields:
% 32.62/9.65 | (549) apart_point_and_line(all_1_4_4, all_1_2_2) = all_271_1_103
% 32.62/9.65 | (550) convergent_lines(all_1_2_2, all_1_2_2) = all_271_2_104
% 32.62/9.65 | (551) distinct_points(all_1_4_4, all_24_1_19) = all_271_0_102
% 32.62/9.65 | (552) ~ (all_271_2_104 = 0) | all_271_0_102 = 0 | ( ~ (all_271_1_103 = 0) & ~ (all_111_1_59 = 0))
% 32.62/9.65 |
% 32.62/9.65 | Instantiating (540) with all_283_0_120, all_283_1_121, all_283_2_122 yields:
% 32.62/9.65 | (553) line_connecting(all_1_4_4, all_1_5_5) = all_283_2_122 & apart_point_and_line(all_1_3_3, all_283_2_122) = all_283_1_121 & distinct_points(all_1_3_3, all_1_4_4) = all_283_0_120 & ( ~ (all_283_1_121 = 0) | all_283_0_120 = 0)
% 32.62/9.65 |
% 32.62/9.65 | Applying alpha-rule on (553) yields:
% 32.62/9.65 | (554) line_connecting(all_1_4_4, all_1_5_5) = all_283_2_122
% 32.62/9.65 | (555) apart_point_and_line(all_1_3_3, all_283_2_122) = all_283_1_121
% 32.62/9.65 | (556) distinct_points(all_1_3_3, all_1_4_4) = all_283_0_120
% 32.62/9.65 | (557) ~ (all_283_1_121 = 0) | all_283_0_120 = 0
% 32.62/9.65 |
% 32.62/9.65 | Instantiating (534) with all_287_0_126, all_287_1_127, all_287_2_128 yields:
% 32.62/9.65 | (558) apart_point_and_line(all_1_4_4, all_106_1_56) = all_287_1_127 & distinct_points(all_1_4_4, all_1_4_4) = all_287_0_126 & distinct_points(all_1_4_4, all_1_5_5) = all_287_2_128 & ( ~ (all_287_1_127 = 0) | ~ (all_287_2_128 = 0) | all_287_0_126 = 0)
% 32.62/9.65 |
% 32.62/9.65 | Applying alpha-rule on (558) yields:
% 32.62/9.65 | (559) apart_point_and_line(all_1_4_4, all_106_1_56) = all_287_1_127
% 32.62/9.65 | (560) distinct_points(all_1_4_4, all_1_4_4) = all_287_0_126
% 32.62/9.65 | (561) distinct_points(all_1_4_4, all_1_5_5) = all_287_2_128
% 32.62/9.65 | (562) ~ (all_287_1_127 = 0) | ~ (all_287_2_128 = 0) | all_287_0_126 = 0
% 32.62/9.65 |
% 32.62/9.65 | Instantiating (533) with all_289_0_129, all_289_1_130, all_289_2_131 yields:
% 32.62/9.65 | (563) apart_point_and_line(all_1_4_4, all_1_2_2) = all_289_1_130 & distinct_points(all_1_4_4, all_1_4_4) = all_289_0_129 & distinct_points(all_1_5_5, all_1_4_4) = all_289_2_131 & ( ~ (all_289_1_130 = 0) | ~ (all_289_2_131 = 0) | all_289_0_129 = 0)
% 32.62/9.66 |
% 32.62/9.66 | Applying alpha-rule on (563) yields:
% 32.62/9.66 | (564) apart_point_and_line(all_1_4_4, all_1_2_2) = all_289_1_130
% 32.62/9.66 | (565) distinct_points(all_1_4_4, all_1_4_4) = all_289_0_129
% 32.62/9.66 | (566) distinct_points(all_1_5_5, all_1_4_4) = all_289_2_131
% 32.62/9.66 | (567) ~ (all_289_1_130 = 0) | ~ (all_289_2_131 = 0) | all_289_0_129 = 0
% 32.62/9.66 |
% 32.62/9.66 | Instantiating (532) with all_291_0_132, all_291_1_133, all_291_2_134 yields:
% 32.62/9.66 | (568) line_connecting(all_1_4_4, all_1_5_5) = all_291_2_134 & apart_point_and_line(all_1_4_4, all_291_2_134) = all_291_1_133 & distinct_points(all_1_4_4, all_1_4_4) = all_291_0_132 & ( ~ (all_291_1_133 = 0) | all_291_0_132 = 0)
% 32.62/9.66 |
% 32.62/9.66 | Applying alpha-rule on (568) yields:
% 32.62/9.66 | (569) line_connecting(all_1_4_4, all_1_5_5) = all_291_2_134
% 32.62/9.66 | (570) apart_point_and_line(all_1_4_4, all_291_2_134) = all_291_1_133
% 32.62/9.66 | (571) distinct_points(all_1_4_4, all_1_4_4) = all_291_0_132
% 32.62/9.66 | (572) ~ (all_291_1_133 = 0) | all_291_0_132 = 0
% 32.62/9.66 |
% 32.62/9.66 | Instantiating (531) with all_295_0_138, all_295_1_139, all_295_2_140 yields:
% 32.62/9.66 | (573) line_connecting(all_1_5_5, all_1_4_4) = all_295_2_140 & apart_point_and_line(all_1_4_4, all_295_2_140) = all_295_1_139 & distinct_points(all_1_4_4, all_1_4_4) = all_295_0_138 & ( ~ (all_295_1_139 = 0) | all_295_0_138 = 0)
% 32.62/9.66 |
% 32.62/9.66 | Applying alpha-rule on (573) yields:
% 32.62/9.66 | (574) line_connecting(all_1_5_5, all_1_4_4) = all_295_2_140
% 32.62/9.66 | (575) apart_point_and_line(all_1_4_4, all_295_2_140) = all_295_1_139
% 32.62/9.66 | (576) distinct_points(all_1_4_4, all_1_4_4) = all_295_0_138
% 32.62/9.66 | (577) ~ (all_295_1_139 = 0) | all_295_0_138 = 0
% 32.62/9.66 |
% 32.62/9.66 | Instantiating (479) with all_303_0_150, all_303_1_151, all_303_2_152 yields:
% 32.62/9.66 | (578) apart_point_and_line(all_1_3_3, all_106_1_56) = all_303_1_151 & distinct_points(all_1_3_3, all_1_4_4) = all_303_0_150 & distinct_points(all_1_4_4, all_1_5_5) = all_303_2_152 & ( ~ (all_303_1_151 = 0) | ~ (all_303_2_152 = 0) | all_303_0_150 = 0)
% 32.62/9.66 |
% 32.62/9.66 | Applying alpha-rule on (578) yields:
% 32.62/9.66 | (579) apart_point_and_line(all_1_3_3, all_106_1_56) = all_303_1_151
% 32.62/9.66 | (580) distinct_points(all_1_3_3, all_1_4_4) = all_303_0_150
% 32.62/9.66 | (581) distinct_points(all_1_4_4, all_1_5_5) = all_303_2_152
% 32.62/9.66 | (582) ~ (all_303_1_151 = 0) | ~ (all_303_2_152 = 0) | all_303_0_150 = 0
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (490), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (583) all_80_1_44 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (583) can reduce 477 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (477) ~ (all_80_1_44 = 0)
% 32.62/9.66 | (586) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (491), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (583) all_80_1_44 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (583) can reduce 477 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (477) ~ (all_80_1_44 = 0)
% 32.62/9.66 | (590) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (492), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (583) all_80_1_44 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (583) can reduce 477 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (477) ~ (all_80_1_44 = 0)
% 32.62/9.66 | (594) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (493), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (583) all_80_1_44 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (583) can reduce 477 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (477) ~ (all_80_1_44 = 0)
% 32.62/9.66 | (598) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (480), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (599) all_226_1_97 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (599) can reduce 478 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (478) ~ (all_226_1_97 = 0)
% 32.62/9.66 | (602) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_1_1_1, all_92_1_50) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (481), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (599) all_226_1_97 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (599) can reduce 478 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (478) ~ (all_226_1_97 = 0)
% 32.62/9.66 | (606) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_92_1_50, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (482), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (599) all_226_1_97 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (599) can reduce 478 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (478) ~ (all_226_1_97 = 0)
% 32.62/9.66 | (610) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_92_1_50, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (483), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (599) all_226_1_97 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (599) can reduce 478 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (478) ~ (all_226_1_97 = 0)
% 32.62/9.66 | (614) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_1_1_1, all_92_1_50) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (529), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (615) apart_point_and_line(all_1_3_3, all_1_1_1) = 0
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (590), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (87) all_1_0_0 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (87) can reduce 53 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (53) ~ (all_1_0_0 = 0)
% 32.62/9.66 | (619) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 | Instantiating (619) with all_358_0_168, all_358_1_169, all_358_2_170, all_358_3_171 yields:
% 32.62/9.66 | (620) apart_point_and_line(all_1_3_3, all_1_1_1) = all_358_1_169 & apart_point_and_line(all_1_5_5, all_70_2_30) = all_358_0_168 & distinct_lines(all_70_2_30, all_1_1_1) = all_358_2_170 & distinct_points(all_1_3_3, all_1_5_5) = all_358_3_171 & ( ~ (all_358_2_170 = 0) | ~ (all_358_3_171 = 0) | all_358_0_168 = 0 | all_358_1_169 = 0)
% 32.62/9.66 |
% 32.62/9.66 | Applying alpha-rule on (620) yields:
% 32.62/9.66 | (621) ~ (all_358_2_170 = 0) | ~ (all_358_3_171 = 0) | all_358_0_168 = 0 | all_358_1_169 = 0
% 32.62/9.66 | (622) distinct_points(all_1_3_3, all_1_5_5) = all_358_3_171
% 32.62/9.66 | (623) distinct_lines(all_70_2_30, all_1_1_1) = all_358_2_170
% 32.62/9.66 | (624) apart_point_and_line(all_1_5_5, all_70_2_30) = all_358_0_168
% 32.62/9.66 | (625) apart_point_and_line(all_1_3_3, all_1_1_1) = all_358_1_169
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (594), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (87) all_1_0_0 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (87) can reduce 53 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (53) ~ (all_1_0_0 = 0)
% 32.62/9.66 | (629) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 | Instantiating (629) with all_363_0_172, all_363_1_173, all_363_2_174, all_363_3_175 yields:
% 32.62/9.66 | (630) apart_point_and_line(all_1_3_3, all_1_1_1) = all_363_0_172 & apart_point_and_line(all_1_5_5, all_70_2_30) = all_363_1_173 & distinct_lines(all_70_2_30, all_1_1_1) = all_363_2_174 & distinct_points(all_1_5_5, all_1_3_3) = all_363_3_175 & ( ~ (all_363_2_174 = 0) | ~ (all_363_3_175 = 0) | all_363_0_172 = 0 | all_363_1_173 = 0)
% 32.62/9.66 |
% 32.62/9.66 | Applying alpha-rule on (630) yields:
% 32.62/9.66 | (631) distinct_lines(all_70_2_30, all_1_1_1) = all_363_2_174
% 32.62/9.66 | (632) distinct_points(all_1_5_5, all_1_3_3) = all_363_3_175
% 32.62/9.66 | (633) apart_point_and_line(all_1_3_3, all_1_1_1) = all_363_0_172
% 32.62/9.66 | (634) ~ (all_363_2_174 = 0) | ~ (all_363_3_175 = 0) | all_363_0_172 = 0 | all_363_1_173 = 0
% 32.62/9.66 | (635) apart_point_and_line(all_1_5_5, all_70_2_30) = all_363_1_173
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (606), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (87) all_1_0_0 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (87) can reduce 53 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (53) ~ (all_1_0_0 = 0)
% 32.62/9.66 | (639) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_92_1_50, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.66 |
% 32.62/9.66 | Instantiating (639) with all_465_0_206, all_465_1_207, all_465_2_208, all_465_3_209 yields:
% 32.62/9.66 | (640) apart_point_and_line(all_1_3_3, all_1_1_1) = all_465_1_207 & apart_point_and_line(all_1_5_5, all_92_1_50) = all_465_0_206 & distinct_lines(all_92_1_50, all_1_1_1) = all_465_2_208 & distinct_points(all_1_3_3, all_1_5_5) = all_465_3_209 & ( ~ (all_465_2_208 = 0) | ~ (all_465_3_209 = 0) | all_465_0_206 = 0 | all_465_1_207 = 0)
% 32.62/9.66 |
% 32.62/9.66 | Applying alpha-rule on (640) yields:
% 32.62/9.66 | (641) distinct_points(all_1_3_3, all_1_5_5) = all_465_3_209
% 32.62/9.66 | (642) apart_point_and_line(all_1_3_3, all_1_1_1) = all_465_1_207
% 32.62/9.66 | (643) apart_point_and_line(all_1_5_5, all_92_1_50) = all_465_0_206
% 32.62/9.66 | (644) distinct_lines(all_92_1_50, all_1_1_1) = all_465_2_208
% 32.62/9.66 | (645) ~ (all_465_2_208 = 0) | ~ (all_465_3_209 = 0) | all_465_0_206 = 0 | all_465_1_207 = 0
% 32.62/9.66 |
% 32.62/9.66 +-Applying beta-rule and splitting (610), into two cases.
% 32.62/9.66 |-Branch one:
% 32.62/9.66 | (87) all_1_0_0 = 0
% 32.62/9.66 |
% 32.62/9.66 | Equations (87) can reduce 53 to:
% 32.62/9.66 | (88) $false
% 32.62/9.66 |
% 32.62/9.66 |-The branch is then unsatisfiable
% 32.62/9.66 |-Branch two:
% 32.62/9.66 | (53) ~ (all_1_0_0 = 0)
% 32.62/9.66 | (649) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_92_1_50, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 | Instantiating (649) with all_470_0_210, all_470_1_211, all_470_2_212, all_470_3_213 yields:
% 32.62/9.67 | (650) apart_point_and_line(all_1_3_3, all_1_1_1) = all_470_0_210 & apart_point_and_line(all_1_5_5, all_92_1_50) = all_470_1_211 & distinct_lines(all_92_1_50, all_1_1_1) = all_470_2_212 & distinct_points(all_1_5_5, all_1_3_3) = all_470_3_213 & ( ~ (all_470_2_212 = 0) | ~ (all_470_3_213 = 0) | all_470_0_210 = 0 | all_470_1_211 = 0)
% 32.62/9.67 |
% 32.62/9.67 | Applying alpha-rule on (650) yields:
% 32.62/9.67 | (651) apart_point_and_line(all_1_3_3, all_1_1_1) = all_470_0_210
% 32.62/9.67 | (652) apart_point_and_line(all_1_5_5, all_92_1_50) = all_470_1_211
% 32.62/9.67 | (653) distinct_points(all_1_5_5, all_1_3_3) = all_470_3_213
% 32.62/9.67 | (654) ~ (all_470_2_212 = 0) | ~ (all_470_3_213 = 0) | all_470_0_210 = 0 | all_470_1_211 = 0
% 32.62/9.67 | (655) distinct_lines(all_92_1_50, all_1_1_1) = all_470_2_212
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (545), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (659) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & distinct_lines(all_106_1_56, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (537), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (663) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v2 & apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & distinct_lines(all_106_1_56, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (520), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (667) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & distinct_lines(all_106_1_56, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (547), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (671) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & apart_point_and_line(all_1_3_3, all_70_2_30) = v2 & distinct_lines(all_106_1_56, all_70_2_30) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (525), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (675) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (526), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (679) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (546), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (683) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_3_3, all_70_2_30) = v1 & distinct_lines(all_70_2_30, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (539), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (687) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & apart_point_and_line(all_1_4_4, all_70_2_30) = v2 & distinct_lines(all_106_1_56, all_70_2_30) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (508), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (691) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (538), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (695) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v2 & apart_point_and_line(all_1_4_4, all_70_2_30) = v1 & distinct_lines(all_70_2_30, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (524), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (699) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_106_1_56, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (527), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (703) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_106_1_56, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (509), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (707) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_106_1_56, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (510), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (711) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_106_1_56, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (521), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (712) all_72_1_32 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (712) can reduce 476 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (476) ~ (all_72_1_32 = 0)
% 32.62/9.67 | (715) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_70_2_30) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (522), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (712) all_72_1_32 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (712) can reduce 476 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (476) ~ (all_72_1_32 = 0)
% 32.62/9.67 | (719) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_70_2_30) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (511), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (723) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (516), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (727) all_72_1_32 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.67 |
% 32.62/9.67 +-Applying beta-rule and splitting (517), into two cases.
% 32.62/9.67 |-Branch one:
% 32.62/9.67 | (656) all_106_0_55 = 0
% 32.62/9.67 |
% 32.62/9.67 | Equations (656) can reduce 425 to:
% 32.62/9.67 | (88) $false
% 32.62/9.67 |
% 32.62/9.67 |-The branch is then unsatisfiable
% 32.62/9.67 |-Branch two:
% 32.62/9.67 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.67 | (731) all_72_1_32 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (512), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (656) all_106_0_55 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (656) can reduce 425 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.68 | (735) all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_106_1_56) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (513), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (656) all_106_0_55 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (656) can reduce 425 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.68 | (739) all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_106_1_56, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (514), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (656) all_106_0_55 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (656) can reduce 425 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.68 | (743) all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_106_1_56, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (515), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (656) all_106_0_55 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (656) can reduce 425 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.68 | (747) all_80_1_44 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (518), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (656) all_106_0_55 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (656) can reduce 425 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.68 | (751) all_72_1_32 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (519), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (656) all_106_0_55 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (656) can reduce 425 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (425) ~ (all_106_0_55 = 0)
% 32.62/9.68 | (755) all_72_1_32 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (598), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (87) all_1_0_0 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (87) can reduce 53 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (53) ~ (all_1_0_0 = 0)
% 32.62/9.68 | (759) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_1_1_1, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 | Instantiating (759) with all_762_0_224, all_762_1_225, all_762_2_226, all_762_3_227 yields:
% 32.62/9.68 | (760) apart_point_and_line(all_1_3_3, all_1_1_1) = all_762_1_225 & apart_point_and_line(all_1_5_5, all_70_2_30) = all_762_0_224 & distinct_lines(all_1_1_1, all_70_2_30) = all_762_2_226 & distinct_points(all_1_3_3, all_1_5_5) = all_762_3_227 & ( ~ (all_762_2_226 = 0) | ~ (all_762_3_227 = 0) | all_762_0_224 = 0 | all_762_1_225 = 0)
% 32.62/9.68 |
% 32.62/9.68 | Applying alpha-rule on (760) yields:
% 32.62/9.68 | (761) distinct_points(all_1_3_3, all_1_5_5) = all_762_3_227
% 32.62/9.68 | (762) apart_point_and_line(all_1_5_5, all_70_2_30) = all_762_0_224
% 32.62/9.68 | (763) distinct_lines(all_1_1_1, all_70_2_30) = all_762_2_226
% 32.62/9.68 | (764) apart_point_and_line(all_1_3_3, all_1_1_1) = all_762_1_225
% 32.62/9.68 | (765) ~ (all_762_2_226 = 0) | ~ (all_762_3_227 = 0) | all_762_0_224 = 0 | all_762_1_225 = 0
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (602), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (87) all_1_0_0 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (87) can reduce 53 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (53) ~ (all_1_0_0 = 0)
% 32.62/9.68 | (769) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_1_1_1, all_92_1_50) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 | Instantiating (769) with all_767_0_228, all_767_1_229, all_767_2_230, all_767_3_231 yields:
% 32.62/9.68 | (770) apart_point_and_line(all_1_3_3, all_1_1_1) = all_767_0_228 & apart_point_and_line(all_1_5_5, all_92_1_50) = all_767_1_229 & distinct_lines(all_1_1_1, all_92_1_50) = all_767_2_230 & distinct_points(all_1_5_5, all_1_3_3) = all_767_3_231 & ( ~ (all_767_2_230 = 0) | ~ (all_767_3_231 = 0) | all_767_0_228 = 0 | all_767_1_229 = 0)
% 32.62/9.68 |
% 32.62/9.68 | Applying alpha-rule on (770) yields:
% 32.62/9.68 | (771) apart_point_and_line(all_1_5_5, all_92_1_50) = all_767_1_229
% 32.62/9.68 | (772) apart_point_and_line(all_1_3_3, all_1_1_1) = all_767_0_228
% 32.62/9.68 | (773) distinct_lines(all_1_1_1, all_92_1_50) = all_767_2_230
% 32.62/9.68 | (774) ~ (all_767_2_230 = 0) | ~ (all_767_3_231 = 0) | all_767_0_228 = 0 | all_767_1_229 = 0
% 32.62/9.68 | (775) distinct_points(all_1_5_5, all_1_3_3) = all_767_3_231
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (614), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (87) all_1_0_0 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (87) can reduce 53 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (53) ~ (all_1_0_0 = 0)
% 32.62/9.68 | (779) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_1_1_1, all_92_1_50) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 | Instantiating (779) with all_772_0_232, all_772_1_233, all_772_2_234, all_772_3_235 yields:
% 32.62/9.68 | (780) apart_point_and_line(all_1_3_3, all_1_1_1) = all_772_1_233 & apart_point_and_line(all_1_5_5, all_92_1_50) = all_772_0_232 & distinct_lines(all_1_1_1, all_92_1_50) = all_772_2_234 & distinct_points(all_1_3_3, all_1_5_5) = all_772_3_235 & ( ~ (all_772_2_234 = 0) | ~ (all_772_3_235 = 0) | all_772_0_232 = 0 | all_772_1_233 = 0)
% 32.62/9.68 |
% 32.62/9.68 | Applying alpha-rule on (780) yields:
% 32.62/9.68 | (781) apart_point_and_line(all_1_5_5, all_92_1_50) = all_772_0_232
% 32.62/9.68 | (782) distinct_lines(all_1_1_1, all_92_1_50) = all_772_2_234
% 32.62/9.68 | (783) distinct_points(all_1_3_3, all_1_5_5) = all_772_3_235
% 32.62/9.68 | (784) ~ (all_772_2_234 = 0) | ~ (all_772_3_235 = 0) | all_772_0_232 = 0 | all_772_1_233 = 0
% 32.62/9.68 | (785) apart_point_and_line(all_1_3_3, all_1_1_1) = all_772_1_233
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (727), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (712) all_72_1_32 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (712) can reduce 476 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (476) ~ (all_72_1_32 = 0)
% 32.62/9.68 | (789) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (731), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (712) all_72_1_32 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (712) can reduce 476 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (476) ~ (all_72_1_32 = 0)
% 32.62/9.68 | (793) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (751), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (712) all_72_1_32 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (712) can reduce 476 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (476) ~ (all_72_1_32 = 0)
% 32.62/9.68 | (797) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 +-Applying beta-rule and splitting (755), into two cases.
% 32.62/9.68 |-Branch one:
% 32.62/9.68 | (712) all_72_1_32 = 0
% 32.62/9.68 |
% 32.62/9.68 | Equations (712) can reduce 476 to:
% 32.62/9.68 | (88) $false
% 32.62/9.68 |
% 32.62/9.68 |-The branch is then unsatisfiable
% 32.62/9.68 |-Branch two:
% 32.62/9.68 | (476) ~ (all_72_1_32 = 0)
% 32.62/9.68 | (801) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.62/9.68 |
% 32.62/9.68 | Instantiating formula (15) with all_1_3_3, all_1_1_1, all_762_1_225, all_772_1_233 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_772_1_233, apart_point_and_line(all_1_3_3, all_1_1_1) = all_762_1_225, yields:
% 32.62/9.68 | (802) all_772_1_233 = all_762_1_225
% 32.62/9.68 |
% 32.62/9.68 | Instantiating formula (15) with all_1_3_3, all_1_1_1, all_762_1_225, all_767_0_228 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_767_0_228, apart_point_and_line(all_1_3_3, all_1_1_1) = all_762_1_225, yields:
% 32.62/9.68 | (803) all_767_0_228 = all_762_1_225
% 32.62/9.68 |
% 32.62/9.68 | Instantiating formula (15) with all_1_3_3, all_1_1_1, all_470_0_210, all_772_1_233 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_772_1_233, apart_point_and_line(all_1_3_3, all_1_1_1) = all_470_0_210, yields:
% 32.62/9.68 | (804) all_772_1_233 = all_470_0_210
% 32.62/9.68 |
% 32.62/9.68 | Instantiating formula (15) with all_1_3_3, all_1_1_1, all_465_1_207, all_72_1_32 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_465_1_207, apart_point_and_line(all_1_3_3, all_1_1_1) = all_72_1_32, yields:
% 32.62/9.68 | (805) all_465_1_207 = all_72_1_32
% 32.62/9.68 |
% 32.62/9.68 | Instantiating formula (15) with all_1_3_3, all_1_1_1, all_465_1_207, all_762_1_225 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_762_1_225, apart_point_and_line(all_1_3_3, all_1_1_1) = all_465_1_207, yields:
% 32.62/9.68 | (806) all_762_1_225 = all_465_1_207
% 32.62/9.68 |
% 32.62/9.68 | Instantiating formula (15) with all_1_3_3, all_1_1_1, all_363_0_172, all_767_0_228 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_767_0_228, apart_point_and_line(all_1_3_3, all_1_1_1) = all_363_0_172, yields:
% 32.62/9.68 | (807) all_767_0_228 = all_363_0_172
% 32.62/9.68 |
% 32.62/9.68 | Instantiating formula (15) with all_1_3_3, all_1_1_1, all_358_1_169, all_465_1_207 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_465_1_207, apart_point_and_line(all_1_3_3, all_1_1_1) = all_358_1_169, yields:
% 32.62/9.68 | (808) all_465_1_207 = all_358_1_169
% 32.62/9.68 |
% 32.62/9.68 | Instantiating formula (15) with all_1_3_3, all_1_1_1, 0, all_358_1_169 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_358_1_169, apart_point_and_line(all_1_3_3, all_1_1_1) = 0, yields:
% 32.62/9.68 | (809) all_358_1_169 = 0
% 32.62/9.68 |
% 32.62/9.68 | Combining equations (802,804) yields a new equation:
% 32.62/9.68 | (810) all_762_1_225 = all_470_0_210
% 32.62/9.68 |
% 32.62/9.68 | Simplifying 810 yields:
% 32.62/9.68 | (811) all_762_1_225 = all_470_0_210
% 32.62/9.68 |
% 32.62/9.68 | Combining equations (803,807) yields a new equation:
% 32.62/9.68 | (812) all_762_1_225 = all_363_0_172
% 32.62/9.68 |
% 32.62/9.68 | Simplifying 812 yields:
% 32.62/9.68 | (813) all_762_1_225 = all_363_0_172
% 32.62/9.68 |
% 32.62/9.68 | Combining equations (813,811) yields a new equation:
% 32.62/9.68 | (814) all_470_0_210 = all_363_0_172
% 32.62/9.68 |
% 32.62/9.68 | Combining equations (806,811) yields a new equation:
% 32.62/9.68 | (815) all_470_0_210 = all_465_1_207
% 32.62/9.68 |
% 32.62/9.68 | Combining equations (815,814) yields a new equation:
% 32.62/9.69 | (816) all_465_1_207 = all_363_0_172
% 32.62/9.69 |
% 32.62/9.69 | Simplifying 816 yields:
% 32.62/9.69 | (817) all_465_1_207 = all_363_0_172
% 32.62/9.69 |
% 32.62/9.69 | Combining equations (805,817) yields a new equation:
% 32.62/9.69 | (818) all_363_0_172 = all_72_1_32
% 32.62/9.69 |
% 32.62/9.69 | Combining equations (808,817) yields a new equation:
% 32.62/9.69 | (819) all_363_0_172 = all_358_1_169
% 32.62/9.69 |
% 32.62/9.69 | Combining equations (819,818) yields a new equation:
% 32.62/9.69 | (820) all_358_1_169 = all_72_1_32
% 32.62/9.69 |
% 32.62/9.69 | Simplifying 820 yields:
% 32.62/9.69 | (821) all_358_1_169 = all_72_1_32
% 32.62/9.69 |
% 32.62/9.69 | Combining equations (809,821) yields a new equation:
% 32.62/9.69 | (712) all_72_1_32 = 0
% 32.62/9.69 |
% 32.62/9.69 | Equations (712) can reduce 476 to:
% 32.62/9.69 | (88) $false
% 32.62/9.69 |
% 32.62/9.69 |-The branch is then unsatisfiable
% 32.62/9.69 |-Branch two:
% 32.62/9.69 | (824) ~ (apart_point_and_line(all_1_3_3, all_1_1_1) = 0)
% 32.62/9.69 | (825) all_146_2_64 = 0
% 32.62/9.69 |
% 32.62/9.69 | From (825) and (270) follows:
% 32.62/9.69 | (826) distinct_lines(all_1_2_2, all_1_1_1) = 0
% 32.62/9.69 |
% 32.62/9.69 +-Applying beta-rule and splitting (530), into two cases.
% 32.62/9.69 |-Branch one:
% 32.62/9.69 | (827) ~ (distinct_lines(all_1_2_2, all_1_1_1) = 0)
% 32.62/9.69 |
% 32.62/9.69 | Using (826) and (827) yields:
% 32.62/9.69 | (136) $false
% 32.62/9.69 |
% 32.62/9.69 |-The branch is then unsatisfiable
% 32.62/9.69 |-Branch two:
% 32.62/9.69 | (826) distinct_lines(all_1_2_2, all_1_1_1) = 0
% 32.62/9.69 | (830) all_156_2_70 = 0
% 32.62/9.69 |
% 32.62/9.69 | Combining equations (830,363) yields a new equation:
% 32.62/9.69 | (831) all_176_2_85 = 0
% 32.62/9.69 |
% 32.62/9.69 | From (830) and (287) follows:
% 32.62/9.69 | (832) distinct_lines(all_1_1_1, all_1_2_2) = 0
% 32.62/9.69 |
% 32.62/9.69 +-Applying beta-rule and splitting (498), into two cases.
% 32.62/9.69 |-Branch one:
% 32.62/9.69 | (583) all_80_1_44 = 0
% 32.62/9.69 |
% 32.62/9.69 | Equations (583) can reduce 477 to:
% 32.62/9.69 | (88) $false
% 32.62/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (477) ~ (all_80_1_44 = 0)
% 32.95/9.69 | (836) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_70_2_30) = v2 & apart_point_and_line(all_1_4_4, all_70_2_30) = v1 & distinct_lines(all_70_2_30, all_70_2_30) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (543), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (583) all_80_1_44 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (583) can reduce 477 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (477) ~ (all_80_1_44 = 0)
% 32.95/9.69 | (840) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v1 & distinct_lines(all_70_2_30, all_70_2_30) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (499), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (583) all_80_1_44 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (583) can reduce 477 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (477) ~ (all_80_1_44 = 0)
% 32.95/9.69 | (844) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_70_2_30) = v3 & apart_point_and_line(all_1_3_3, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (488), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (599) all_226_1_97 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (599) can reduce 478 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (478) ~ (all_226_1_97 = 0)
% 32.95/9.69 | (848) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_92_1_50) = v2 & apart_point_and_line(all_1_4_4, all_92_1_50) = v1 & distinct_lines(all_92_1_50, all_92_1_50) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (542), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (599) all_226_1_97 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (599) can reduce 478 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (478) ~ (all_226_1_97 = 0)
% 32.95/9.69 | (852) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v1 & distinct_lines(all_92_1_50, all_92_1_50) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (489), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (599) all_226_1_97 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (599) can reduce 478 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (478) ~ (all_226_1_97 = 0)
% 32.95/9.69 | (856) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_92_1_50) = v3 & apart_point_and_line(all_1_3_3, all_92_1_50) = v2 & distinct_lines(all_92_1_50, all_92_1_50) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (487), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (599) all_226_1_97 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (599) can reduce 478 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (478) ~ (all_226_1_97 = 0)
% 32.95/9.69 | (860) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_1_2_2, all_92_1_50) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (494), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (583) all_80_1_44 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (583) can reduce 477 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (477) ~ (all_80_1_44 = 0)
% 32.95/9.69 | (864) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_1_2_2, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (495), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (583) all_80_1_44 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (583) can reduce 477 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (477) ~ (all_80_1_44 = 0)
% 32.95/9.69 | (868) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (484), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (599) all_226_1_97 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (599) can reduce 478 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (478) ~ (all_226_1_97 = 0)
% 32.95/9.69 | (872) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_1_2_2, all_92_1_50) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (485), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (599) all_226_1_97 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (599) can reduce 478 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (478) ~ (all_226_1_97 = 0)
% 32.95/9.69 | (876) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_92_1_50, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (486), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (599) all_226_1_97 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (599) can reduce 478 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (478) ~ (all_226_1_97 = 0)
% 32.95/9.69 | (880) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_92_1_50, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (496), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (583) all_80_1_44 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (583) can reduce 477 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (477) ~ (all_80_1_44 = 0)
% 32.95/9.69 | (884) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (497), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (583) all_80_1_44 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (583) can reduce 477 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (477) ~ (all_80_1_44 = 0)
% 32.95/9.69 | (888) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_1_2_2, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (545), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (656) all_106_0_55 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (656) can reduce 425 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.69 | (659) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & distinct_lines(all_106_1_56, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (537), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (656) all_106_0_55 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (656) can reduce 425 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.69 | (663) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v2 & apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & distinct_lines(all_106_1_56, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (520), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (656) all_106_0_55 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (656) can reduce 425 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.69 | (667) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & distinct_lines(all_106_1_56, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (504), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (656) all_106_0_55 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (656) can reduce 425 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.69 | (904) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.69 |
% 32.95/9.69 +-Applying beta-rule and splitting (505), into two cases.
% 32.95/9.69 |-Branch one:
% 32.95/9.69 | (656) all_106_0_55 = 0
% 32.95/9.69 |
% 32.95/9.69 | Equations (656) can reduce 425 to:
% 32.95/9.69 | (88) $false
% 32.95/9.69 |
% 32.95/9.69 |-The branch is then unsatisfiable
% 32.95/9.69 |-Branch two:
% 32.95/9.69 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.69 | (908) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (506), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (656) all_106_0_55 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (656) can reduce 425 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.70 | (912) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_106_1_56, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (507), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (656) all_106_0_55 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (656) can reduce 425 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.70 | (916) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_106_1_56) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_106_1_56) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (536), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (656) all_106_0_55 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (656) can reduce 425 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.70 | (920) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (544), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (656) all_106_0_55 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (656) can reduce 425 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.70 | (924) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_106_1_56) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (541), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (656) all_106_0_55 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (656) can reduce 425 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.70 | (928) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_106_1_56, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (535), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (656) all_106_0_55 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (656) can reduce 425 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (425) ~ (all_106_0_55 = 0)
% 32.95/9.70 | (932) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_106_1_56, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (860), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (936) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_1_2_2, all_92_1_50) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (864), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (940) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_1_2_2, all_70_2_30) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (868), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (944) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_70_2_30, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (872), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (948) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_1_2_2, all_92_1_50) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (876), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (952) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_92_1_50) = v3 & distinct_lines(all_92_1_50, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (880), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (956) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_92_1_50) = v2 & distinct_lines(all_92_1_50, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (884), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (960) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_70_2_30) = v2 & distinct_lines(all_70_2_30, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (888), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (964) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_70_2_30) = v3 & distinct_lines(all_1_2_2, all_70_2_30) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (928), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (968) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_106_1_56) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_106_1_56, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.70 |
% 32.95/9.70 +-Applying beta-rule and splitting (932), into two cases.
% 32.95/9.70 |-Branch one:
% 32.95/9.70 | (222) all_16_1_7 = 0
% 32.95/9.70 |
% 32.95/9.70 | Equations (222) can reduce 139 to:
% 32.95/9.70 | (88) $false
% 32.95/9.70 |
% 32.95/9.70 |-The branch is then unsatisfiable
% 32.95/9.70 |-Branch two:
% 32.95/9.70 | (139) ~ (all_16_1_7 = 0)
% 32.95/9.70 | (972) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_106_1_56) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_106_1_56, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.70 |
% 32.95/9.70 | Instantiating (972) with all_870_0_553, all_870_1_554, all_870_2_555 yields:
% 32.95/9.70 | (973) apart_point_and_line(all_1_4_4, all_106_1_56) = all_870_1_554 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_870_0_553 & distinct_lines(all_106_1_56, all_1_2_2) = all_870_2_555 & ( ~ (all_870_2_555 = 0) | all_870_0_553 = 0 | all_870_1_554 = 0)
% 32.95/9.70 |
% 32.95/9.70 | Applying alpha-rule on (973) yields:
% 32.95/9.70 | (974) apart_point_and_line(all_1_4_4, all_106_1_56) = all_870_1_554
% 32.95/9.70 | (975) apart_point_and_line(all_1_4_4, all_1_2_2) = all_870_0_553
% 32.95/9.70 | (976) distinct_lines(all_106_1_56, all_1_2_2) = all_870_2_555
% 32.95/9.70 | (977) ~ (all_870_2_555 = 0) | all_870_0_553 = 0 | all_870_1_554 = 0
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_289_1_130, all_111_1_59 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_289_1_130, apart_point_and_line(all_1_4_4, all_1_2_2) = all_111_1_59, yields:
% 32.95/9.70 | (978) all_289_1_130 = all_111_1_59
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_289_1_130, all_870_0_553 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_870_0_553, apart_point_and_line(all_1_4_4, all_1_2_2) = all_289_1_130, yields:
% 32.95/9.70 | (979) all_870_0_553 = all_289_1_130
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_271_1_103, all_870_0_553 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_870_0_553, apart_point_and_line(all_1_4_4, all_1_2_2) = all_271_1_103, yields:
% 32.95/9.70 | (980) all_870_0_553 = all_271_1_103
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (33) with all_1_3_3, all_1_4_4, all_303_0_150, 0 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_303_0_150, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 32.95/9.70 | (981) all_303_0_150 = 0
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (33) with all_1_3_3, all_1_4_4, all_283_0_120, all_303_0_150 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_303_0_150, distinct_points(all_1_3_3, all_1_4_4) = all_283_0_120, yields:
% 32.95/9.70 | (982) all_303_0_150 = all_283_0_120
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (33) with all_1_4_4, all_1_4_4, all_291_0_132, all_295_0_138 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_295_0_138, distinct_points(all_1_4_4, all_1_4_4) = all_291_0_132, yields:
% 32.95/9.70 | (983) all_295_0_138 = all_291_0_132
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (33) with all_1_4_4, all_1_4_4, all_289_0_129, all_295_0_138 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_295_0_138, distinct_points(all_1_4_4, all_1_4_4) = all_289_0_129, yields:
% 32.95/9.70 | (984) all_295_0_138 = all_289_0_129
% 32.95/9.70 |
% 32.95/9.70 | Using (565) and (141) yields:
% 32.95/9.70 | (985) ~ (all_289_0_129 = 0)
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (33) with all_1_4_4, all_1_4_4, all_287_0_126, all_295_0_138 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_295_0_138, distinct_points(all_1_4_4, all_1_4_4) = all_287_0_126, yields:
% 32.95/9.70 | (986) all_295_0_138 = all_287_0_126
% 32.95/9.70 |
% 32.95/9.70 | Instantiating formula (33) with all_1_5_5, all_1_4_4, all_289_2_131, 0 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_289_2_131, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 32.95/9.70 | (987) all_289_2_131 = 0
% 32.95/9.70 |
% 32.95/9.70 | Combining equations (979,980) yields a new equation:
% 32.95/9.70 | (988) all_289_1_130 = all_271_1_103
% 32.95/9.70 |
% 32.95/9.70 | Simplifying 988 yields:
% 32.95/9.70 | (989) all_289_1_130 = all_271_1_103
% 32.95/9.70 |
% 32.95/9.70 | Combining equations (981,982) yields a new equation:
% 32.95/9.70 | (990) all_283_0_120 = 0
% 32.95/9.70 |
% 32.95/9.70 | Combining equations (984,983) yields a new equation:
% 32.95/9.70 | (991) all_291_0_132 = all_289_0_129
% 32.95/9.70 |
% 32.95/9.71 | Combining equations (986,983) yields a new equation:
% 32.95/9.71 | (992) all_291_0_132 = all_287_0_126
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (991,992) yields a new equation:
% 32.95/9.71 | (993) all_289_0_129 = all_287_0_126
% 32.95/9.71 |
% 32.95/9.71 | Simplifying 993 yields:
% 32.95/9.71 | (994) all_289_0_129 = all_287_0_126
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (978,989) yields a new equation:
% 32.95/9.71 | (995) all_271_1_103 = all_111_1_59
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (995,989) yields a new equation:
% 32.95/9.71 | (978) all_289_1_130 = all_111_1_59
% 32.95/9.71 |
% 32.95/9.71 | Equations (994) can reduce 985 to:
% 32.95/9.71 | (997) ~ (all_287_0_126 = 0)
% 32.95/9.71 |
% 32.95/9.71 | From (990) and (556) follows:
% 32.95/9.71 | (133) distinct_points(all_1_3_3, all_1_4_4) = 0
% 32.95/9.71 |
% 32.95/9.71 | From (994) and (565) follows:
% 32.95/9.71 | (560) distinct_points(all_1_4_4, all_1_4_4) = all_287_0_126
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (567), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1000) ~ (all_289_1_130 = 0)
% 32.95/9.71 |
% 32.95/9.71 | Equations (978) can reduce 1000 to:
% 32.95/9.71 | (1001) ~ (all_111_1_59 = 0)
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (523), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1002) all_111_1_59 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1002) can reduce 1001 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (1001) ~ (all_111_1_59 = 0)
% 32.95/9.71 | (1005) all_70_1_29 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_70_2_30) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_70_2_30) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (502), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1002) all_111_1_59 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1002) can reduce 1001 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (1001) ~ (all_111_1_59 = 0)
% 32.95/9.71 | (1009) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (528), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1010) ~ (distinct_lines(all_1_1_1, all_1_2_2) = 0)
% 32.95/9.71 |
% 32.95/9.71 | Using (832) and (1010) yields:
% 32.95/9.71 | (136) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (832) distinct_lines(all_1_1_1, all_1_2_2) = 0
% 32.95/9.71 | (1013) all_111_1_59 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (1013), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1002) all_111_1_59 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1002) can reduce 1001 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (1001) ~ (all_111_1_59 = 0)
% 32.95/9.71 | (1017) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (500), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1018) all_151_0_65 = 0
% 32.95/9.71 |
% 32.95/9.71 | From (1018) and (277) follows:
% 32.95/9.71 | (1019) apart_point_and_line(all_1_4_4, all_1_1_1) = 0
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (501), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1020) ~ (apart_point_and_line(all_1_4_4, all_1_1_1) = 0)
% 32.95/9.71 |
% 32.95/9.71 | Using (1019) and (1020) yields:
% 32.95/9.71 | (136) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (1019) apart_point_and_line(all_1_4_4, all_1_1_1) = 0
% 32.95/9.71 | (1023) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 32.95/9.71 |
% 32.95/9.71 | Instantiating (1023) with all_1026_0_620, all_1026_1_621, all_1026_2_622 yields:
% 32.95/9.71 | (1024) distinct_points(all_1_3_3, all_1_4_4) = all_1026_2_622 & distinct_points(all_1_4_4, all_1_3_3) = all_1026_1_621 & distinct_points(all_1_4_4, all_1_4_4) = all_1026_0_620 & ( ~ (all_1026_2_622 = 0) | (all_1026_0_620 = 0 & all_1026_1_621 = 0))
% 32.95/9.71 |
% 32.95/9.71 | Applying alpha-rule on (1024) yields:
% 32.95/9.71 | (1025) distinct_points(all_1_3_3, all_1_4_4) = all_1026_2_622
% 32.95/9.71 | (1026) distinct_points(all_1_4_4, all_1_3_3) = all_1026_1_621
% 32.95/9.71 | (1027) distinct_points(all_1_4_4, all_1_4_4) = all_1026_0_620
% 32.95/9.71 | (1028) ~ (all_1026_2_622 = 0) | (all_1026_0_620 = 0 & all_1026_1_621 = 0)
% 32.95/9.71 |
% 32.95/9.71 | Instantiating formula (33) with all_1_3_3, all_1_4_4, all_1026_2_622, 0 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_1026_2_622, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 32.95/9.71 | (1029) all_1026_2_622 = 0
% 32.95/9.71 |
% 32.95/9.71 | Instantiating formula (33) with all_1_4_4, all_1_4_4, all_1026_0_620, all_287_0_126 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_1026_0_620, distinct_points(all_1_4_4, all_1_4_4) = all_287_0_126, yields:
% 32.95/9.71 | (1030) all_1026_0_620 = all_287_0_126
% 32.95/9.71 |
% 32.95/9.71 | Using (1027) and (141) yields:
% 32.95/9.71 | (1031) ~ (all_1026_0_620 = 0)
% 32.95/9.71 |
% 32.95/9.71 | Equations (1030) can reduce 1031 to:
% 32.95/9.71 | (997) ~ (all_287_0_126 = 0)
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (1028), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1033) ~ (all_1026_2_622 = 0)
% 32.95/9.71 |
% 32.95/9.71 | Equations (1029) can reduce 1033 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (1029) all_1026_2_622 = 0
% 32.95/9.71 | (1036) all_1026_0_620 = 0 & all_1026_1_621 = 0
% 32.95/9.71 |
% 32.95/9.71 | Applying alpha-rule on (1036) yields:
% 32.95/9.71 | (1037) all_1026_0_620 = 0
% 32.95/9.71 | (1038) all_1026_1_621 = 0
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (1037,1030) yields a new equation:
% 32.95/9.71 | (1039) all_287_0_126 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1039) can reduce 997 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (1041) ~ (all_151_0_65 = 0)
% 32.95/9.71 | (1042) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (328), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1043) ~ (all_176_2_85 = 0)
% 32.95/9.71 |
% 32.95/9.71 | Equations (831) can reduce 1043 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (831) all_176_2_85 = 0
% 32.95/9.71 | (1046) all_176_0_83 = 0 | all_176_1_84 = 0
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (1046), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1047) all_176_0_83 = 0
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (349,1047) yields a new equation:
% 32.95/9.71 | (1048) all_111_1_59 = 0
% 32.95/9.71 |
% 32.95/9.71 | Simplifying 1048 yields:
% 32.95/9.71 | (1002) all_111_1_59 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1002) can reduce 1001 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (1051) ~ (all_176_0_83 = 0)
% 32.95/9.71 | (1052) all_176_1_84 = 0
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (346,1052) yields a new equation:
% 32.95/9.71 | (1053) all_151_0_65 = 0
% 32.95/9.71 |
% 32.95/9.71 | Simplifying 1053 yields:
% 32.95/9.71 | (1018) all_151_0_65 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1018) can reduce 1041 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (1056) all_289_1_130 = 0
% 32.95/9.71 | (1057) ~ (all_289_2_131 = 0) | all_289_0_129 = 0
% 32.95/9.71 |
% 32.95/9.71 +-Applying beta-rule and splitting (1057), into two cases.
% 32.95/9.71 |-Branch one:
% 32.95/9.71 | (1058) ~ (all_289_2_131 = 0)
% 32.95/9.71 |
% 32.95/9.71 | Equations (987) can reduce 1058 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (987) all_289_2_131 = 0
% 32.95/9.71 | (1061) all_289_0_129 = 0
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (994,1061) yields a new equation:
% 32.95/9.71 | (1062) all_287_0_126 = 0
% 32.95/9.71 |
% 32.95/9.71 | Simplifying 1062 yields:
% 32.95/9.71 | (1039) all_287_0_126 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1039) can reduce 997 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (599) all_226_1_97 = 0
% 32.95/9.71 | (1066) all_226_0_96 = 0
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (1066,470) yields a new equation:
% 32.95/9.71 | (1067) all_72_0_31 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1067) can reduce 473 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (583) all_80_1_44 = 0
% 32.95/9.71 | (1070) all_80_0_43 = 0
% 32.95/9.71 |
% 32.95/9.71 | Combining equations (370,1070) yields a new equation:
% 32.95/9.71 | (1071) all_72_0_31 = 0
% 32.95/9.71 |
% 32.95/9.71 | Simplifying 1071 yields:
% 32.95/9.71 | (1067) all_72_0_31 = 0
% 32.95/9.71 |
% 32.95/9.71 | Equations (1067) can reduce 473 to:
% 32.95/9.71 | (88) $false
% 32.95/9.71 |
% 32.95/9.71 |-The branch is then unsatisfiable
% 32.95/9.71 |-Branch two:
% 32.95/9.71 | (712) all_72_1_32 = 0
% 32.95/9.71 | (1075) ~ (all_72_2_33 = 0) | all_72_0_31 = 0
% 32.95/9.71 |
% 32.95/9.72 +-Applying beta-rule and splitting (1075), into two cases.
% 32.95/9.72 |-Branch one:
% 32.95/9.72 | (1076) ~ (all_72_2_33 = 0)
% 32.95/9.72 |
% 32.95/9.72 | Equations (371) can reduce 1076 to:
% 32.95/9.72 | (88) $false
% 32.95/9.72 |
% 32.95/9.72 |-The branch is then unsatisfiable
% 32.95/9.72 |-Branch two:
% 32.95/9.72 | (371) all_72_2_33 = 0
% 32.95/9.72 | (1067) all_72_0_31 = 0
% 32.95/9.72 |
% 32.95/9.72 | Equations (1067) can reduce 473 to:
% 32.95/9.72 | (88) $false
% 32.95/9.72 |
% 32.95/9.72 |-The branch is then unsatisfiable
% 32.95/9.72 |-Branch two:
% 32.95/9.72 | (656) all_106_0_55 = 0
% 32.95/9.72 | (1082) ~ (all_106_2_57 = 0)
% 32.95/9.72 |
% 32.95/9.72 | Equations (373) can reduce 1082 to:
% 32.95/9.72 | (88) $false
% 32.95/9.72 |
% 32.95/9.72 |-The branch is then unsatisfiable
% 32.95/9.72 |-Branch two:
% 32.95/9.72 | (1084) all_20_0_12 = 0 & all_16_0_6 = 0
% 32.95/9.72 |
% 32.95/9.72 | Applying alpha-rule on (1084) yields:
% 32.95/9.72 | (445) all_20_0_12 = 0
% 32.95/9.72 | (209) all_16_0_6 = 0
% 32.95/9.72 |
% 32.95/9.72 | Equations (209) can reduce 119 to:
% 32.95/9.72 | (88) $false
% 32.95/9.72 |
% 32.95/9.72 |-The branch is then unsatisfiable
% 32.95/9.72 |-Branch two:
% 32.95/9.72 | (1084) all_20_0_12 = 0 & all_16_0_6 = 0
% 32.95/9.72 |
% 32.95/9.72 | Applying alpha-rule on (1084) yields:
% 32.95/9.72 | (445) all_20_0_12 = 0
% 32.95/9.72 | (209) all_16_0_6 = 0
% 32.95/9.72 |
% 32.95/9.72 | Equations (209) can reduce 119 to:
% 32.95/9.72 | (88) $false
% 32.95/9.72 |
% 32.95/9.72 |-The branch is then unsatisfiable
% 32.95/9.72 |-Branch two:
% 32.95/9.72 | (1092) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 32.95/9.72 | (209) all_16_0_6 = 0
% 32.95/9.72 |
% 32.95/9.72 | Equations (209) can reduce 119 to:
% 32.95/9.72 | (88) $false
% 32.95/9.72 |
% 32.95/9.72 |-The branch is then unsatisfiable
% 32.95/9.72 |-Branch two:
% 32.95/9.72 | (1095) all_22_1_16 = 0
% 32.95/9.72 | (1096) all_22_0_15 = 0
% 32.95/9.72 |
% 32.95/9.72 | Combining equations (116,1096) yields a new equation:
% 32.95/9.72 | (1097) all_16_0_6 = 0
% 32.95/9.72 |
% 32.95/9.72 | Simplifying 1097 yields:
% 32.95/9.72 | (209) all_16_0_6 = 0
% 32.95/9.72 |
% 32.95/9.72 | Equations (209) can reduce 119 to:
% 32.95/9.72 | (88) $false
% 32.95/9.72 |
% 32.95/9.72 |-The branch is then unsatisfiable
% 32.95/9.72 % SZS output end Proof for theBenchmark
% 32.95/9.72
% 32.95/9.72 9121ms
%------------------------------------------------------------------------------