TSTP Solution File: GEO187+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 03:48:23 EDT 2022
% Result : Theorem 13.93s 4.03s
% Output : Proof 31.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n015.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 17:03:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.58/0.58 ____ _
% 0.58/0.58 ___ / __ \_____(_)___ ________ __________
% 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.58
% 0.58/0.58 A Theorem Prover for First-Order Logic
% 0.58/0.58 (ePrincess v.1.0)
% 0.58/0.58
% 0.58/0.58 (c) Philipp Rümmer, 2009-2015
% 0.58/0.58 (c) Peter Backeman, 2014-2015
% 0.58/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.58 Bug reports to peter@backeman.se
% 0.58/0.58
% 0.58/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.58
% 0.58/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.78/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.73/0.96 Prover 0: Preprocessing ...
% 2.03/1.10 Prover 0: Warning: ignoring some quantifiers
% 2.03/1.11 Prover 0: Constructing countermodel ...
% 2.76/1.35 Prover 0: gave up
% 2.76/1.36 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.95/1.38 Prover 1: Preprocessing ...
% 3.29/1.46 Prover 1: Constructing countermodel ...
% 3.54/1.53 Prover 1: gave up
% 3.54/1.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.56/1.55 Prover 2: Preprocessing ...
% 3.96/1.67 Prover 2: Warning: ignoring some quantifiers
% 3.96/1.67 Prover 2: Constructing countermodel ...
% 4.84/1.86 Prover 2: gave up
% 4.84/1.86 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.84/1.87 Prover 3: Preprocessing ...
% 4.84/1.88 Prover 3: Warning: ignoring some quantifiers
% 4.84/1.89 Prover 3: Constructing countermodel ...
% 5.25/1.94 Prover 3: gave up
% 5.25/1.94 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.25/1.96 Prover 4: Preprocessing ...
% 5.64/2.02 Prover 4: Warning: ignoring some quantifiers
% 5.64/2.02 Prover 4: Constructing countermodel ...
% 10.43/3.15 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.43/3.17 Prover 5: Preprocessing ...
% 10.74/3.25 Prover 5: Constructing countermodel ...
% 13.93/4.03 Prover 5: proved (874ms)
% 13.93/4.03 Prover 4: stopped
% 13.93/4.03
% 13.93/4.03 No countermodel exists, formula is valid
% 13.93/4.03 % SZS status Theorem for theBenchmark
% 13.93/4.03
% 13.93/4.03 Generating proof ... found it (size 844)
% 30.30/8.41
% 30.30/8.41 % SZS output start Proof for theBenchmark
% 30.30/8.41 Assumed formulas after preprocessing and simplification:
% 30.30/8.41 | (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] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & ~ (v5 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) = v7 & apart_point_and_line(v3, v7) = v9 & apart_point_and_line(v2, v7) = v8 & apart_point_and_line(v1, v4) = v6 & apart_point_and_line(v0, v4) = v5 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & (v9 = 0 | v8 = 0))
% 30.54/8.47 | Applying alpha-rule on (0) yields:
% 30.54/8.47 | (1) ! [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)))))
% 30.54/8.47 | (2) ! [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)
% 30.54/8.47 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 30.54/8.47 | (4) ! [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)))))
% 30.54/8.47 | (5) ! [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)))
% 30.54/8.47 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 30.54/8.48 | (7) ! [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))
% 30.54/8.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 30.54/8.48 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 30.54/8.48 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & ~ (v5 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) = v7 & apart_point_and_line(v3, v7) = v9 & apart_point_and_line(v2, v7) = v8 & apart_point_and_line(v1, v4) = v6 & apart_point_and_line(v0, v4) = v5 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & (v9 = 0 | v8 = 0))
% 30.54/8.48 | (11) ! [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)))
% 30.54/8.48 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 30.54/8.48 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 30.54/8.48 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 30.54/8.48 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 30.54/8.48 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 30.54/8.48 | (17) ! [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))
% 30.54/8.48 | (18) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 30.54/8.48 | (19) ! [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))
% 30.83/8.48 | (20) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 30.83/8.48 | (21) ! [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))))
% 30.83/8.48 | (22) ! [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)))
% 30.83/8.48 | (23) ! [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)
% 30.83/8.48 | (24) ! [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)
% 30.83/8.49 | (25) ! [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)
% 30.83/8.49 | (26) ! [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)))))
% 30.83/8.49 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 30.83/8.49 | (28) ! [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))
% 30.83/8.49 | (29) ! [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))))
% 30.83/8.49 | (30) ! [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))))
% 30.83/8.49 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 30.83/8.49 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 30.83/8.49 | (33) ! [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)))
% 30.83/8.49 | (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)))))
% 30.83/8.49 | (35) ! [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))
% 30.83/8.49 | (36) ! [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))))
% 30.83/8.49 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 30.83/8.49 | (38) ! [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)))))
% 30.83/8.49 | (39) ! [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)))
% 30.83/8.49 | (40) ! [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)))
% 30.83/8.50 | (41) ! [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))
% 30.83/8.50 | (42) ! [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)))
% 30.83/8.50 | (43) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 30.83/8.50 | (44) ! [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)))
% 30.83/8.50 | (45) ! [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))))
% 30.83/8.50 | (46) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 30.83/8.50 |
% 30.83/8.50 | Instantiating (10) 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, all_1_6_6, all_1_7_7, all_1_8_8, all_1_9_9 yields:
% 30.83/8.50 | (47) ~ (all_1_3_3 = 0) & ~ (all_1_4_4 = 0) & line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5 & line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2 & apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1 & apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4 & distinct_points(all_1_7_7, all_1_6_6) = 0 & distinct_points(all_1_9_9, all_1_8_8) = 0 & (all_1_0_0 = 0 | all_1_1_1 = 0)
% 30.83/8.50 |
% 30.83/8.50 | Applying alpha-rule on (47) yields:
% 30.83/8.50 | (48) apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0
% 30.83/8.50 | (49) all_1_0_0 = 0 | all_1_1_1 = 0
% 30.83/8.50 | (50) line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2
% 30.83/8.50 | (51) ~ (all_1_3_3 = 0)
% 30.83/8.50 | (52) apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1
% 30.83/8.50 | (53) ~ (all_1_4_4 = 0)
% 30.83/8.50 | (54) distinct_points(all_1_9_9, all_1_8_8) = 0
% 30.83/8.50 | (55) line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5
% 30.83/8.50 | (56) apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3
% 30.83/8.50 | (57) apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4
% 30.83/8.50 | (58) distinct_points(all_1_7_7, all_1_6_6) = 0
% 30.83/8.50 |
% 30.83/8.50 | Instantiating formula (43) with all_1_7_7 yields:
% 30.83/8.50 | (59) ~ (distinct_points(all_1_7_7, all_1_7_7) = 0)
% 30.83/8.50 |
% 30.83/8.50 | Instantiating formula (43) with all_1_9_9 yields:
% 30.83/8.50 | (60) ~ (distinct_points(all_1_9_9, all_1_9_9) = 0)
% 30.83/8.50 |
% 30.83/8.50 | Instantiating formula (29) with all_1_2_2, all_1_6_6, all_1_8_8, all_1_9_9 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, yields:
% 30.83/8.50 | (61) ~ (apart_point_and_line(all_1_6_6, all_1_2_2) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_6_6, all_1_8_8) = v2 & distinct_points(all_1_6_6, all_1_9_9) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 30.83/8.50 |
% 30.83/8.50 | Instantiating formula (11) with all_1_3_3, all_1_3_3, all_1_5_5, all_1_5_5, all_1_8_8, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 30.83/8.50 | (62) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.50 |
% 30.83/8.50 | Instantiating formula (11) with all_1_4_4, all_1_3_3, all_1_5_5, all_1_5_5, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.50 | (63) all_1_3_3 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.50 |
% 30.83/8.50 | Instantiating formula (11) with all_1_3_3, all_1_4_4, all_1_5_5, all_1_5_5, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.50 | (64) all_1_3_3 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.50 |
% 30.83/8.50 | Instantiating formula (11) with all_1_4_4, all_1_4_4, all_1_5_5, all_1_5_5, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.50 | (65) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.51 |
% 30.83/8.51 | Instantiating formula (21) with 0, all_1_7_7, all_1_6_6, all_1_7_7 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 30.83/8.51 | (66) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_7_7, all_1_6_6) = v0 & apart_point_and_line(all_1_7_7, v0) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 30.83/8.51 |
% 30.83/8.51 | Instantiating formula (45) with 0, all_1_5_5, all_1_7_7, all_1_6_6, all_1_7_7 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 30.83/8.51 | (67) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & distinct_points(all_1_7_7, all_1_7_7) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 30.83/8.51 |
% 30.83/8.51 | Instantiating formula (21) with 0, all_1_9_9, all_1_8_8, all_1_9_9 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.51 | (68) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_9_9, all_1_8_8) = v0 & apart_point_and_line(all_1_9_9, v0) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 30.83/8.51 |
% 30.83/8.51 | Instantiating formula (45) with 0, all_1_2_2, all_1_9_9, all_1_8_8, all_1_9_9 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.51 | (69) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & distinct_points(all_1_9_9, all_1_9_9) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 30.83/8.51 |
% 30.83/8.51 | Instantiating formula (44) with all_1_3_3, all_1_3_3, all_1_5_5, all_1_5_5, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.51 | (70) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.51 |
% 30.83/8.51 | Instantiating formula (5) with all_1_4_4, all_1_4_4, all_1_5_5, all_1_5_5, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.51 | (71) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.51 |
% 30.83/8.51 | Instantiating (69) with all_16_0_10, all_16_1_11, all_16_2_12 yields:
% 30.83/8.51 | (72) apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11 & distinct_points(all_1_9_9, all_1_8_8) = all_16_2_12 & distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10 & ( ~ (all_16_1_11 = 0) | ~ (all_16_2_12 = 0) | all_16_0_10 = 0)
% 30.83/8.51 |
% 30.83/8.51 | Applying alpha-rule on (72) yields:
% 30.83/8.51 | (73) apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11
% 30.83/8.51 | (74) distinct_points(all_1_9_9, all_1_8_8) = all_16_2_12
% 30.83/8.51 | (75) distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10
% 30.83/8.51 | (76) ~ (all_16_1_11 = 0) | ~ (all_16_2_12 = 0) | all_16_0_10 = 0
% 30.83/8.51 |
% 30.83/8.51 | Instantiating (66) with all_18_0_13, all_18_1_14, all_18_2_15 yields:
% 30.83/8.51 | (77) line_connecting(all_1_7_7, all_1_6_6) = all_18_2_15 & apart_point_and_line(all_1_7_7, all_18_2_15) = all_18_1_14 & distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13 & ( ~ (all_18_1_14 = 0) | all_18_0_13 = 0)
% 30.83/8.51 |
% 30.83/8.51 | Applying alpha-rule on (77) yields:
% 30.83/8.51 | (78) line_connecting(all_1_7_7, all_1_6_6) = all_18_2_15
% 30.83/8.51 | (79) apart_point_and_line(all_1_7_7, all_18_2_15) = all_18_1_14
% 30.83/8.51 | (80) distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13
% 30.83/8.51 | (81) ~ (all_18_1_14 = 0) | all_18_0_13 = 0
% 30.83/8.51 |
% 30.83/8.51 | Instantiating (68) with all_20_0_16, all_20_1_17, all_20_2_18 yields:
% 30.83/8.51 | (82) line_connecting(all_1_9_9, all_1_8_8) = all_20_2_18 & apart_point_and_line(all_1_9_9, all_20_2_18) = all_20_1_17 & distinct_points(all_1_9_9, all_1_9_9) = all_20_0_16 & ( ~ (all_20_1_17 = 0) | all_20_0_16 = 0)
% 30.83/8.51 |
% 30.83/8.51 | Applying alpha-rule on (82) yields:
% 30.83/8.51 | (83) line_connecting(all_1_9_9, all_1_8_8) = all_20_2_18
% 30.83/8.51 | (84) apart_point_and_line(all_1_9_9, all_20_2_18) = all_20_1_17
% 30.83/8.51 | (85) distinct_points(all_1_9_9, all_1_9_9) = all_20_0_16
% 30.83/8.51 | (86) ~ (all_20_1_17 = 0) | all_20_0_16 = 0
% 30.83/8.51 |
% 30.83/8.51 | Instantiating (67) with all_22_0_19, all_22_1_20, all_22_2_21 yields:
% 30.83/8.51 | (87) apart_point_and_line(all_1_7_7, all_1_5_5) = all_22_1_20 & distinct_points(all_1_7_7, all_1_6_6) = all_22_2_21 & distinct_points(all_1_7_7, all_1_7_7) = all_22_0_19 & ( ~ (all_22_1_20 = 0) | ~ (all_22_2_21 = 0) | all_22_0_19 = 0)
% 30.83/8.51 |
% 30.83/8.51 | Applying alpha-rule on (87) yields:
% 30.83/8.51 | (88) apart_point_and_line(all_1_7_7, all_1_5_5) = all_22_1_20
% 30.83/8.51 | (89) distinct_points(all_1_7_7, all_1_6_6) = all_22_2_21
% 30.83/8.51 | (90) distinct_points(all_1_7_7, all_1_7_7) = all_22_0_19
% 30.83/8.51 | (91) ~ (all_22_1_20 = 0) | ~ (all_22_2_21 = 0) | all_22_0_19 = 0
% 30.83/8.51 |
% 30.83/8.51 +-Applying beta-rule and splitting (62), into two cases.
% 30.83/8.51 |-Branch one:
% 30.83/8.51 | (92) all_1_3_3 = 0
% 30.83/8.51 |
% 30.83/8.51 | Equations (92) can reduce 51 to:
% 30.83/8.51 | (93) $false
% 30.83/8.51 |
% 30.83/8.51 |-The branch is then unsatisfiable
% 30.83/8.51 |-Branch two:
% 30.83/8.51 | (51) ~ (all_1_3_3 = 0)
% 30.83/8.51 | (95) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.51 |
% 30.83/8.51 | Instantiating (95) with all_28_0_22, all_28_1_23, all_28_2_24, all_28_3_25 yields:
% 30.83/8.51 | (96) apart_point_and_line(all_1_8_8, all_1_5_5) = all_28_0_22 & apart_point_and_line(all_1_8_8, all_1_5_5) = all_28_1_23 & distinct_lines(all_1_5_5, all_1_5_5) = all_28_2_24 & distinct_points(all_1_8_8, all_1_8_8) = all_28_3_25 & ( ~ (all_28_2_24 = 0) | ~ (all_28_3_25 = 0) | all_28_0_22 = 0 | all_28_1_23 = 0)
% 30.83/8.52 |
% 30.83/8.52 | Applying alpha-rule on (96) yields:
% 30.83/8.52 | (97) distinct_lines(all_1_5_5, all_1_5_5) = all_28_2_24
% 30.83/8.52 | (98) distinct_points(all_1_8_8, all_1_8_8) = all_28_3_25
% 30.83/8.52 | (99) apart_point_and_line(all_1_8_8, all_1_5_5) = all_28_1_23
% 30.83/8.52 | (100) ~ (all_28_2_24 = 0) | ~ (all_28_3_25 = 0) | all_28_0_22 = 0 | all_28_1_23 = 0
% 30.83/8.52 | (101) apart_point_and_line(all_1_8_8, all_1_5_5) = all_28_0_22
% 30.83/8.52 |
% 30.83/8.52 +-Applying beta-rule and splitting (65), into two cases.
% 30.83/8.52 |-Branch one:
% 30.83/8.52 | (102) all_1_4_4 = 0
% 30.83/8.52 |
% 30.83/8.52 | Equations (102) can reduce 53 to:
% 30.83/8.52 | (93) $false
% 30.83/8.52 |
% 30.83/8.52 |-The branch is then unsatisfiable
% 30.83/8.52 |-Branch two:
% 30.83/8.52 | (53) ~ (all_1_4_4 = 0)
% 30.83/8.52 | (105) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.52 |
% 30.83/8.52 | Instantiating (105) with all_33_0_26, all_33_1_27, all_33_2_28, all_33_3_29 yields:
% 30.83/8.52 | (106) apart_point_and_line(all_1_9_9, all_1_5_5) = all_33_0_26 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_33_1_27 & distinct_lines(all_1_5_5, all_1_5_5) = all_33_2_28 & distinct_points(all_1_9_9, all_1_9_9) = all_33_3_29 & ( ~ (all_33_2_28 = 0) | ~ (all_33_3_29 = 0) | all_33_0_26 = 0 | all_33_1_27 = 0)
% 30.83/8.52 |
% 30.83/8.52 | Applying alpha-rule on (106) yields:
% 30.83/8.52 | (107) distinct_lines(all_1_5_5, all_1_5_5) = all_33_2_28
% 30.83/8.52 | (108) apart_point_and_line(all_1_9_9, all_1_5_5) = all_33_0_26
% 30.83/8.52 | (109) distinct_points(all_1_9_9, all_1_9_9) = all_33_3_29
% 30.83/8.52 | (110) ~ (all_33_2_28 = 0) | ~ (all_33_3_29 = 0) | all_33_0_26 = 0 | all_33_1_27 = 0
% 30.83/8.52 | (111) apart_point_and_line(all_1_9_9, all_1_5_5) = all_33_1_27
% 30.83/8.52 |
% 30.83/8.52 +-Applying beta-rule and splitting (70), into two cases.
% 30.83/8.52 |-Branch one:
% 30.83/8.52 | (92) all_1_3_3 = 0
% 30.83/8.52 |
% 30.83/8.52 | Equations (92) can reduce 51 to:
% 30.83/8.52 | (93) $false
% 30.83/8.52 |
% 30.83/8.52 |-The branch is then unsatisfiable
% 30.83/8.52 |-Branch two:
% 30.83/8.52 | (51) ~ (all_1_3_3 = 0)
% 30.83/8.52 | (115) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.52 |
% 30.83/8.52 | Instantiating (115) with all_38_0_30, all_38_1_31, all_38_2_32 yields:
% 30.83/8.52 | (116) apart_point_and_line(all_1_9_9, all_1_5_5) = all_38_0_30 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_38_1_31 & distinct_lines(all_1_5_5, all_1_5_5) = all_38_2_32 & ( ~ (all_38_2_32 = 0) | all_38_0_30 = 0 | all_38_1_31 = 0)
% 30.83/8.52 |
% 30.83/8.52 | Applying alpha-rule on (116) yields:
% 30.83/8.52 | (117) apart_point_and_line(all_1_9_9, all_1_5_5) = all_38_0_30
% 30.83/8.52 | (118) apart_point_and_line(all_1_9_9, all_1_5_5) = all_38_1_31
% 30.83/8.52 | (119) distinct_lines(all_1_5_5, all_1_5_5) = all_38_2_32
% 30.83/8.52 | (120) ~ (all_38_2_32 = 0) | all_38_0_30 = 0 | all_38_1_31 = 0
% 30.83/8.52 |
% 30.83/8.52 +-Applying beta-rule and splitting (71), into two cases.
% 30.83/8.52 |-Branch one:
% 30.83/8.52 | (102) all_1_4_4 = 0
% 30.83/8.52 |
% 30.83/8.52 | Equations (102) can reduce 53 to:
% 30.83/8.52 | (93) $false
% 30.83/8.52 |
% 30.83/8.52 |-The branch is then unsatisfiable
% 30.83/8.52 |-Branch two:
% 30.83/8.52 | (53) ~ (all_1_4_4 = 0)
% 30.83/8.52 | (124) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.52 |
% 30.83/8.52 | Instantiating (124) with all_43_0_33, all_43_1_34, all_43_2_35 yields:
% 30.83/8.52 | (125) apart_point_and_line(all_1_8_8, all_1_5_5) = all_43_0_33 & apart_point_and_line(all_1_8_8, all_1_5_5) = all_43_1_34 & distinct_lines(all_1_5_5, all_1_5_5) = all_43_2_35 & ( ~ (all_43_2_35 = 0) | all_43_0_33 = 0 | all_43_1_34 = 0)
% 30.83/8.52 |
% 30.83/8.52 | Applying alpha-rule on (125) yields:
% 30.83/8.52 | (126) apart_point_and_line(all_1_8_8, all_1_5_5) = all_43_0_33
% 30.83/8.52 | (127) apart_point_and_line(all_1_8_8, all_1_5_5) = all_43_1_34
% 30.83/8.52 | (128) distinct_lines(all_1_5_5, all_1_5_5) = all_43_2_35
% 30.83/8.52 | (129) ~ (all_43_2_35 = 0) | all_43_0_33 = 0 | all_43_1_34 = 0
% 30.83/8.52 |
% 30.83/8.52 +-Applying beta-rule and splitting (63), into two cases.
% 30.83/8.52 |-Branch one:
% 30.83/8.52 | (92) all_1_3_3 = 0
% 30.83/8.52 |
% 30.83/8.52 | Equations (92) can reduce 51 to:
% 30.83/8.52 | (93) $false
% 30.83/8.52 |
% 30.83/8.52 |-The branch is then unsatisfiable
% 30.83/8.52 |-Branch two:
% 30.83/8.52 | (51) ~ (all_1_3_3 = 0)
% 30.83/8.52 | (133) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.52 |
% 30.83/8.52 +-Applying beta-rule and splitting (64), into two cases.
% 30.83/8.52 |-Branch one:
% 30.83/8.52 | (92) all_1_3_3 = 0
% 30.83/8.52 |
% 30.83/8.52 | Equations (92) can reduce 51 to:
% 30.83/8.52 | (93) $false
% 30.83/8.52 |
% 30.83/8.52 |-The branch is then unsatisfiable
% 30.83/8.52 |-Branch two:
% 30.83/8.52 | (51) ~ (all_1_3_3 = 0)
% 30.83/8.52 | (137) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.52 |
% 30.83/8.52 +-Applying beta-rule and splitting (133), into two cases.
% 30.83/8.52 |-Branch one:
% 30.83/8.52 | (102) all_1_4_4 = 0
% 30.83/8.52 |
% 30.83/8.52 | Equations (102) can reduce 53 to:
% 30.83/8.52 | (93) $false
% 30.83/8.52 |
% 30.83/8.52 |-The branch is then unsatisfiable
% 30.83/8.52 |-Branch two:
% 30.83/8.52 | (53) ~ (all_1_4_4 = 0)
% 30.83/8.52 | (141) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.52 |
% 30.83/8.52 | Instantiating (141) with all_55_0_36, all_55_1_37, all_55_2_38, all_55_3_39 yields:
% 30.83/8.53 | (142) apart_point_and_line(all_1_8_8, all_1_5_5) = all_55_1_37 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_55_0_36 & distinct_lines(all_1_5_5, all_1_5_5) = all_55_2_38 & distinct_points(all_1_8_8, all_1_9_9) = all_55_3_39 & ( ~ (all_55_2_38 = 0) | ~ (all_55_3_39 = 0) | all_55_0_36 = 0 | all_55_1_37 = 0)
% 30.83/8.53 |
% 30.83/8.53 | Applying alpha-rule on (142) yields:
% 30.83/8.53 | (143) ~ (all_55_2_38 = 0) | ~ (all_55_3_39 = 0) | all_55_0_36 = 0 | all_55_1_37 = 0
% 30.83/8.53 | (144) distinct_lines(all_1_5_5, all_1_5_5) = all_55_2_38
% 30.83/8.53 | (145) apart_point_and_line(all_1_9_9, all_1_5_5) = all_55_0_36
% 30.83/8.53 | (146) apart_point_and_line(all_1_8_8, all_1_5_5) = all_55_1_37
% 30.83/8.53 | (147) distinct_points(all_1_8_8, all_1_9_9) = all_55_3_39
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (27) with all_1_7_7, all_1_6_6, all_18_2_15, all_1_5_5 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_18_2_15, line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, yields:
% 30.83/8.53 | (148) all_18_2_15 = all_1_5_5
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (27) with all_1_9_9, all_1_8_8, all_20_2_18, all_1_2_2 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_20_2_18, line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, yields:
% 30.83/8.53 | (149) all_20_2_18 = all_1_2_2
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_7_7, all_1_5_5, all_22_1_20, all_18_1_14 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_22_1_20, yields:
% 30.83/8.53 | (150) all_22_1_20 = all_18_1_14 | ~ (apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14)
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_43_0_33, all_1_3_3 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_43_0_33, apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 30.83/8.53 | (151) all_43_0_33 = all_1_3_3
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_43_1_34, all_55_1_37 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_55_1_37, apart_point_and_line(all_1_8_8, all_1_5_5) = all_43_1_34, yields:
% 30.83/8.53 | (152) all_55_1_37 = all_43_1_34
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_28_0_22, all_43_0_33 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_43_0_33, apart_point_and_line(all_1_8_8, all_1_5_5) = all_28_0_22, yields:
% 30.83/8.53 | (153) all_43_0_33 = all_28_0_22
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_28_0_22, all_43_1_34 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_43_1_34, apart_point_and_line(all_1_8_8, all_1_5_5) = all_28_0_22, yields:
% 30.83/8.53 | (154) all_43_1_34 = all_28_0_22
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_28_1_23, all_55_1_37 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_55_1_37, apart_point_and_line(all_1_8_8, all_1_5_5) = all_28_1_23, yields:
% 30.83/8.53 | (155) all_55_1_37 = all_28_1_23
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_9_9, all_1_2_2, all_16_1_11, all_20_1_17 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.53 | (156) all_20_1_17 = all_16_1_11 | ~ (apart_point_and_line(all_1_9_9, all_1_2_2) = all_20_1_17)
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_38_0_30, all_1_4_4 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_38_0_30, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.53 | (157) all_38_0_30 = all_1_4_4
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_38_0_30, all_55_0_36 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_55_0_36, apart_point_and_line(all_1_9_9, all_1_5_5) = all_38_0_30, yields:
% 30.83/8.53 | (158) all_55_0_36 = all_38_0_30
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_38_1_31, all_55_0_36 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_55_0_36, apart_point_and_line(all_1_9_9, all_1_5_5) = all_38_1_31, yields:
% 30.83/8.53 | (159) all_55_0_36 = all_38_1_31
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_33_0_26, all_38_0_30 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_38_0_30, apart_point_and_line(all_1_9_9, all_1_5_5) = all_33_0_26, yields:
% 30.83/8.53 | (160) all_38_0_30 = all_33_0_26
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_33_1_27, all_55_0_36 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_55_0_36, apart_point_and_line(all_1_9_9, all_1_5_5) = all_33_1_27, yields:
% 30.83/8.53 | (161) all_55_0_36 = all_33_1_27
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (37) with all_1_7_7, all_1_6_6, all_22_2_21, 0 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = all_22_2_21, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 30.83/8.53 | (162) all_22_2_21 = 0
% 30.83/8.53 |
% 30.83/8.53 | Using (90) and (59) yields:
% 30.83/8.53 | (163) ~ (all_22_0_19 = 0)
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (37) with all_1_7_7, all_1_7_7, all_18_0_13, all_22_0_19 and discharging atoms distinct_points(all_1_7_7, all_1_7_7) = all_22_0_19, distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13, yields:
% 30.83/8.53 | (164) all_22_0_19 = all_18_0_13
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (43) with all_1_8_8 yields:
% 30.83/8.53 | (165) ~ (distinct_points(all_1_8_8, all_1_8_8) = 0)
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (37) with all_1_9_9, all_1_8_8, all_16_2_12, 0 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_16_2_12, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.53 | (166) all_16_2_12 = 0
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (37) with all_1_9_9, all_1_9_9, all_20_0_16, all_33_3_29 and discharging atoms distinct_points(all_1_9_9, all_1_9_9) = all_33_3_29, distinct_points(all_1_9_9, all_1_9_9) = all_20_0_16, yields:
% 30.83/8.53 | (167) all_33_3_29 = all_20_0_16
% 30.83/8.53 |
% 30.83/8.53 | Using (85) and (60) yields:
% 30.83/8.53 | (168) ~ (all_20_0_16 = 0)
% 30.83/8.53 |
% 30.83/8.53 | Instantiating formula (37) with all_1_9_9, all_1_9_9, all_16_0_10, all_33_3_29 and discharging atoms distinct_points(all_1_9_9, all_1_9_9) = all_33_3_29, distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10, yields:
% 30.83/8.53 | (169) all_33_3_29 = all_16_0_10
% 30.83/8.53 |
% 30.83/8.53 | Combining equations (161,159) yields a new equation:
% 30.83/8.53 | (170) all_38_1_31 = all_33_1_27
% 30.83/8.53 |
% 30.83/8.53 | Combining equations (158,159) yields a new equation:
% 30.83/8.53 | (171) all_38_0_30 = all_38_1_31
% 30.83/8.53 |
% 30.83/8.53 | Simplifying 171 yields:
% 30.83/8.53 | (172) all_38_0_30 = all_38_1_31
% 30.83/8.53 |
% 30.83/8.53 | Combining equations (152,155) yields a new equation:
% 30.83/8.53 | (173) all_43_1_34 = all_28_1_23
% 30.83/8.53 |
% 30.83/8.53 | Simplifying 173 yields:
% 30.83/8.53 | (174) all_43_1_34 = all_28_1_23
% 30.83/8.53 |
% 30.83/8.53 | Combining equations (153,151) yields a new equation:
% 30.83/8.53 | (175) all_28_0_22 = all_1_3_3
% 30.83/8.53 |
% 30.83/8.53 | Simplifying 175 yields:
% 30.83/8.53 | (176) all_28_0_22 = all_1_3_3
% 30.83/8.53 |
% 30.83/8.53 | Combining equations (154,174) yields a new equation:
% 30.83/8.53 | (177) all_28_0_22 = all_28_1_23
% 30.83/8.54 |
% 30.83/8.54 | Simplifying 177 yields:
% 30.83/8.54 | (178) all_28_0_22 = all_28_1_23
% 30.83/8.54 |
% 30.83/8.54 | Combining equations (157,160) yields a new equation:
% 30.83/8.54 | (179) all_33_0_26 = all_1_4_4
% 30.83/8.54 |
% 30.83/8.54 | Combining equations (172,160) yields a new equation:
% 30.83/8.54 | (180) all_38_1_31 = all_33_0_26
% 30.83/8.54 |
% 30.83/8.54 | Simplifying 180 yields:
% 30.83/8.54 | (181) all_38_1_31 = all_33_0_26
% 30.83/8.54 |
% 30.83/8.54 | Combining equations (181,170) yields a new equation:
% 30.83/8.54 | (182) all_33_0_26 = all_33_1_27
% 30.83/8.54 |
% 30.83/8.54 | Simplifying 182 yields:
% 30.83/8.54 | (183) all_33_0_26 = all_33_1_27
% 30.83/8.54 |
% 30.83/8.54 | Combining equations (179,183) yields a new equation:
% 30.83/8.54 | (184) all_33_1_27 = all_1_4_4
% 30.83/8.54 |
% 30.83/8.54 | Combining equations (169,167) yields a new equation:
% 30.83/8.54 | (185) all_20_0_16 = all_16_0_10
% 30.83/8.54 |
% 30.83/8.54 | Combining equations (178,176) yields a new equation:
% 30.83/8.54 | (186) all_28_1_23 = all_1_3_3
% 30.83/8.54 |
% 30.83/8.54 | Simplifying 186 yields:
% 30.83/8.54 | (187) all_28_1_23 = all_1_3_3
% 30.83/8.54 |
% 30.83/8.54 | Equations (164) can reduce 163 to:
% 30.83/8.54 | (188) ~ (all_18_0_13 = 0)
% 30.83/8.54 |
% 30.83/8.54 | Equations (185) can reduce 168 to:
% 30.83/8.54 | (189) ~ (all_16_0_10 = 0)
% 30.83/8.54 |
% 30.83/8.54 | From (148) and (78) follows:
% 30.83/8.54 | (55) line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5
% 30.83/8.54 |
% 30.83/8.54 | From (149) and (83) follows:
% 30.83/8.54 | (50) line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2
% 30.83/8.54 |
% 30.83/8.54 | From (148) and (79) follows:
% 30.83/8.54 | (192) apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14
% 30.83/8.54 |
% 30.83/8.54 | From (187) and (99) follows:
% 30.83/8.54 | (56) apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3
% 30.83/8.54 |
% 30.83/8.54 | From (149) and (84) follows:
% 30.83/8.54 | (194) apart_point_and_line(all_1_9_9, all_1_2_2) = all_20_1_17
% 30.83/8.54 |
% 30.83/8.54 | From (184) and (111) follows:
% 30.83/8.54 | (57) apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4
% 30.83/8.54 |
% 30.83/8.54 | From (162) and (89) follows:
% 30.83/8.54 | (58) distinct_points(all_1_7_7, all_1_6_6) = 0
% 30.83/8.54 |
% 30.83/8.54 | From (164) and (90) follows:
% 30.83/8.54 | (80) distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13
% 30.83/8.54 |
% 30.83/8.54 | From (166) and (74) follows:
% 30.83/8.54 | (54) distinct_points(all_1_9_9, all_1_8_8) = 0
% 30.83/8.54 |
% 30.83/8.54 | From (185) and (85) follows:
% 30.83/8.54 | (75) distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10
% 30.83/8.54 |
% 30.83/8.54 +-Applying beta-rule and splitting (86), into two cases.
% 30.83/8.54 |-Branch one:
% 30.83/8.54 | (200) ~ (all_20_1_17 = 0)
% 30.83/8.54 |
% 30.83/8.54 +-Applying beta-rule and splitting (91), into two cases.
% 30.83/8.54 |-Branch one:
% 30.83/8.54 | (201) ~ (all_22_1_20 = 0)
% 30.83/8.54 |
% 30.83/8.54 +-Applying beta-rule and splitting (156), into two cases.
% 30.83/8.54 |-Branch one:
% 30.83/8.54 | (202) ~ (apart_point_and_line(all_1_9_9, all_1_2_2) = all_20_1_17)
% 30.83/8.54 |
% 30.83/8.54 | Using (194) and (202) yields:
% 30.83/8.54 | (203) $false
% 30.83/8.54 |
% 30.83/8.54 |-The branch is then unsatisfiable
% 30.83/8.54 |-Branch two:
% 30.83/8.54 | (194) apart_point_and_line(all_1_9_9, all_1_2_2) = all_20_1_17
% 30.83/8.54 | (205) all_20_1_17 = all_16_1_11
% 30.83/8.54 |
% 30.83/8.54 | Equations (205) can reduce 200 to:
% 30.83/8.54 | (206) ~ (all_16_1_11 = 0)
% 30.83/8.54 |
% 30.83/8.54 | From (205) and (194) follows:
% 30.83/8.54 | (73) apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11
% 30.83/8.54 |
% 30.83/8.54 +-Applying beta-rule and splitting (150), into two cases.
% 30.83/8.54 |-Branch one:
% 30.83/8.54 | (208) ~ (apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14)
% 30.83/8.54 |
% 30.83/8.54 | Using (192) and (208) yields:
% 30.83/8.54 | (203) $false
% 30.83/8.54 |
% 30.83/8.54 |-The branch is then unsatisfiable
% 30.83/8.54 |-Branch two:
% 30.83/8.54 | (192) apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14
% 30.83/8.54 | (211) all_22_1_20 = all_18_1_14
% 30.83/8.54 |
% 30.83/8.54 | Equations (211) can reduce 201 to:
% 30.83/8.54 | (212) ~ (all_18_1_14 = 0)
% 30.83/8.54 |
% 30.83/8.54 | From (211) and (88) follows:
% 30.83/8.54 | (192) apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14
% 30.83/8.54 |
% 30.83/8.54 | Using (98) and (165) yields:
% 30.83/8.54 | (214) ~ (all_28_3_25 = 0)
% 30.83/8.54 |
% 30.83/8.54 | Instantiating formula (23) with all_18_1_14, all_1_5_5, all_1_2_2, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 30.83/8.54 | (215) all_18_1_14 = 0 | ~ (apart_point_and_line(all_1_7_7, all_1_2_2) = 0) | distinct_lines(all_1_2_2, all_1_5_5) = 0
% 30.83/8.54 |
% 30.83/8.54 | Instantiating formula (11) with all_18_1_14, all_1_3_3, all_1_5_5, all_1_5_5, all_1_7_7, all_1_8_8 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 30.83/8.54 | (216) all_18_1_14 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.54 |
% 30.83/8.54 | Instantiating formula (11) with all_1_3_3, all_18_1_14, all_1_5_5, all_1_5_5, all_1_8_8, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 30.83/8.55 | (217) all_18_1_14 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (11) with all_18_1_14, all_1_4_4, all_1_5_5, all_1_5_5, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.55 | (218) all_18_1_14 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (11) with all_1_4_4, all_18_1_14, all_1_5_5, all_1_5_5, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.55 | (219) all_18_1_14 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (5) with all_18_1_14, all_18_1_14, all_1_5_5, all_1_5_5, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 30.83/8.55 | (220) all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (24) with all_16_1_11, all_1_9_9, all_1_2_2, all_1_6_6 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.55 | (221) all_16_1_11 = 0 | ~ (apart_point_and_line(all_1_6_6, all_1_2_2) = 0) | distinct_points(all_1_6_6, all_1_9_9) = 0
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (11) with all_16_1_11, all_1_3_3, all_1_2_2, all_1_5_5, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.55 | (222) all_16_1_11 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (11) with all_1_3_3, all_16_1_11, all_1_5_5, all_1_2_2, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.55 | (223) all_16_1_11 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (33) with all_16_1_11, all_1_3_3, all_1_5_5, all_1_2_2, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.55 | (224) all_16_1_11 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (33) with all_1_3_3, all_16_1_11, all_1_2_2, all_1_5_5, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.55 | (225) all_16_1_11 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (5) with all_16_1_11, all_1_4_4, all_1_2_2, all_1_5_5, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.55 | (226) all_16_1_11 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (5) with all_1_4_4, all_16_1_11, all_1_5_5, all_1_2_2, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.55 | (227) all_16_1_11 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (11) with all_16_1_11, all_1_4_4, all_1_2_2, all_1_5_5, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.55 | (228) all_16_1_11 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (11) with all_1_4_4, all_16_1_11, all_1_5_5, all_1_2_2, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.55 | (229) all_16_1_11 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.55 |
% 30.83/8.55 | Instantiating formula (33) with all_16_1_11, all_1_4_4, all_1_5_5, all_1_2_2, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.55 | (230) all_16_1_11 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (33) with all_1_4_4, all_16_1_11, all_1_2_2, all_1_5_5, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 30.83/8.56 | (231) all_16_1_11 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (11) with all_16_1_11, all_18_1_14, all_1_2_2, all_1_5_5, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.56 | (232) all_18_1_14 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (11) with all_18_1_14, all_16_1_11, all_1_5_5, all_1_2_2, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.56 | (233) all_18_1_14 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (33) with all_16_1_11, all_18_1_14, all_1_5_5, all_1_2_2, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.56 | (234) all_18_1_14 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (33) with all_18_1_14, all_16_1_11, all_1_2_2, all_1_5_5, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.56 | (235) all_18_1_14 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (5) with all_16_1_11, all_16_1_11, all_1_2_2, all_1_2_2, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.56 | (236) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (11) with all_16_1_11, all_16_1_11, all_1_2_2, all_1_2_2, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 30.83/8.56 | (237) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (13) with all_18_0_13, all_1_7_7, all_1_6_6, all_1_7_7 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = 0, distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13, yields:
% 30.83/8.56 | (238) all_18_0_13 = 0 | distinct_points(all_1_6_6, all_1_7_7) = 0
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (35) with all_18_0_13, 0, all_1_7_7, all_1_7_7, all_1_6_6 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = 0, distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13, yields:
% 30.83/8.56 | (239) all_18_0_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_6_6, all_1_7_7) = v1 & apart_point_and_line(all_1_7_7, v1) = v2 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (35) with all_18_0_13, all_18_0_13, all_1_7_7, all_1_7_7, all_1_7_7 and discharging atoms distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13, yields:
% 30.83/8.56 | (240) all_18_0_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_7_7, all_1_7_7) = v1 & apart_point_and_line(all_1_7_7, v1) = v2 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (21) with all_28_3_25, all_1_8_8, all_1_8_8, all_1_9_9 and discharging atoms distinct_points(all_1_8_8, all_1_8_8) = all_28_3_25, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 30.83/8.56 | (241) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_9_9, all_1_8_8) = v0 & apart_point_and_line(all_1_8_8, v0) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_28_3_25 = 0)))
% 30.83/8.56 |
% 30.83/8.56 | Instantiating formula (45) with all_28_3_25, all_1_2_2, all_1_8_8, all_1_8_8, all_1_9_9 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, distinct_points(all_1_8_8, all_1_8_8) = all_28_3_25, yields:
% 30.83/8.56 | (242) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v2 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_28_3_25 = 0)))
% 30.83/8.57 |
% 30.83/8.57 | Instantiating formula (13) with all_16_0_10, all_1_9_9, all_1_8_8, all_1_9_9 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = 0, distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10, yields:
% 30.83/8.57 | (243) all_16_0_10 = 0 | distinct_points(all_1_8_8, all_1_9_9) = 0
% 30.83/8.57 |
% 30.83/8.57 | Instantiating formula (35) with all_16_0_10, 0, all_1_9_9, all_1_9_9, all_1_8_8 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = 0, distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10, yields:
% 30.83/8.57 | (244) all_16_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_9_9) = v1 & apart_point_and_line(all_1_9_9, v1) = v2 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 30.83/8.57 |
% 30.83/8.57 | Instantiating formula (35) with all_16_0_10, all_16_0_10, all_1_9_9, all_1_9_9, all_1_9_9 and discharging atoms distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10, yields:
% 30.83/8.57 | (245) all_16_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_9_9, all_1_9_9) = v1 & apart_point_and_line(all_1_9_9, v1) = v2 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 30.83/8.57 |
% 30.83/8.57 | Instantiating (242) with all_98_0_40, all_98_1_41, all_98_2_42 yields:
% 30.83/8.57 | (246) apart_point_and_line(all_1_8_8, all_1_2_2) = all_98_1_41 & distinct_points(all_1_8_8, all_1_9_9) = all_98_0_40 & distinct_points(all_1_9_9, all_1_8_8) = all_98_2_42 & ( ~ (all_98_1_41 = 0) | ~ (all_98_2_42 = 0) | (all_98_0_40 = 0 & all_28_3_25 = 0))
% 30.83/8.57 |
% 30.83/8.57 | Applying alpha-rule on (246) yields:
% 30.83/8.57 | (247) apart_point_and_line(all_1_8_8, all_1_2_2) = all_98_1_41
% 30.83/8.57 | (248) distinct_points(all_1_8_8, all_1_9_9) = all_98_0_40
% 30.83/8.57 | (249) distinct_points(all_1_9_9, all_1_8_8) = all_98_2_42
% 30.83/8.57 | (250) ~ (all_98_1_41 = 0) | ~ (all_98_2_42 = 0) | (all_98_0_40 = 0 & all_28_3_25 = 0)
% 30.83/8.57 |
% 30.83/8.57 | Instantiating (241) with all_100_0_43, all_100_1_44, all_100_2_45 yields:
% 30.83/8.57 | (251) line_connecting(all_1_9_9, all_1_8_8) = all_100_2_45 & apart_point_and_line(all_1_8_8, all_100_2_45) = all_100_1_44 & distinct_points(all_1_8_8, all_1_9_9) = all_100_0_43 & ( ~ (all_100_1_44 = 0) | (all_100_0_43 = 0 & all_28_3_25 = 0))
% 30.83/8.57 |
% 30.83/8.57 | Applying alpha-rule on (251) yields:
% 30.83/8.57 | (252) line_connecting(all_1_9_9, all_1_8_8) = all_100_2_45
% 30.83/8.57 | (253) apart_point_and_line(all_1_8_8, all_100_2_45) = all_100_1_44
% 30.83/8.57 | (254) distinct_points(all_1_8_8, all_1_9_9) = all_100_0_43
% 30.83/8.57 | (255) ~ (all_100_1_44 = 0) | (all_100_0_43 = 0 & all_28_3_25 = 0)
% 30.83/8.57 |
% 30.83/8.57 +-Applying beta-rule and splitting (238), into two cases.
% 30.83/8.57 |-Branch one:
% 30.83/8.57 | (256) distinct_points(all_1_6_6, all_1_7_7) = 0
% 30.83/8.57 |
% 30.83/8.57 +-Applying beta-rule and splitting (245), into two cases.
% 30.83/8.57 |-Branch one:
% 30.83/8.57 | (257) all_16_0_10 = 0
% 30.83/8.57 |
% 30.83/8.57 | Equations (257) can reduce 189 to:
% 30.83/8.57 | (93) $false
% 30.83/8.57 |
% 30.83/8.57 |-The branch is then unsatisfiable
% 30.83/8.57 |-Branch two:
% 30.83/8.57 | (189) ~ (all_16_0_10 = 0)
% 30.83/8.57 | (260) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_9_9, all_1_9_9) = v1 & apart_point_and_line(all_1_9_9, v1) = v2 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 30.83/8.57 |
% 30.83/8.57 +-Applying beta-rule and splitting (243), into two cases.
% 30.83/8.57 |-Branch one:
% 30.83/8.57 | (261) distinct_points(all_1_8_8, all_1_9_9) = 0
% 30.83/8.57 |
% 30.83/8.57 +-Applying beta-rule and splitting (255), into two cases.
% 30.83/8.57 |-Branch one:
% 30.83/8.57 | (262) ~ (all_100_1_44 = 0)
% 30.83/8.57 |
% 30.83/8.57 +-Applying beta-rule and splitting (244), into two cases.
% 30.83/8.57 |-Branch one:
% 30.83/8.57 | (257) all_16_0_10 = 0
% 30.83/8.57 |
% 30.83/8.57 | Equations (257) can reduce 189 to:
% 30.83/8.57 | (93) $false
% 30.83/8.57 |
% 30.83/8.57 |-The branch is then unsatisfiable
% 30.83/8.57 |-Branch two:
% 30.83/8.57 | (189) ~ (all_16_0_10 = 0)
% 30.83/8.57 | (266) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_9_9) = v1 & apart_point_and_line(all_1_9_9, v1) = v2 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 30.83/8.57 |
% 30.83/8.57 | Instantiating (266) with all_127_0_52, all_127_1_53, all_127_2_54 yields:
% 30.83/8.57 | (267) line_connecting(all_1_8_8, all_1_9_9) = all_127_1_53 & apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52 & distinct_points(all_1_8_8, all_1_9_9) = all_127_2_54 & ( ~ (all_127_0_52 = 0) | ~ (all_127_2_54 = 0))
% 30.83/8.57 |
% 30.83/8.57 | Applying alpha-rule on (267) yields:
% 30.83/8.57 | (268) line_connecting(all_1_8_8, all_1_9_9) = all_127_1_53
% 30.83/8.57 | (269) apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52
% 30.83/8.57 | (270) distinct_points(all_1_8_8, all_1_9_9) = all_127_2_54
% 30.83/8.57 | (271) ~ (all_127_0_52 = 0) | ~ (all_127_2_54 = 0)
% 30.83/8.57 |
% 30.83/8.57 +-Applying beta-rule and splitting (220), into two cases.
% 30.83/8.57 |-Branch one:
% 30.83/8.57 | (272) all_18_1_14 = 0
% 30.83/8.57 |
% 30.83/8.57 | Equations (272) can reduce 212 to:
% 30.83/8.57 | (93) $false
% 30.83/8.57 |
% 30.83/8.57 |-The branch is then unsatisfiable
% 30.83/8.57 |-Branch two:
% 30.83/8.57 | (212) ~ (all_18_1_14 = 0)
% 30.83/8.57 | (275) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 30.83/8.57 |
% 30.83/8.57 | Instantiating (275) with all_132_0_55, all_132_1_56, all_132_2_57 yields:
% 31.29/8.58 | (276) apart_point_and_line(all_1_6_6, all_1_5_5) = all_132_0_55 & apart_point_and_line(all_1_6_6, all_1_5_5) = all_132_1_56 & distinct_lines(all_1_5_5, all_1_5_5) = all_132_2_57 & ( ~ (all_132_2_57 = 0) | all_132_0_55 = 0 | all_132_1_56 = 0)
% 31.29/8.58 |
% 31.29/8.58 | Applying alpha-rule on (276) yields:
% 31.29/8.58 | (277) apart_point_and_line(all_1_6_6, all_1_5_5) = all_132_0_55
% 31.29/8.58 | (278) apart_point_and_line(all_1_6_6, all_1_5_5) = all_132_1_56
% 31.29/8.58 | (279) distinct_lines(all_1_5_5, all_1_5_5) = all_132_2_57
% 31.29/8.58 | (280) ~ (all_132_2_57 = 0) | all_132_0_55 = 0 | all_132_1_56 = 0
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (236), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (281) all_16_1_11 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (281) can reduce 206 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.58 | (284) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (237), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (281) all_16_1_11 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (281) can reduce 206 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.58 | (288) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.58 |
% 31.29/8.58 | Instantiating (288) with all_142_0_61, all_142_1_62, all_142_2_63, all_142_3_64 yields:
% 31.29/8.58 | (289) apart_point_and_line(all_1_9_9, all_1_2_2) = all_142_0_61 & apart_point_and_line(all_1_9_9, all_1_2_2) = all_142_1_62 & distinct_lines(all_1_2_2, all_1_2_2) = all_142_2_63 & distinct_points(all_1_9_9, all_1_9_9) = all_142_3_64 & ( ~ (all_142_2_63 = 0) | ~ (all_142_3_64 = 0) | all_142_0_61 = 0 | all_142_1_62 = 0)
% 31.29/8.58 |
% 31.29/8.58 | Applying alpha-rule on (289) yields:
% 31.29/8.58 | (290) apart_point_and_line(all_1_9_9, all_1_2_2) = all_142_1_62
% 31.29/8.58 | (291) apart_point_and_line(all_1_9_9, all_1_2_2) = all_142_0_61
% 31.29/8.58 | (292) distinct_points(all_1_9_9, all_1_9_9) = all_142_3_64
% 31.29/8.58 | (293) distinct_lines(all_1_2_2, all_1_2_2) = all_142_2_63
% 31.29/8.58 | (294) ~ (all_142_2_63 = 0) | ~ (all_142_3_64 = 0) | all_142_0_61 = 0 | all_142_1_62 = 0
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (240), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (295) all_18_0_13 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (295) can reduce 188 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (188) ~ (all_18_0_13 = 0)
% 31.29/8.58 | (298) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_7_7, all_1_7_7) = v1 & apart_point_and_line(all_1_7_7, v1) = v2 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (239), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (295) all_18_0_13 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (295) can reduce 188 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (188) ~ (all_18_0_13 = 0)
% 31.29/8.58 | (302) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_6_6, all_1_7_7) = v1 & apart_point_and_line(all_1_7_7, v1) = v2 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 31.29/8.58 |
% 31.29/8.58 | Instantiating (302) with all_152_0_68, all_152_1_69, all_152_2_70 yields:
% 31.29/8.58 | (303) line_connecting(all_1_6_6, all_1_7_7) = all_152_1_69 & apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68 & distinct_points(all_1_6_6, all_1_7_7) = all_152_2_70 & ( ~ (all_152_0_68 = 0) | ~ (all_152_2_70 = 0))
% 31.29/8.58 |
% 31.29/8.58 | Applying alpha-rule on (303) yields:
% 31.29/8.58 | (304) line_connecting(all_1_6_6, all_1_7_7) = all_152_1_69
% 31.29/8.58 | (305) apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68
% 31.29/8.58 | (306) distinct_points(all_1_6_6, all_1_7_7) = all_152_2_70
% 31.29/8.58 | (307) ~ (all_152_0_68 = 0) | ~ (all_152_2_70 = 0)
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (232), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (272) all_18_1_14 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (272) can reduce 212 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (212) ~ (all_18_1_14 = 0)
% 31.29/8.58 | (311) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (233), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (272) all_18_1_14 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (272) can reduce 212 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (212) ~ (all_18_1_14 = 0)
% 31.29/8.58 | (315) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (224), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (281) all_16_1_11 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (281) can reduce 206 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.58 | (319) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (225), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (281) all_16_1_11 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (281) can reduce 206 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.58 | (323) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (226), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (281) all_16_1_11 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (281) can reduce 206 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.58 | (327) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.29/8.58 |
% 31.29/8.58 +-Applying beta-rule and splitting (227), into two cases.
% 31.29/8.58 |-Branch one:
% 31.29/8.58 | (281) all_16_1_11 = 0
% 31.29/8.58 |
% 31.29/8.58 | Equations (281) can reduce 206 to:
% 31.29/8.58 | (93) $false
% 31.29/8.58 |
% 31.29/8.58 |-The branch is then unsatisfiable
% 31.29/8.58 |-Branch two:
% 31.29/8.58 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.58 | (331) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (230), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (281) all_16_1_11 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (281) can reduce 206 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.59 | (335) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (234), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (272) all_18_1_14 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (272) can reduce 212 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (212) ~ (all_18_1_14 = 0)
% 31.29/8.59 | (339) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (228), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (281) all_16_1_11 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (281) can reduce 206 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.59 | (343) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (229), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (281) all_16_1_11 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (281) can reduce 206 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.59 | (347) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (231), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (281) all_16_1_11 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (281) can reduce 206 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.59 | (351) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (235), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (272) all_18_1_14 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (272) can reduce 212 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (212) ~ (all_18_1_14 = 0)
% 31.29/8.59 | (355) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (222), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (281) all_16_1_11 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (281) can reduce 206 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.59 | (359) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (223), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (281) all_16_1_11 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (281) can reduce 206 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (206) ~ (all_16_1_11 = 0)
% 31.29/8.59 | (363) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.29/8.59 |
% 31.29/8.59 +-Applying beta-rule and splitting (217), into two cases.
% 31.29/8.59 |-Branch one:
% 31.29/8.59 | (272) all_18_1_14 = 0
% 31.29/8.59 |
% 31.29/8.59 | Equations (272) can reduce 212 to:
% 31.29/8.59 | (93) $false
% 31.29/8.59 |
% 31.29/8.59 |-The branch is then unsatisfiable
% 31.29/8.59 |-Branch two:
% 31.29/8.59 | (212) ~ (all_18_1_14 = 0)
% 31.29/8.59 | (367) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.59 |
% 31.37/8.59 +-Applying beta-rule and splitting (218), into two cases.
% 31.37/8.59 |-Branch one:
% 31.37/8.59 | (272) all_18_1_14 = 0
% 31.37/8.59 |
% 31.37/8.59 | Equations (272) can reduce 212 to:
% 31.37/8.59 | (93) $false
% 31.37/8.59 |
% 31.37/8.59 |-The branch is then unsatisfiable
% 31.37/8.59 |-Branch two:
% 31.37/8.59 | (212) ~ (all_18_1_14 = 0)
% 31.37/8.59 | (371) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.59 |
% 31.37/8.59 +-Applying beta-rule and splitting (216), into two cases.
% 31.37/8.59 |-Branch one:
% 31.37/8.59 | (272) all_18_1_14 = 0
% 31.37/8.59 |
% 31.37/8.59 | Equations (272) can reduce 212 to:
% 31.37/8.59 | (93) $false
% 31.37/8.59 |
% 31.37/8.59 |-The branch is then unsatisfiable
% 31.37/8.59 |-Branch two:
% 31.37/8.59 | (212) ~ (all_18_1_14 = 0)
% 31.37/8.59 | (375) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.59 |
% 31.37/8.59 +-Applying beta-rule and splitting (219), into two cases.
% 31.37/8.59 |-Branch one:
% 31.37/8.59 | (272) all_18_1_14 = 0
% 31.37/8.59 |
% 31.37/8.59 | Equations (272) can reduce 212 to:
% 31.37/8.59 | (93) $false
% 31.37/8.59 |
% 31.37/8.59 |-The branch is then unsatisfiable
% 31.37/8.59 |-Branch two:
% 31.37/8.59 | (212) ~ (all_18_1_14 = 0)
% 31.37/8.59 | (379) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.59 |
% 31.37/8.59 +-Applying beta-rule and splitting (311), into two cases.
% 31.37/8.59 |-Branch one:
% 31.37/8.59 | (281) all_16_1_11 = 0
% 31.37/8.59 |
% 31.37/8.59 | Equations (281) can reduce 206 to:
% 31.37/8.59 | (93) $false
% 31.37/8.59 |
% 31.37/8.59 |-The branch is then unsatisfiable
% 31.37/8.59 |-Branch two:
% 31.37/8.59 | (206) ~ (all_16_1_11 = 0)
% 31.37/8.59 | (383) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.59 |
% 31.37/8.59 | Instantiating (383) with all_217_0_72, all_217_1_73, all_217_2_74, all_217_3_75 yields:
% 31.37/8.59 | (384) apart_point_and_line(all_1_7_7, all_1_2_2) = all_217_1_73 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_217_0_72 & distinct_lines(all_1_5_5, all_1_2_2) = all_217_2_74 & distinct_points(all_1_7_7, all_1_9_9) = all_217_3_75 & ( ~ (all_217_2_74 = 0) | ~ (all_217_3_75 = 0) | all_217_0_72 = 0 | all_217_1_73 = 0)
% 31.37/8.59 |
% 31.37/8.59 | Applying alpha-rule on (384) yields:
% 31.37/8.59 | (385) distinct_lines(all_1_5_5, all_1_2_2) = all_217_2_74
% 31.37/8.59 | (386) ~ (all_217_2_74 = 0) | ~ (all_217_3_75 = 0) | all_217_0_72 = 0 | all_217_1_73 = 0
% 31.37/8.59 | (387) apart_point_and_line(all_1_9_9, all_1_5_5) = all_217_0_72
% 31.37/8.59 | (388) apart_point_and_line(all_1_7_7, all_1_2_2) = all_217_1_73
% 31.37/8.59 | (389) distinct_points(all_1_7_7, all_1_9_9) = all_217_3_75
% 31.37/8.59 |
% 31.37/8.59 +-Applying beta-rule and splitting (315), into two cases.
% 31.37/8.59 |-Branch one:
% 31.37/8.59 | (281) all_16_1_11 = 0
% 31.37/8.59 |
% 31.37/8.59 | Equations (281) can reduce 206 to:
% 31.37/8.59 | (93) $false
% 31.37/8.59 |
% 31.37/8.59 |-The branch is then unsatisfiable
% 31.37/8.59 |-Branch two:
% 31.37/8.59 | (206) ~ (all_16_1_11 = 0)
% 31.37/8.59 | (393) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.59 |
% 31.37/8.59 | Instantiating (393) with all_222_0_76, all_222_1_77, all_222_2_78, all_222_3_79 yields:
% 31.37/8.59 | (394) apart_point_and_line(all_1_7_7, all_1_2_2) = all_222_0_76 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_222_1_77 & distinct_lines(all_1_2_2, all_1_5_5) = all_222_2_78 & distinct_points(all_1_9_9, all_1_7_7) = all_222_3_79 & ( ~ (all_222_2_78 = 0) | ~ (all_222_3_79 = 0) | all_222_0_76 = 0 | all_222_1_77 = 0)
% 31.37/8.60 |
% 31.37/8.60 | Applying alpha-rule on (394) yields:
% 31.37/8.60 | (395) distinct_lines(all_1_2_2, all_1_5_5) = all_222_2_78
% 31.37/8.60 | (396) ~ (all_222_2_78 = 0) | ~ (all_222_3_79 = 0) | all_222_0_76 = 0 | all_222_1_77 = 0
% 31.37/8.60 | (397) distinct_points(all_1_9_9, all_1_7_7) = all_222_3_79
% 31.37/8.60 | (398) apart_point_and_line(all_1_9_9, all_1_5_5) = all_222_1_77
% 31.37/8.60 | (399) apart_point_and_line(all_1_7_7, all_1_2_2) = all_222_0_76
% 31.37/8.60 |
% 31.37/8.60 +-Applying beta-rule and splitting (319), into two cases.
% 31.37/8.60 |-Branch one:
% 31.37/8.60 | (92) all_1_3_3 = 0
% 31.37/8.60 |
% 31.37/8.60 | Equations (92) can reduce 51 to:
% 31.37/8.60 | (93) $false
% 31.37/8.60 |
% 31.37/8.60 |-The branch is then unsatisfiable
% 31.37/8.60 |-Branch two:
% 31.37/8.60 | (51) ~ (all_1_3_3 = 0)
% 31.37/8.60 | (403) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.60 |
% 31.37/8.60 | Instantiating (403) with all_227_0_80, all_227_1_81, all_227_2_82, all_227_3_83 yields:
% 31.37/8.60 | (404) apart_point_and_line(all_1_8_8, all_1_2_2) = all_227_1_81 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_227_0_80 & distinct_lines(all_1_2_2, all_1_5_5) = all_227_2_82 & distinct_points(all_1_8_8, all_1_9_9) = all_227_3_83 & ( ~ (all_227_2_82 = 0) | ~ (all_227_3_83 = 0) | all_227_0_80 = 0 | all_227_1_81 = 0)
% 31.37/8.60 |
% 31.37/8.60 | Applying alpha-rule on (404) yields:
% 31.37/8.60 | (405) apart_point_and_line(all_1_9_9, all_1_5_5) = all_227_0_80
% 31.37/8.60 | (406) distinct_lines(all_1_2_2, all_1_5_5) = all_227_2_82
% 31.37/8.60 | (407) apart_point_and_line(all_1_8_8, all_1_2_2) = all_227_1_81
% 31.37/8.60 | (408) ~ (all_227_2_82 = 0) | ~ (all_227_3_83 = 0) | all_227_0_80 = 0 | all_227_1_81 = 0
% 31.37/8.60 | (409) distinct_points(all_1_8_8, all_1_9_9) = all_227_3_83
% 31.37/8.60 |
% 31.37/8.60 +-Applying beta-rule and splitting (323), into two cases.
% 31.37/8.60 |-Branch one:
% 31.37/8.60 | (92) all_1_3_3 = 0
% 31.37/8.60 |
% 31.37/8.60 | Equations (92) can reduce 51 to:
% 31.37/8.60 | (93) $false
% 31.37/8.60 |
% 31.37/8.60 |-The branch is then unsatisfiable
% 31.37/8.60 |-Branch two:
% 31.37/8.60 | (51) ~ (all_1_3_3 = 0)
% 31.37/8.60 | (413) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.60 |
% 31.37/8.60 | Instantiating (413) with all_232_0_84, all_232_1_85, all_232_2_86, all_232_3_87 yields:
% 31.37/8.60 | (414) apart_point_and_line(all_1_8_8, all_1_2_2) = all_232_0_84 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_232_1_85 & distinct_lines(all_1_5_5, all_1_2_2) = all_232_2_86 & distinct_points(all_1_9_9, all_1_8_8) = all_232_3_87 & ( ~ (all_232_2_86 = 0) | ~ (all_232_3_87 = 0) | all_232_0_84 = 0 | all_232_1_85 = 0)
% 31.37/8.60 |
% 31.37/8.60 | Applying alpha-rule on (414) yields:
% 31.37/8.60 | (415) distinct_lines(all_1_5_5, all_1_2_2) = all_232_2_86
% 31.37/8.60 | (416) ~ (all_232_2_86 = 0) | ~ (all_232_3_87 = 0) | all_232_0_84 = 0 | all_232_1_85 = 0
% 31.37/8.60 | (417) distinct_points(all_1_9_9, all_1_8_8) = all_232_3_87
% 31.37/8.60 | (418) apart_point_and_line(all_1_9_9, all_1_5_5) = all_232_1_85
% 31.37/8.60 | (419) apart_point_and_line(all_1_8_8, all_1_2_2) = all_232_0_84
% 31.37/8.60 |
% 31.37/8.60 +-Applying beta-rule and splitting (327), into two cases.
% 31.37/8.60 |-Branch one:
% 31.37/8.60 | (102) all_1_4_4 = 0
% 31.37/8.60 |
% 31.37/8.60 | Equations (102) can reduce 53 to:
% 31.37/8.60 | (93) $false
% 31.37/8.60 |
% 31.37/8.60 |-The branch is then unsatisfiable
% 31.37/8.60 |-Branch two:
% 31.37/8.60 | (53) ~ (all_1_4_4 = 0)
% 31.37/8.60 | (423) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.37/8.60 |
% 31.37/8.60 | Instantiating (423) with all_237_0_88, all_237_1_89, all_237_2_90 yields:
% 31.37/8.60 | (424) apart_point_and_line(all_1_8_8, all_1_2_2) = all_237_0_88 & apart_point_and_line(all_1_8_8, all_1_5_5) = all_237_1_89 & distinct_lines(all_1_5_5, all_1_2_2) = all_237_2_90 & ( ~ (all_237_2_90 = 0) | all_237_0_88 = 0 | all_237_1_89 = 0)
% 31.37/8.60 |
% 31.37/8.60 | Applying alpha-rule on (424) yields:
% 31.37/8.60 | (425) apart_point_and_line(all_1_8_8, all_1_2_2) = all_237_0_88
% 31.37/8.60 | (426) apart_point_and_line(all_1_8_8, all_1_5_5) = all_237_1_89
% 31.37/8.60 | (427) distinct_lines(all_1_5_5, all_1_2_2) = all_237_2_90
% 31.37/8.60 | (428) ~ (all_237_2_90 = 0) | all_237_0_88 = 0 | all_237_1_89 = 0
% 31.37/8.60 |
% 31.37/8.60 +-Applying beta-rule and splitting (331), into two cases.
% 31.37/8.60 |-Branch one:
% 31.37/8.60 | (102) all_1_4_4 = 0
% 31.37/8.60 |
% 31.37/8.60 | Equations (102) can reduce 53 to:
% 31.37/8.60 | (93) $false
% 31.37/8.60 |
% 31.37/8.60 |-The branch is then unsatisfiable
% 31.37/8.60 |-Branch two:
% 31.37/8.60 | (53) ~ (all_1_4_4 = 0)
% 31.37/8.60 | (432) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.37/8.60 |
% 31.37/8.60 | Instantiating (432) with all_242_0_91, all_242_1_92, all_242_2_93 yields:
% 31.37/8.60 | (433) apart_point_and_line(all_1_8_8, all_1_2_2) = all_242_1_92 & apart_point_and_line(all_1_8_8, all_1_5_5) = all_242_0_91 & distinct_lines(all_1_2_2, all_1_5_5) = all_242_2_93 & ( ~ (all_242_2_93 = 0) | all_242_0_91 = 0 | all_242_1_92 = 0)
% 31.37/8.60 |
% 31.37/8.60 | Applying alpha-rule on (433) yields:
% 31.37/8.60 | (434) apart_point_and_line(all_1_8_8, all_1_2_2) = all_242_1_92
% 31.37/8.60 | (435) apart_point_and_line(all_1_8_8, all_1_5_5) = all_242_0_91
% 31.37/8.60 | (436) distinct_lines(all_1_2_2, all_1_5_5) = all_242_2_93
% 31.37/8.60 | (437) ~ (all_242_2_93 = 0) | all_242_0_91 = 0 | all_242_1_92 = 0
% 31.37/8.60 |
% 31.37/8.60 +-Applying beta-rule and splitting (335), into two cases.
% 31.37/8.60 |-Branch one:
% 31.37/8.60 | (102) all_1_4_4 = 0
% 31.37/8.60 |
% 31.37/8.60 | Equations (102) can reduce 53 to:
% 31.37/8.60 | (93) $false
% 31.37/8.60 |
% 31.37/8.60 |-The branch is then unsatisfiable
% 31.37/8.60 |-Branch two:
% 31.37/8.60 | (53) ~ (all_1_4_4 = 0)
% 31.37/8.60 | (441) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.60 |
% 31.37/8.60 | Instantiating (441) with all_247_0_94, all_247_1_95, all_247_2_96, all_247_3_97 yields:
% 31.37/8.60 | (442) apart_point_and_line(all_1_9_9, all_1_2_2) = all_247_1_95 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_247_0_94 & distinct_lines(all_1_2_2, all_1_5_5) = all_247_2_96 & distinct_points(all_1_9_9, all_1_9_9) = all_247_3_97 & ( ~ (all_247_2_96 = 0) | ~ (all_247_3_97 = 0) | all_247_0_94 = 0 | all_247_1_95 = 0)
% 31.37/8.60 |
% 31.37/8.60 | Applying alpha-rule on (442) yields:
% 31.37/8.60 | (443) apart_point_and_line(all_1_9_9, all_1_2_2) = all_247_1_95
% 31.37/8.60 | (444) apart_point_and_line(all_1_9_9, all_1_5_5) = all_247_0_94
% 31.37/8.60 | (445) distinct_lines(all_1_2_2, all_1_5_5) = all_247_2_96
% 31.37/8.60 | (446) ~ (all_247_2_96 = 0) | ~ (all_247_3_97 = 0) | all_247_0_94 = 0 | all_247_1_95 = 0
% 31.37/8.60 | (447) distinct_points(all_1_9_9, all_1_9_9) = all_247_3_97
% 31.37/8.60 |
% 31.37/8.60 +-Applying beta-rule and splitting (339), into two cases.
% 31.37/8.60 |-Branch one:
% 31.37/8.60 | (281) all_16_1_11 = 0
% 31.37/8.60 |
% 31.37/8.60 | Equations (281) can reduce 206 to:
% 31.37/8.60 | (93) $false
% 31.37/8.60 |
% 31.37/8.60 |-The branch is then unsatisfiable
% 31.37/8.60 |-Branch two:
% 31.37/8.60 | (206) ~ (all_16_1_11 = 0)
% 31.37/8.60 | (451) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.60 |
% 31.37/8.60 | Instantiating (451) with all_252_0_98, all_252_1_99, all_252_2_100, all_252_3_101 yields:
% 31.37/8.60 | (452) apart_point_and_line(all_1_7_7, all_1_2_2) = all_252_1_99 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_252_0_98 & distinct_lines(all_1_2_2, all_1_5_5) = all_252_2_100 & distinct_points(all_1_7_7, all_1_9_9) = all_252_3_101 & ( ~ (all_252_2_100 = 0) | ~ (all_252_3_101 = 0) | all_252_0_98 = 0 | all_252_1_99 = 0)
% 31.37/8.60 |
% 31.37/8.60 | Applying alpha-rule on (452) yields:
% 31.37/8.60 | (453) apart_point_and_line(all_1_7_7, all_1_2_2) = all_252_1_99
% 31.37/8.60 | (454) distinct_lines(all_1_2_2, all_1_5_5) = all_252_2_100
% 31.37/8.60 | (455) ~ (all_252_2_100 = 0) | ~ (all_252_3_101 = 0) | all_252_0_98 = 0 | all_252_1_99 = 0
% 31.37/8.60 | (456) distinct_points(all_1_7_7, all_1_9_9) = all_252_3_101
% 31.37/8.60 | (457) apart_point_and_line(all_1_9_9, all_1_5_5) = all_252_0_98
% 31.37/8.60 |
% 31.37/8.60 +-Applying beta-rule and splitting (343), into two cases.
% 31.37/8.60 |-Branch one:
% 31.37/8.60 | (102) all_1_4_4 = 0
% 31.37/8.60 |
% 31.37/8.60 | Equations (102) can reduce 53 to:
% 31.37/8.60 | (93) $false
% 31.37/8.60 |
% 31.37/8.60 |-The branch is then unsatisfiable
% 31.37/8.60 |-Branch two:
% 31.37/8.60 | (53) ~ (all_1_4_4 = 0)
% 31.37/8.60 | (461) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.60 |
% 31.37/8.60 | Instantiating (461) with all_257_0_102, all_257_1_103, all_257_2_104, all_257_3_105 yields:
% 31.37/8.60 | (462) apart_point_and_line(all_1_9_9, all_1_2_2) = all_257_1_103 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_257_0_102 & distinct_lines(all_1_5_5, all_1_2_2) = all_257_2_104 & distinct_points(all_1_9_9, all_1_9_9) = all_257_3_105 & ( ~ (all_257_2_104 = 0) | ~ (all_257_3_105 = 0) | all_257_0_102 = 0 | all_257_1_103 = 0)
% 31.37/8.60 |
% 31.37/8.60 | Applying alpha-rule on (462) yields:
% 31.37/8.60 | (463) distinct_lines(all_1_5_5, all_1_2_2) = all_257_2_104
% 31.37/8.60 | (464) distinct_points(all_1_9_9, all_1_9_9) = all_257_3_105
% 31.37/8.60 | (465) apart_point_and_line(all_1_9_9, all_1_2_2) = all_257_1_103
% 31.37/8.60 | (466) ~ (all_257_2_104 = 0) | ~ (all_257_3_105 = 0) | all_257_0_102 = 0 | all_257_1_103 = 0
% 31.37/8.60 | (467) apart_point_and_line(all_1_9_9, all_1_5_5) = all_257_0_102
% 31.37/8.60 |
% 31.37/8.60 +-Applying beta-rule and splitting (347), into two cases.
% 31.37/8.60 |-Branch one:
% 31.37/8.60 | (102) all_1_4_4 = 0
% 31.37/8.60 |
% 31.37/8.60 | Equations (102) can reduce 53 to:
% 31.37/8.60 | (93) $false
% 31.37/8.60 |
% 31.37/8.60 |-The branch is then unsatisfiable
% 31.37/8.60 |-Branch two:
% 31.37/8.61 | (53) ~ (all_1_4_4 = 0)
% 31.37/8.61 | (471) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.61 |
% 31.37/8.61 | Instantiating (471) with all_262_0_106, all_262_1_107, all_262_2_108, all_262_3_109 yields:
% 31.37/8.61 | (472) apart_point_and_line(all_1_9_9, all_1_2_2) = all_262_0_106 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_262_1_107 & distinct_lines(all_1_2_2, all_1_5_5) = all_262_2_108 & distinct_points(all_1_9_9, all_1_9_9) = all_262_3_109 & ( ~ (all_262_2_108 = 0) | ~ (all_262_3_109 = 0) | all_262_0_106 = 0 | all_262_1_107 = 0)
% 31.37/8.61 |
% 31.37/8.61 | Applying alpha-rule on (472) yields:
% 31.37/8.61 | (473) ~ (all_262_2_108 = 0) | ~ (all_262_3_109 = 0) | all_262_0_106 = 0 | all_262_1_107 = 0
% 31.37/8.61 | (474) distinct_points(all_1_9_9, all_1_9_9) = all_262_3_109
% 31.37/8.61 | (475) apart_point_and_line(all_1_9_9, all_1_2_2) = all_262_0_106
% 31.37/8.61 | (476) distinct_lines(all_1_2_2, all_1_5_5) = all_262_2_108
% 31.37/8.61 | (477) apart_point_and_line(all_1_9_9, all_1_5_5) = all_262_1_107
% 31.37/8.61 |
% 31.37/8.61 +-Applying beta-rule and splitting (351), into two cases.
% 31.37/8.61 |-Branch one:
% 31.37/8.61 | (102) all_1_4_4 = 0
% 31.37/8.61 |
% 31.37/8.61 | Equations (102) can reduce 53 to:
% 31.37/8.61 | (93) $false
% 31.37/8.61 |
% 31.37/8.61 |-The branch is then unsatisfiable
% 31.37/8.61 |-Branch two:
% 31.37/8.61 | (53) ~ (all_1_4_4 = 0)
% 31.37/8.61 | (481) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.61 |
% 31.37/8.61 | Instantiating (481) with all_267_0_110, all_267_1_111, all_267_2_112, all_267_3_113 yields:
% 31.37/8.61 | (482) apart_point_and_line(all_1_9_9, all_1_2_2) = all_267_0_110 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_267_1_111 & distinct_lines(all_1_5_5, all_1_2_2) = all_267_2_112 & distinct_points(all_1_9_9, all_1_9_9) = all_267_3_113 & ( ~ (all_267_2_112 = 0) | ~ (all_267_3_113 = 0) | all_267_0_110 = 0 | all_267_1_111 = 0)
% 31.37/8.61 |
% 31.37/8.61 | Applying alpha-rule on (482) yields:
% 31.37/8.61 | (483) distinct_lines(all_1_5_5, all_1_2_2) = all_267_2_112
% 31.37/8.61 | (484) apart_point_and_line(all_1_9_9, all_1_2_2) = all_267_0_110
% 31.37/8.61 | (485) distinct_points(all_1_9_9, all_1_9_9) = all_267_3_113
% 31.37/8.61 | (486) ~ (all_267_2_112 = 0) | ~ (all_267_3_113 = 0) | all_267_0_110 = 0 | all_267_1_111 = 0
% 31.37/8.61 | (487) apart_point_and_line(all_1_9_9, all_1_5_5) = all_267_1_111
% 31.37/8.61 |
% 31.37/8.61 +-Applying beta-rule and splitting (355), into two cases.
% 31.37/8.61 |-Branch one:
% 31.37/8.61 | (281) all_16_1_11 = 0
% 31.37/8.61 |
% 31.37/8.61 | Equations (281) can reduce 206 to:
% 31.37/8.61 | (93) $false
% 31.37/8.61 |
% 31.37/8.61 |-The branch is then unsatisfiable
% 31.37/8.61 |-Branch two:
% 31.37/8.61 | (206) ~ (all_16_1_11 = 0)
% 31.37/8.61 | (491) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.61 |
% 31.37/8.61 | Instantiating (491) with all_272_0_114, all_272_1_115, all_272_2_116, all_272_3_117 yields:
% 31.37/8.61 | (492) apart_point_and_line(all_1_7_7, all_1_2_2) = all_272_0_114 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_272_1_115 & distinct_lines(all_1_5_5, all_1_2_2) = all_272_2_116 & distinct_points(all_1_9_9, all_1_7_7) = all_272_3_117 & ( ~ (all_272_2_116 = 0) | ~ (all_272_3_117 = 0) | all_272_0_114 = 0 | all_272_1_115 = 0)
% 31.37/8.61 |
% 31.37/8.61 | Applying alpha-rule on (492) yields:
% 31.37/8.61 | (493) distinct_points(all_1_9_9, all_1_7_7) = all_272_3_117
% 31.37/8.61 | (494) ~ (all_272_2_116 = 0) | ~ (all_272_3_117 = 0) | all_272_0_114 = 0 | all_272_1_115 = 0
% 31.37/8.61 | (495) apart_point_and_line(all_1_9_9, all_1_5_5) = all_272_1_115
% 31.37/8.61 | (496) apart_point_and_line(all_1_7_7, all_1_2_2) = all_272_0_114
% 31.37/8.61 | (497) distinct_lines(all_1_5_5, all_1_2_2) = all_272_2_116
% 31.37/8.61 |
% 31.37/8.61 +-Applying beta-rule and splitting (359), into two cases.
% 31.37/8.61 |-Branch one:
% 31.37/8.61 | (92) all_1_3_3 = 0
% 31.37/8.61 |
% 31.37/8.61 | Equations (92) can reduce 51 to:
% 31.37/8.61 | (93) $false
% 31.37/8.61 |
% 31.37/8.61 |-The branch is then unsatisfiable
% 31.37/8.61 |-Branch two:
% 31.37/8.61 | (51) ~ (all_1_3_3 = 0)
% 31.37/8.61 | (501) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.61 |
% 31.37/8.61 | Instantiating (501) with all_277_0_118, all_277_1_119, all_277_2_120, all_277_3_121 yields:
% 31.37/8.61 | (502) apart_point_and_line(all_1_8_8, all_1_2_2) = all_277_1_119 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_277_0_118 & distinct_lines(all_1_5_5, all_1_2_2) = all_277_2_120 & distinct_points(all_1_8_8, all_1_9_9) = all_277_3_121 & ( ~ (all_277_2_120 = 0) | ~ (all_277_3_121 = 0) | all_277_0_118 = 0 | all_277_1_119 = 0)
% 31.37/8.61 |
% 31.37/8.61 | Applying alpha-rule on (502) yields:
% 31.37/8.61 | (503) apart_point_and_line(all_1_8_8, all_1_2_2) = all_277_1_119
% 31.37/8.61 | (504) apart_point_and_line(all_1_9_9, all_1_5_5) = all_277_0_118
% 31.37/8.61 | (505) distinct_points(all_1_8_8, all_1_9_9) = all_277_3_121
% 31.37/8.61 | (506) distinct_lines(all_1_5_5, all_1_2_2) = all_277_2_120
% 31.37/8.61 | (507) ~ (all_277_2_120 = 0) | ~ (all_277_3_121 = 0) | all_277_0_118 = 0 | all_277_1_119 = 0
% 31.37/8.61 |
% 31.37/8.61 +-Applying beta-rule and splitting (363), into two cases.
% 31.37/8.61 |-Branch one:
% 31.37/8.61 | (92) all_1_3_3 = 0
% 31.37/8.61 |
% 31.37/8.61 | Equations (92) can reduce 51 to:
% 31.37/8.61 | (93) $false
% 31.37/8.61 |
% 31.37/8.61 |-The branch is then unsatisfiable
% 31.37/8.61 |-Branch two:
% 31.37/8.61 | (51) ~ (all_1_3_3 = 0)
% 31.37/8.61 | (511) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.61 |
% 31.37/8.61 | Instantiating (511) with all_282_0_122, all_282_1_123, all_282_2_124, all_282_3_125 yields:
% 31.37/8.61 | (512) apart_point_and_line(all_1_8_8, all_1_2_2) = all_282_0_122 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_282_1_123 & distinct_lines(all_1_2_2, all_1_5_5) = all_282_2_124 & distinct_points(all_1_9_9, all_1_8_8) = all_282_3_125 & ( ~ (all_282_2_124 = 0) | ~ (all_282_3_125 = 0) | all_282_0_122 = 0 | all_282_1_123 = 0)
% 31.37/8.61 |
% 31.37/8.61 | Applying alpha-rule on (512) yields:
% 31.37/8.61 | (513) distinct_points(all_1_9_9, all_1_8_8) = all_282_3_125
% 31.37/8.61 | (514) apart_point_and_line(all_1_9_9, all_1_5_5) = all_282_1_123
% 31.37/8.61 | (515) apart_point_and_line(all_1_8_8, all_1_2_2) = all_282_0_122
% 31.37/8.61 | (516) ~ (all_282_2_124 = 0) | ~ (all_282_3_125 = 0) | all_282_0_122 = 0 | all_282_1_123 = 0
% 31.37/8.61 | (517) distinct_lines(all_1_2_2, all_1_5_5) = all_282_2_124
% 31.37/8.61 |
% 31.37/8.61 +-Applying beta-rule and splitting (367), into two cases.
% 31.37/8.61 |-Branch one:
% 31.37/8.61 | (92) all_1_3_3 = 0
% 31.37/8.61 |
% 31.37/8.61 | Equations (92) can reduce 51 to:
% 31.37/8.61 | (93) $false
% 31.37/8.61 |
% 31.37/8.61 |-The branch is then unsatisfiable
% 31.37/8.61 |-Branch two:
% 31.37/8.61 | (51) ~ (all_1_3_3 = 0)
% 31.37/8.61 | (521) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.61 |
% 31.37/8.61 | Instantiating (521) with all_287_0_126, all_287_1_127, all_287_2_128, all_287_3_129 yields:
% 31.37/8.61 | (522) apart_point_and_line(all_1_7_7, all_1_5_5) = all_287_1_127 & apart_point_and_line(all_1_8_8, all_1_5_5) = all_287_0_126 & distinct_lines(all_1_5_5, all_1_5_5) = all_287_2_128 & distinct_points(all_1_7_7, all_1_8_8) = all_287_3_129 & ( ~ (all_287_2_128 = 0) | ~ (all_287_3_129 = 0) | all_287_0_126 = 0 | all_287_1_127 = 0)
% 31.37/8.61 |
% 31.37/8.61 | Applying alpha-rule on (522) yields:
% 31.37/8.61 | (523) ~ (all_287_2_128 = 0) | ~ (all_287_3_129 = 0) | all_287_0_126 = 0 | all_287_1_127 = 0
% 31.37/8.61 | (524) distinct_lines(all_1_5_5, all_1_5_5) = all_287_2_128
% 31.37/8.61 | (525) apart_point_and_line(all_1_8_8, all_1_5_5) = all_287_0_126
% 31.37/8.61 | (526) apart_point_and_line(all_1_7_7, all_1_5_5) = all_287_1_127
% 31.37/8.61 | (527) distinct_points(all_1_7_7, all_1_8_8) = all_287_3_129
% 31.37/8.61 |
% 31.37/8.61 +-Applying beta-rule and splitting (371), into two cases.
% 31.37/8.61 |-Branch one:
% 31.37/8.61 | (102) all_1_4_4 = 0
% 31.37/8.61 |
% 31.37/8.61 | Equations (102) can reduce 53 to:
% 31.37/8.61 | (93) $false
% 31.37/8.61 |
% 31.37/8.61 |-The branch is then unsatisfiable
% 31.37/8.61 |-Branch two:
% 31.37/8.61 | (53) ~ (all_1_4_4 = 0)
% 31.37/8.61 | (531) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.37/8.61 |
% 31.37/8.61 | Instantiating (531) with all_292_0_130, all_292_1_131, all_292_2_132, all_292_3_133 yields:
% 31.37/8.61 | (532) apart_point_and_line(all_1_7_7, all_1_5_5) = all_292_0_130 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_292_1_131 & distinct_lines(all_1_5_5, all_1_5_5) = all_292_2_132 & distinct_points(all_1_9_9, all_1_7_7) = all_292_3_133 & ( ~ (all_292_2_132 = 0) | ~ (all_292_3_133 = 0) | all_292_0_130 = 0 | all_292_1_131 = 0)
% 31.37/8.61 |
% 31.37/8.61 | Applying alpha-rule on (532) yields:
% 31.37/8.61 | (533) apart_point_and_line(all_1_9_9, all_1_5_5) = all_292_1_131
% 31.37/8.61 | (534) apart_point_and_line(all_1_7_7, all_1_5_5) = all_292_0_130
% 31.37/8.61 | (535) ~ (all_292_2_132 = 0) | ~ (all_292_3_133 = 0) | all_292_0_130 = 0 | all_292_1_131 = 0
% 31.37/8.61 | (536) distinct_lines(all_1_5_5, all_1_5_5) = all_292_2_132
% 31.48/8.61 | (537) distinct_points(all_1_9_9, all_1_7_7) = all_292_3_133
% 31.48/8.61 |
% 31.48/8.61 +-Applying beta-rule and splitting (375), into two cases.
% 31.48/8.61 |-Branch one:
% 31.48/8.61 | (92) all_1_3_3 = 0
% 31.48/8.61 |
% 31.48/8.61 | Equations (92) can reduce 51 to:
% 31.48/8.61 | (93) $false
% 31.48/8.61 |
% 31.48/8.61 |-The branch is then unsatisfiable
% 31.48/8.61 |-Branch two:
% 31.48/8.61 | (51) ~ (all_1_3_3 = 0)
% 31.48/8.61 | (541) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.48/8.61 |
% 31.48/8.61 | Instantiating (541) with all_297_0_134, all_297_1_135, all_297_2_136, all_297_3_137 yields:
% 31.48/8.61 | (542) apart_point_and_line(all_1_7_7, all_1_5_5) = all_297_0_134 & apart_point_and_line(all_1_8_8, all_1_5_5) = all_297_1_135 & distinct_lines(all_1_5_5, all_1_5_5) = all_297_2_136 & distinct_points(all_1_8_8, all_1_7_7) = all_297_3_137 & ( ~ (all_297_2_136 = 0) | ~ (all_297_3_137 = 0) | all_297_0_134 = 0 | all_297_1_135 = 0)
% 31.48/8.61 |
% 31.48/8.61 | Applying alpha-rule on (542) yields:
% 31.48/8.61 | (543) ~ (all_297_2_136 = 0) | ~ (all_297_3_137 = 0) | all_297_0_134 = 0 | all_297_1_135 = 0
% 31.48/8.61 | (544) apart_point_and_line(all_1_8_8, all_1_5_5) = all_297_1_135
% 31.48/8.61 | (545) distinct_lines(all_1_5_5, all_1_5_5) = all_297_2_136
% 31.48/8.61 | (546) distinct_points(all_1_8_8, all_1_7_7) = all_297_3_137
% 31.48/8.61 | (547) apart_point_and_line(all_1_7_7, all_1_5_5) = all_297_0_134
% 31.48/8.61 |
% 31.48/8.61 +-Applying beta-rule and splitting (379), into two cases.
% 31.48/8.61 |-Branch one:
% 31.48/8.61 | (102) all_1_4_4 = 0
% 31.48/8.61 |
% 31.48/8.61 | Equations (102) can reduce 53 to:
% 31.48/8.61 | (93) $false
% 31.48/8.61 |
% 31.48/8.61 |-The branch is then unsatisfiable
% 31.48/8.61 |-Branch two:
% 31.48/8.61 | (53) ~ (all_1_4_4 = 0)
% 31.48/8.61 | (551) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.48/8.61 |
% 31.48/8.61 | Instantiating (551) with all_302_0_138, all_302_1_139, all_302_2_140, all_302_3_141 yields:
% 31.48/8.61 | (552) apart_point_and_line(all_1_7_7, all_1_5_5) = all_302_1_139 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_302_0_138 & distinct_lines(all_1_5_5, all_1_5_5) = all_302_2_140 & distinct_points(all_1_7_7, all_1_9_9) = all_302_3_141 & ( ~ (all_302_2_140 = 0) | ~ (all_302_3_141 = 0) | all_302_0_138 = 0 | all_302_1_139 = 0)
% 31.48/8.62 |
% 31.48/8.62 | Applying alpha-rule on (552) yields:
% 31.48/8.62 | (553) distinct_points(all_1_7_7, all_1_9_9) = all_302_3_141
% 31.48/8.62 | (554) distinct_lines(all_1_5_5, all_1_5_5) = all_302_2_140
% 31.48/8.62 | (555) apart_point_and_line(all_1_7_7, all_1_5_5) = all_302_1_139
% 31.48/8.62 | (556) apart_point_and_line(all_1_9_9, all_1_5_5) = all_302_0_138
% 31.48/8.62 | (557) ~ (all_302_2_140 = 0) | ~ (all_302_3_141 = 0) | all_302_0_138 = 0 | all_302_1_139 = 0
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (27) with all_1_9_9, all_1_8_8, all_100_2_45, all_1_2_2 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_100_2_45, line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, yields:
% 31.48/8.62 | (558) all_100_2_45 = all_1_2_2
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_6_6, all_1_5_5, all_132_1_56, all_1_0_0 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_132_1_56, yields:
% 31.48/8.62 | (559) all_132_1_56 = all_1_0_0 | ~ (apart_point_and_line(all_1_6_6, all_1_5_5) = all_1_0_0)
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_7_7, all_1_2_2, all_252_1_99, all_1_1_1 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_252_1_99, apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, yields:
% 31.48/8.62 | (560) all_252_1_99 = all_1_1_1
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_7_7, all_1_2_2, all_252_1_99, all_272_0_114 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_272_0_114, apart_point_and_line(all_1_7_7, all_1_2_2) = all_252_1_99, yields:
% 31.48/8.62 | (561) all_272_0_114 = all_252_1_99
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_7_7, all_1_2_2, all_222_0_76, all_272_0_114 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_272_0_114, apart_point_and_line(all_1_7_7, all_1_2_2) = all_222_0_76, yields:
% 31.48/8.62 | (562) all_272_0_114 = all_222_0_76
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_7_7, all_1_2_2, all_217_1_73, all_252_1_99 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_252_1_99, apart_point_and_line(all_1_7_7, all_1_2_2) = all_217_1_73, yields:
% 31.48/8.62 | (563) all_252_1_99 = all_217_1_73
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_7_7, all_1_5_5, all_297_0_134, all_18_1_14 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_297_0_134, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 31.48/8.62 | (564) all_297_0_134 = all_18_1_14
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_7_7, all_1_5_5, all_297_0_134, all_302_1_139 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_302_1_139, apart_point_and_line(all_1_7_7, all_1_5_5) = all_297_0_134, yields:
% 31.48/8.62 | (565) all_302_1_139 = all_297_0_134
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_7_7, all_1_5_5, all_292_0_130, all_302_1_139 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_302_1_139, apart_point_and_line(all_1_7_7, all_1_5_5) = all_292_0_130, yields:
% 31.48/8.62 | (566) all_302_1_139 = all_292_0_130
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_7_7, all_1_5_5, all_287_1_127, all_297_0_134 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_297_0_134, apart_point_and_line(all_1_7_7, all_1_5_5) = all_287_1_127, yields:
% 31.48/8.62 | (567) all_297_0_134 = all_287_1_127
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_2_2, all_277_1_119, all_100_1_44 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_277_1_119, yields:
% 31.48/8.62 | (568) all_277_1_119 = all_100_1_44 | ~ (apart_point_and_line(all_1_8_8, all_1_2_2) = all_100_1_44)
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_2_2, all_277_1_119, all_282_0_122 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_282_0_122, apart_point_and_line(all_1_8_8, all_1_2_2) = all_277_1_119, yields:
% 31.48/8.62 | (569) all_282_0_122 = all_277_1_119
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_2_2, all_242_1_92, all_282_0_122 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_282_0_122, apart_point_and_line(all_1_8_8, all_1_2_2) = all_242_1_92, yields:
% 31.48/8.62 | (570) all_282_0_122 = all_242_1_92
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_2_2, all_237_0_88, all_282_0_122 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_282_0_122, apart_point_and_line(all_1_8_8, all_1_2_2) = all_237_0_88, yields:
% 31.48/8.62 | (571) all_282_0_122 = all_237_0_88
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_2_2, all_98_1_41, all_242_1_92 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_242_1_92, apart_point_and_line(all_1_8_8, all_1_2_2) = all_98_1_41, yields:
% 31.48/8.62 | (572) all_242_1_92 = all_98_1_41
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_287_0_126, all_297_1_135 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_297_1_135, apart_point_and_line(all_1_8_8, all_1_5_5) = all_287_0_126, yields:
% 31.48/8.62 | (573) all_297_1_135 = all_287_0_126
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_242_0_91, all_1_3_3 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_242_0_91, apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 31.48/8.62 | (574) all_242_0_91 = all_1_3_3
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_242_0_91, all_287_0_126 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_287_0_126, apart_point_and_line(all_1_8_8, all_1_5_5) = all_242_0_91, yields:
% 31.48/8.62 | (575) all_287_0_126 = all_242_0_91
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_8_8, all_1_5_5, all_237_1_89, all_297_1_135 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_297_1_135, apart_point_and_line(all_1_8_8, all_1_5_5) = all_237_1_89, yields:
% 31.48/8.62 | (576) all_297_1_135 = all_237_1_89
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_9_9, all_1_2_2, all_262_0_106, all_267_0_110 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_267_0_110, apart_point_and_line(all_1_9_9, all_1_2_2) = all_262_0_106, yields:
% 31.48/8.62 | (577) all_267_0_110 = all_262_0_106
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_9_9, all_1_2_2, all_257_1_103, all_267_0_110 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_267_0_110, apart_point_and_line(all_1_9_9, all_1_2_2) = all_257_1_103, yields:
% 31.48/8.62 | (578) all_267_0_110 = all_257_1_103
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_9_9, all_1_2_2, all_247_1_95, all_16_1_11 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_247_1_95, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.48/8.62 | (579) all_247_1_95 = all_16_1_11
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_9_9, all_1_2_2, all_247_1_95, all_257_1_103 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_257_1_103, apart_point_and_line(all_1_9_9, all_1_2_2) = all_247_1_95, yields:
% 31.48/8.62 | (580) all_257_1_103 = all_247_1_95
% 31.48/8.62 |
% 31.48/8.62 | Instantiating formula (9) with all_1_9_9, all_1_2_2, all_142_0_61, all_267_0_110 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_267_0_110, apart_point_and_line(all_1_9_9, all_1_2_2) = all_142_0_61, yields:
% 31.48/8.62 | (581) all_267_0_110 = all_142_0_61
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_2_2, all_142_1_62, all_247_1_95 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_247_1_95, apart_point_and_line(all_1_9_9, all_1_2_2) = all_142_1_62, yields:
% 31.51/8.62 | (582) all_247_1_95 = all_142_1_62
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_302_0_138, all_1_4_4 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_302_0_138, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 31.51/8.62 | (583) all_302_0_138 = all_1_4_4
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_292_1_131, all_302_0_138 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_302_0_138, apart_point_and_line(all_1_9_9, all_1_5_5) = all_292_1_131, yields:
% 31.51/8.62 | (584) all_302_0_138 = all_292_1_131
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_272_1_115, all_277_0_118 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_277_0_118, apart_point_and_line(all_1_9_9, all_1_5_5) = all_272_1_115, yields:
% 31.51/8.62 | (585) all_277_0_118 = all_272_1_115
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_267_1_111, all_272_1_115 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_272_1_115, apart_point_and_line(all_1_9_9, all_1_5_5) = all_267_1_111, yields:
% 31.51/8.62 | (586) all_272_1_115 = all_267_1_111
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_262_1_107, all_267_1_111 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_267_1_111, apart_point_and_line(all_1_9_9, all_1_5_5) = all_262_1_107, yields:
% 31.51/8.62 | (587) all_267_1_111 = all_262_1_107
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_257_0_102, all_262_1_107 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_262_1_107, apart_point_and_line(all_1_9_9, all_1_5_5) = all_257_0_102, yields:
% 31.51/8.62 | (588) all_262_1_107 = all_257_0_102
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_252_0_98, all_282_1_123 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_282_1_123, apart_point_and_line(all_1_9_9, all_1_5_5) = all_252_0_98, yields:
% 31.51/8.62 | (589) all_282_1_123 = all_252_0_98
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_252_0_98, all_257_0_102 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_257_0_102, apart_point_and_line(all_1_9_9, all_1_5_5) = all_252_0_98, yields:
% 31.51/8.62 | (590) all_257_0_102 = all_252_0_98
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_247_0_94, all_282_1_123 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_282_1_123, apart_point_and_line(all_1_9_9, all_1_5_5) = all_247_0_94, yields:
% 31.51/8.62 | (591) all_282_1_123 = all_247_0_94
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_232_1_85, all_282_1_123 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_282_1_123, apart_point_and_line(all_1_9_9, all_1_5_5) = all_232_1_85, yields:
% 31.51/8.62 | (592) all_282_1_123 = all_232_1_85
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_227_0_80, all_292_1_131 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_292_1_131, apart_point_and_line(all_1_9_9, all_1_5_5) = all_227_0_80, yields:
% 31.51/8.62 | (593) all_292_1_131 = all_227_0_80
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_227_0_80, all_232_1_85 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_232_1_85, apart_point_and_line(all_1_9_9, all_1_5_5) = all_227_0_80, yields:
% 31.51/8.62 | (594) all_232_1_85 = all_227_0_80
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_222_1_77, all_277_0_118 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_277_0_118, apart_point_and_line(all_1_9_9, all_1_5_5) = all_222_1_77, yields:
% 31.51/8.62 | (595) all_277_0_118 = all_222_1_77
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (9) with all_1_9_9, all_1_5_5, all_217_0_72, all_227_0_80 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_227_0_80, apart_point_and_line(all_1_9_9, all_1_5_5) = all_217_0_72, yields:
% 31.51/8.62 | (596) all_227_0_80 = all_217_0_72
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (6) with all_1_2_2, all_1_5_5, all_262_2_108, all_282_2_124 and discharging atoms distinct_lines(all_1_2_2, all_1_5_5) = all_282_2_124, distinct_lines(all_1_2_2, all_1_5_5) = all_262_2_108, yields:
% 31.51/8.62 | (597) all_282_2_124 = all_262_2_108
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (6) with all_1_2_2, all_1_5_5, all_252_2_100, all_262_2_108 and discharging atoms distinct_lines(all_1_2_2, all_1_5_5) = all_262_2_108, distinct_lines(all_1_2_2, all_1_5_5) = all_252_2_100, yields:
% 31.51/8.62 | (598) all_262_2_108 = all_252_2_100
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (6) with all_1_2_2, all_1_5_5, all_247_2_96, all_252_2_100 and discharging atoms distinct_lines(all_1_2_2, all_1_5_5) = all_252_2_100, distinct_lines(all_1_2_2, all_1_5_5) = all_247_2_96, yields:
% 31.51/8.62 | (599) all_252_2_100 = all_247_2_96
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (6) with all_1_2_2, all_1_5_5, all_242_2_93, all_282_2_124 and discharging atoms distinct_lines(all_1_2_2, all_1_5_5) = all_282_2_124, distinct_lines(all_1_2_2, all_1_5_5) = all_242_2_93, yields:
% 31.51/8.62 | (600) all_282_2_124 = all_242_2_93
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (6) with all_1_2_2, all_1_5_5, all_227_2_82, all_247_2_96 and discharging atoms distinct_lines(all_1_2_2, all_1_5_5) = all_247_2_96, distinct_lines(all_1_2_2, all_1_5_5) = all_227_2_82, yields:
% 31.51/8.62 | (601) all_247_2_96 = all_227_2_82
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (6) with all_1_2_2, all_1_5_5, all_222_2_78, all_247_2_96 and discharging atoms distinct_lines(all_1_2_2, all_1_5_5) = all_247_2_96, distinct_lines(all_1_2_2, all_1_5_5) = all_222_2_78, yields:
% 31.51/8.62 | (602) all_247_2_96 = all_222_2_78
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_6_6, all_1_7_7, 0, all_152_2_70 and discharging atoms distinct_points(all_1_6_6, all_1_7_7) = all_152_2_70, distinct_points(all_1_6_6, all_1_7_7) = 0, yields:
% 31.51/8.62 | (603) all_152_2_70 = 0
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_8_8, all_1_9_9, all_227_3_83, all_277_3_121 and discharging atoms distinct_points(all_1_8_8, all_1_9_9) = all_277_3_121, distinct_points(all_1_8_8, all_1_9_9) = all_227_3_83, yields:
% 31.51/8.62 | (604) all_277_3_121 = all_227_3_83
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_8_8, all_1_9_9, all_127_2_54, all_277_3_121 and discharging atoms distinct_points(all_1_8_8, all_1_9_9) = all_277_3_121, distinct_points(all_1_8_8, all_1_9_9) = all_127_2_54, yields:
% 31.51/8.62 | (605) all_277_3_121 = all_127_2_54
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_8_8, all_1_9_9, all_100_0_43, all_227_3_83 and discharging atoms distinct_points(all_1_8_8, all_1_9_9) = all_227_3_83, distinct_points(all_1_8_8, all_1_9_9) = all_100_0_43, yields:
% 31.51/8.62 | (606) all_227_3_83 = all_100_0_43
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_8_8, all_1_9_9, all_98_0_40, all_277_3_121 and discharging atoms distinct_points(all_1_8_8, all_1_9_9) = all_277_3_121, distinct_points(all_1_8_8, all_1_9_9) = all_98_0_40, yields:
% 31.51/8.62 | (607) all_277_3_121 = all_98_0_40
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_8_8, all_1_9_9, 0, all_227_3_83 and discharging atoms distinct_points(all_1_8_8, all_1_9_9) = all_227_3_83, distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 31.51/8.62 | (608) all_227_3_83 = 0
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_9_9, all_1_7_7, all_272_3_117, all_292_3_133 and discharging atoms distinct_points(all_1_9_9, all_1_7_7) = all_292_3_133, distinct_points(all_1_9_9, all_1_7_7) = all_272_3_117, yields:
% 31.51/8.62 | (609) all_292_3_133 = all_272_3_117
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_9_9, all_1_7_7, all_222_3_79, all_292_3_133 and discharging atoms distinct_points(all_1_9_9, all_1_7_7) = all_292_3_133, distinct_points(all_1_9_9, all_1_7_7) = all_222_3_79, yields:
% 31.51/8.62 | (610) all_292_3_133 = all_222_3_79
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_9_9, all_1_8_8, all_282_3_125, 0 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_282_3_125, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 31.51/8.62 | (611) all_282_3_125 = 0
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_9_9, all_1_8_8, all_232_3_87, all_282_3_125 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_282_3_125, distinct_points(all_1_9_9, all_1_8_8) = all_232_3_87, yields:
% 31.51/8.62 | (612) all_282_3_125 = all_232_3_87
% 31.51/8.62 |
% 31.51/8.62 | Instantiating formula (37) with all_1_9_9, all_1_8_8, all_98_2_42, all_282_3_125 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_282_3_125, distinct_points(all_1_9_9, all_1_8_8) = all_98_2_42, yields:
% 31.51/8.62 | (613) all_282_3_125 = all_98_2_42
% 31.51/8.62 |
% 31.51/8.62 | Combining equations (584,583) yields a new equation:
% 31.51/8.62 | (614) all_292_1_131 = all_1_4_4
% 31.51/8.62 |
% 31.51/8.62 | Simplifying 614 yields:
% 31.51/8.62 | (615) all_292_1_131 = all_1_4_4
% 31.51/8.62 |
% 31.51/8.62 | Combining equations (565,566) yields a new equation:
% 31.51/8.62 | (616) all_297_0_134 = all_292_0_130
% 31.51/8.62 |
% 31.51/8.62 | Simplifying 616 yields:
% 31.51/8.62 | (617) all_297_0_134 = all_292_0_130
% 31.51/8.62 |
% 31.51/8.62 | Combining equations (564,617) yields a new equation:
% 31.51/8.62 | (618) all_292_0_130 = all_18_1_14
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (567,617) yields a new equation:
% 31.51/8.63 | (619) all_292_0_130 = all_287_1_127
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (573,576) yields a new equation:
% 31.51/8.63 | (620) all_287_0_126 = all_237_1_89
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 620 yields:
% 31.51/8.63 | (621) all_287_0_126 = all_237_1_89
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (619,618) yields a new equation:
% 31.51/8.63 | (622) all_287_1_127 = all_18_1_14
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 622 yields:
% 31.51/8.63 | (623) all_287_1_127 = all_18_1_14
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (593,615) yields a new equation:
% 31.51/8.63 | (624) all_227_0_80 = all_1_4_4
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 624 yields:
% 31.51/8.63 | (625) all_227_0_80 = all_1_4_4
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (610,609) yields a new equation:
% 31.51/8.63 | (626) all_272_3_117 = all_222_3_79
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (575,621) yields a new equation:
% 31.51/8.63 | (627) all_242_0_91 = all_237_1_89
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 627 yields:
% 31.51/8.63 | (628) all_242_0_91 = all_237_1_89
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (571,569) yields a new equation:
% 31.51/8.63 | (629) all_277_1_119 = all_237_0_88
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (570,569) yields a new equation:
% 31.51/8.63 | (630) all_277_1_119 = all_242_1_92
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (589,591) yields a new equation:
% 31.51/8.63 | (631) all_252_0_98 = all_247_0_94
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 631 yields:
% 31.51/8.63 | (632) all_252_0_98 = all_247_0_94
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (592,591) yields a new equation:
% 31.51/8.63 | (633) all_247_0_94 = all_232_1_85
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (597,600) yields a new equation:
% 31.51/8.63 | (634) all_262_2_108 = all_242_2_93
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 634 yields:
% 31.51/8.63 | (635) all_262_2_108 = all_242_2_93
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (611,612) yields a new equation:
% 31.51/8.63 | (636) all_232_3_87 = 0
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (613,612) yields a new equation:
% 31.51/8.63 | (637) all_232_3_87 = all_98_2_42
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (585,595) yields a new equation:
% 31.51/8.63 | (638) all_272_1_115 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 638 yields:
% 31.51/8.63 | (639) all_272_1_115 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (630,629) yields a new equation:
% 31.51/8.63 | (640) all_242_1_92 = all_237_0_88
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 640 yields:
% 31.51/8.63 | (641) all_242_1_92 = all_237_0_88
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (604,605) yields a new equation:
% 31.51/8.63 | (642) all_227_3_83 = all_127_2_54
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 642 yields:
% 31.51/8.63 | (643) all_227_3_83 = all_127_2_54
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (607,605) yields a new equation:
% 31.51/8.63 | (644) all_127_2_54 = all_98_0_40
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (561,562) yields a new equation:
% 31.51/8.63 | (645) all_252_1_99 = all_222_0_76
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 645 yields:
% 31.51/8.63 | (646) all_252_1_99 = all_222_0_76
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (586,639) yields a new equation:
% 31.51/8.63 | (647) all_267_1_111 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 647 yields:
% 31.51/8.63 | (648) all_267_1_111 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (581,577) yields a new equation:
% 31.51/8.63 | (649) all_262_0_106 = all_142_0_61
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (578,577) yields a new equation:
% 31.51/8.63 | (650) all_262_0_106 = all_257_1_103
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (587,648) yields a new equation:
% 31.51/8.63 | (651) all_262_1_107 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 651 yields:
% 31.51/8.63 | (652) all_262_1_107 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (650,649) yields a new equation:
% 31.51/8.63 | (653) all_257_1_103 = all_142_0_61
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 653 yields:
% 31.51/8.63 | (654) all_257_1_103 = all_142_0_61
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (588,652) yields a new equation:
% 31.51/8.63 | (655) all_257_0_102 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 655 yields:
% 31.51/8.63 | (656) all_257_0_102 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (598,635) yields a new equation:
% 31.51/8.63 | (657) all_252_2_100 = all_242_2_93
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 657 yields:
% 31.51/8.63 | (658) all_252_2_100 = all_242_2_93
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (590,656) yields a new equation:
% 31.51/8.63 | (659) all_252_0_98 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 659 yields:
% 31.51/8.63 | (660) all_252_0_98 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (580,654) yields a new equation:
% 31.51/8.63 | (661) all_247_1_95 = all_142_0_61
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 661 yields:
% 31.51/8.63 | (662) all_247_1_95 = all_142_0_61
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (632,660) yields a new equation:
% 31.51/8.63 | (663) all_247_0_94 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 663 yields:
% 31.51/8.63 | (664) all_247_0_94 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (563,646) yields a new equation:
% 31.51/8.63 | (665) all_222_0_76 = all_217_1_73
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (560,646) yields a new equation:
% 31.51/8.63 | (666) all_222_0_76 = all_1_1_1
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (599,658) yields a new equation:
% 31.51/8.63 | (667) all_247_2_96 = all_242_2_93
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 667 yields:
% 31.51/8.63 | (668) all_247_2_96 = all_242_2_93
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (633,664) yields a new equation:
% 31.51/8.63 | (669) all_232_1_85 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 669 yields:
% 31.51/8.63 | (670) all_232_1_85 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (582,662) yields a new equation:
% 31.51/8.63 | (671) all_142_0_61 = all_142_1_62
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (579,662) yields a new equation:
% 31.51/8.63 | (672) all_142_0_61 = all_16_1_11
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (602,668) yields a new equation:
% 31.51/8.63 | (673) all_242_2_93 = all_222_2_78
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (601,668) yields a new equation:
% 31.51/8.63 | (674) all_242_2_93 = all_227_2_82
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (628,574) yields a new equation:
% 31.51/8.63 | (675) all_237_1_89 = all_1_3_3
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 675 yields:
% 31.51/8.63 | (676) all_237_1_89 = all_1_3_3
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (641,572) yields a new equation:
% 31.51/8.63 | (677) all_237_0_88 = all_98_1_41
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 677 yields:
% 31.51/8.63 | (678) all_237_0_88 = all_98_1_41
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (674,673) yields a new equation:
% 31.51/8.63 | (679) all_227_2_82 = all_222_2_78
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 679 yields:
% 31.51/8.63 | (680) all_227_2_82 = all_222_2_78
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (594,670) yields a new equation:
% 31.51/8.63 | (681) all_227_0_80 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 681 yields:
% 31.51/8.63 | (682) all_227_0_80 = all_222_1_77
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (636,637) yields a new equation:
% 31.51/8.63 | (683) all_98_2_42 = 0
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (596,682) yields a new equation:
% 31.51/8.63 | (684) all_222_1_77 = all_217_0_72
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (625,682) yields a new equation:
% 31.51/8.63 | (685) all_222_1_77 = all_1_4_4
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (608,606) yields a new equation:
% 31.51/8.63 | (686) all_100_0_43 = 0
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (643,606) yields a new equation:
% 31.51/8.63 | (687) all_127_2_54 = all_100_0_43
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 687 yields:
% 31.51/8.63 | (688) all_127_2_54 = all_100_0_43
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (666,665) yields a new equation:
% 31.51/8.63 | (689) all_217_1_73 = all_1_1_1
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (684,685) yields a new equation:
% 31.51/8.63 | (690) all_217_0_72 = all_1_4_4
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 690 yields:
% 31.51/8.63 | (691) all_217_0_72 = all_1_4_4
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (672,671) yields a new equation:
% 31.51/8.63 | (692) all_142_1_62 = all_16_1_11
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (688,644) yields a new equation:
% 31.51/8.63 | (693) all_100_0_43 = all_98_0_40
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 693 yields:
% 31.51/8.63 | (694) all_100_0_43 = all_98_0_40
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (686,694) yields a new equation:
% 31.51/8.63 | (695) all_98_0_40 = 0
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (695,644) yields a new equation:
% 31.51/8.63 | (696) all_127_2_54 = 0
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (683,637) yields a new equation:
% 31.51/8.63 | (636) all_232_3_87 = 0
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (685,664) yields a new equation:
% 31.51/8.63 | (698) all_247_0_94 = all_1_4_4
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (678,629) yields a new equation:
% 31.51/8.63 | (699) all_277_1_119 = all_98_1_41
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (636,612) yields a new equation:
% 31.51/8.63 | (611) all_282_3_125 = 0
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (673,600) yields a new equation:
% 31.51/8.63 | (701) all_282_2_124 = all_222_2_78
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (698,591) yields a new equation:
% 31.51/8.63 | (702) all_282_1_123 = all_1_4_4
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (699,569) yields a new equation:
% 31.51/8.63 | (703) all_282_0_122 = all_98_1_41
% 31.51/8.63 |
% 31.51/8.63 | From (689) and (388) follows:
% 31.51/8.63 | (52) apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1
% 31.51/8.63 |
% 31.51/8.63 | From (623) and (526) follows:
% 31.51/8.63 | (192) apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14
% 31.51/8.63 |
% 31.51/8.63 | From (558) and (253) follows:
% 31.51/8.63 | (706) apart_point_and_line(all_1_8_8, all_1_2_2) = all_100_1_44
% 31.51/8.63 |
% 31.51/8.63 | From (676) and (426) follows:
% 31.51/8.63 | (56) apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3
% 31.51/8.63 |
% 31.51/8.63 | From (692) and (290) follows:
% 31.51/8.63 | (73) apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11
% 31.51/8.63 |
% 31.51/8.63 | From (691) and (387) follows:
% 31.51/8.63 | (57) apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4
% 31.51/8.63 |
% 31.51/8.63 | From (680) and (406) follows:
% 31.51/8.63 | (395) distinct_lines(all_1_2_2, all_1_5_5) = all_222_2_78
% 31.51/8.63 |
% 31.51/8.63 | From (603) and (306) follows:
% 31.51/8.63 | (256) distinct_points(all_1_6_6, all_1_7_7) = 0
% 31.51/8.63 |
% 31.51/8.63 | From (695) and (248) follows:
% 31.51/8.63 | (261) distinct_points(all_1_8_8, all_1_9_9) = 0
% 31.51/8.63 |
% 31.51/8.63 | From (626) and (493) follows:
% 31.51/8.63 | (397) distinct_points(all_1_9_9, all_1_7_7) = all_222_3_79
% 31.51/8.63 |
% 31.51/8.63 | From (683) and (249) follows:
% 31.51/8.63 | (54) distinct_points(all_1_9_9, all_1_8_8) = 0
% 31.51/8.63 |
% 31.51/8.63 +-Applying beta-rule and splitting (568), into two cases.
% 31.51/8.63 |-Branch one:
% 31.51/8.63 | (715) ~ (apart_point_and_line(all_1_8_8, all_1_2_2) = all_100_1_44)
% 31.51/8.63 |
% 31.51/8.63 | Using (706) and (715) yields:
% 31.51/8.63 | (203) $false
% 31.51/8.63 |
% 31.51/8.63 |-The branch is then unsatisfiable
% 31.51/8.63 |-Branch two:
% 31.51/8.63 | (706) apart_point_and_line(all_1_8_8, all_1_2_2) = all_100_1_44
% 31.51/8.63 | (718) all_277_1_119 = all_100_1_44
% 31.51/8.63 |
% 31.51/8.63 | Combining equations (718,699) yields a new equation:
% 31.51/8.63 | (719) all_100_1_44 = all_98_1_41
% 31.51/8.63 |
% 31.51/8.63 | Simplifying 719 yields:
% 31.51/8.63 | (720) all_100_1_44 = all_98_1_41
% 31.51/8.63 |
% 31.51/8.63 | Equations (720) can reduce 262 to:
% 31.51/8.63 | (721) ~ (all_98_1_41 = 0)
% 31.51/8.63 |
% 31.51/8.63 | From (720) and (706) follows:
% 31.51/8.63 | (247) apart_point_and_line(all_1_8_8, all_1_2_2) = all_98_1_41
% 31.51/8.63 |
% 31.51/8.63 +-Applying beta-rule and splitting (408), into two cases.
% 31.51/8.63 |-Branch one:
% 31.51/8.63 | (723) ~ (all_227_2_82 = 0)
% 31.51/8.63 |
% 31.51/8.63 | Equations (680) can reduce 723 to:
% 31.51/8.63 | (724) ~ (all_222_2_78 = 0)
% 31.51/8.63 |
% 31.51/8.63 +-Applying beta-rule and splitting (307), into two cases.
% 31.51/8.63 |-Branch one:
% 31.51/8.63 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.63 |
% 31.51/8.63 +-Applying beta-rule and splitting (215), into two cases.
% 31.51/8.63 |-Branch one:
% 31.51/8.63 | (726) ~ (apart_point_and_line(all_1_7_7, all_1_2_2) = 0)
% 31.51/8.63 |
% 31.51/8.63 +-Applying beta-rule and splitting (271), into two cases.
% 31.51/8.63 |-Branch one:
% 31.51/8.63 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.63 |
% 31.51/8.63 | Using (52) and (726) yields:
% 31.51/8.63 | (728) ~ (all_1_1_1 = 0)
% 31.51/8.63 |
% 31.51/8.63 +-Applying beta-rule and splitting (49), into two cases.
% 31.51/8.63 |-Branch one:
% 31.51/8.63 | (729) all_1_0_0 = 0
% 31.51/8.63 |
% 31.51/8.63 | From (729) and (48) follows:
% 31.51/8.63 | (730) apart_point_and_line(all_1_6_6, all_1_2_2) = 0
% 31.51/8.63 |
% 31.51/8.63 +-Applying beta-rule and splitting (61), into two cases.
% 31.51/8.63 |-Branch one:
% 31.51/8.63 | (731) ~ (apart_point_and_line(all_1_6_6, all_1_2_2) = 0)
% 31.51/8.63 |
% 31.51/8.63 | Using (730) and (731) yields:
% 31.51/8.63 | (203) $false
% 31.51/8.63 |
% 31.51/8.63 |-The branch is then unsatisfiable
% 31.51/8.63 |-Branch two:
% 31.51/8.63 | (730) apart_point_and_line(all_1_6_6, all_1_2_2) = 0
% 31.51/8.63 | (734) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_6_6, all_1_8_8) = v2 & distinct_points(all_1_6_6, all_1_9_9) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 31.51/8.63 |
% 31.51/8.63 | Instantiating (734) with all_348_0_142, all_348_1_143, all_348_2_144 yields:
% 31.51/8.63 | (735) distinct_points(all_1_6_6, all_1_8_8) = all_348_0_142 & distinct_points(all_1_6_6, all_1_9_9) = all_348_1_143 & distinct_points(all_1_9_9, all_1_8_8) = all_348_2_144 & ( ~ (all_348_2_144 = 0) | (all_348_0_142 = 0 & all_348_1_143 = 0))
% 31.51/8.63 |
% 31.51/8.63 | Applying alpha-rule on (735) yields:
% 31.51/8.63 | (736) distinct_points(all_1_6_6, all_1_8_8) = all_348_0_142
% 31.51/8.63 | (737) distinct_points(all_1_6_6, all_1_9_9) = all_348_1_143
% 31.51/8.63 | (738) distinct_points(all_1_9_9, all_1_8_8) = all_348_2_144
% 31.51/8.63 | (739) ~ (all_348_2_144 = 0) | (all_348_0_142 = 0 & all_348_1_143 = 0)
% 31.51/8.63 |
% 31.51/8.63 +-Applying beta-rule and splitting (221), into two cases.
% 31.51/8.63 |-Branch one:
% 31.51/8.63 | (731) ~ (apart_point_and_line(all_1_6_6, all_1_2_2) = 0)
% 31.51/8.64 |
% 31.51/8.64 | Using (730) and (731) yields:
% 31.51/8.64 | (203) $false
% 31.51/8.64 |
% 31.51/8.64 |-The branch is then unsatisfiable
% 31.51/8.64 |-Branch two:
% 31.51/8.64 | (730) apart_point_and_line(all_1_6_6, all_1_2_2) = 0
% 31.51/8.64 | (743) all_16_1_11 = 0 | distinct_points(all_1_6_6, all_1_9_9) = 0
% 31.51/8.64 |
% 31.51/8.64 +-Applying beta-rule and splitting (743), into two cases.
% 31.51/8.64 |-Branch one:
% 31.51/8.64 | (744) distinct_points(all_1_6_6, all_1_9_9) = 0
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (37) with all_1_6_6, all_1_9_9, all_348_1_143, 0 and discharging atoms distinct_points(all_1_6_6, all_1_9_9) = all_348_1_143, distinct_points(all_1_6_6, all_1_9_9) = 0, yields:
% 31.51/8.64 | (745) all_348_1_143 = 0
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (37) with all_1_9_9, all_1_8_8, all_348_2_144, 0 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_348_2_144, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 31.51/8.64 | (746) all_348_2_144 = 0
% 31.51/8.64 |
% 31.51/8.64 | From (745) and (737) follows:
% 31.51/8.64 | (744) distinct_points(all_1_6_6, all_1_9_9) = 0
% 31.51/8.64 |
% 31.51/8.64 +-Applying beta-rule and splitting (739), into two cases.
% 31.51/8.64 |-Branch one:
% 31.51/8.64 | (748) ~ (all_348_2_144 = 0)
% 31.51/8.64 |
% 31.51/8.64 | Equations (746) can reduce 748 to:
% 31.51/8.64 | (93) $false
% 31.51/8.64 |
% 31.51/8.64 |-The branch is then unsatisfiable
% 31.51/8.64 |-Branch two:
% 31.51/8.64 | (746) all_348_2_144 = 0
% 31.51/8.64 | (751) all_348_0_142 = 0 & all_348_1_143 = 0
% 31.51/8.64 |
% 31.51/8.64 | Applying alpha-rule on (751) yields:
% 31.51/8.64 | (752) all_348_0_142 = 0
% 31.51/8.64 | (745) all_348_1_143 = 0
% 31.51/8.64 |
% 31.51/8.64 | From (752) and (736) follows:
% 31.51/8.64 | (754) distinct_points(all_1_6_6, all_1_8_8) = 0
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_18_1_14, all_152_0_68, all_152_1_69, all_1_5_5, all_1_7_7, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 31.51/8.64 | (755) all_152_0_68 = 0 | all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_152_1_69) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_152_0_68, all_1_3_3, all_152_1_69, all_1_5_5, all_1_7_7, all_1_8_8 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 31.51/8.64 | (756) all_152_0_68 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_152_1_69) = v2 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_8_8, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_1_3_3, all_152_0_68, all_1_5_5, all_152_1_69, all_1_8_8, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 31.51/8.64 | (757) all_152_0_68 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_152_1_69) = v3 & distinct_lines(all_152_1_69, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_152_0_68, all_1_3_3, all_1_5_5, all_152_1_69, all_1_7_7, all_1_8_8 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 31.51/8.64 | (758) all_152_0_68 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_152_1_69) = v2 & distinct_lines(all_152_1_69, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_1_3_3, all_152_0_68, all_152_1_69, all_1_5_5, all_1_8_8, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, yields:
% 31.51/8.64 | (759) all_152_0_68 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_152_1_69) = v3 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_152_0_68, all_16_1_11, all_152_1_69, all_1_2_2, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.51/8.64 | (760) all_152_0_68 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_152_1_69) = v2 & distinct_lines(all_1_2_2, all_152_1_69) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_16_1_11, all_152_0_68, all_1_2_2, all_152_1_69, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.51/8.64 | (761) all_152_0_68 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_152_1_69) = v3 & distinct_lines(all_152_1_69, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_152_0_68, all_16_1_11, all_1_2_2, all_152_1_69, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.51/8.64 | (762) all_152_0_68 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_152_1_69) = v2 & distinct_lines(all_152_1_69, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_16_1_11, all_152_0_68, all_152_1_69, all_1_2_2, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.51/8.64 | (763) all_152_0_68 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_152_1_69) = v3 & distinct_lines(all_1_2_2, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_152_0_68, all_1_4_4, all_152_1_69, all_1_5_5, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 31.51/8.64 | (764) all_152_0_68 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_152_1_69) = v2 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_1_4_4, all_152_0_68, all_152_1_69, all_1_5_5, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 31.51/8.64 | (765) all_152_0_68 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_152_1_69) = v3 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_152_0_68, all_152_0_68, all_152_1_69, all_152_1_69, all_1_7_7, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, yields:
% 31.51/8.64 | (766) all_152_0_68 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_152_1_69) = v3 & apart_point_and_line(all_1_7_7, all_152_1_69) = v2 & distinct_lines(all_152_1_69, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_127_0_52, all_1_1_1, all_127_1_53, all_1_2_2, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (767) all_127_0_52 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_1_1_1, all_127_0_52, all_1_2_2, all_127_1_53, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (768) all_127_0_52 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_127_0_52, all_1_1_1, all_1_2_2, all_127_1_53, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (769) all_127_0_52 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_1_1_1, all_127_0_52, all_127_1_53, all_1_2_2, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (770) all_127_0_52 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_127_0_52, all_18_1_14, all_127_1_53, all_1_5_5, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (771) all_127_0_52 = 0 | all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_18_1_14, all_127_0_52, all_1_5_5, all_127_1_53, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (772) all_127_0_52 = 0 | all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_127_0_52, all_18_1_14, all_1_5_5, all_127_1_53, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (773) all_127_0_52 = 0 | all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (33) with all_18_1_14, all_127_0_52, all_127_1_53, all_1_5_5, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (774) all_127_0_52 = 0 | all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_127_0_52, all_1_3_3, all_127_1_53, all_1_5_5, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (775) all_127_0_52 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.64 | Instantiating formula (11) with all_1_3_3, all_127_0_52, all_1_5_5, all_127_1_53, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.64 | (776) all_127_0_52 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.64 |
% 31.51/8.65 | Instantiating formula (33) with all_127_0_52, all_1_3_3, all_1_5_5, all_127_1_53, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.65 | (777) all_127_0_52 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (33) with all_1_3_3, all_127_0_52, all_127_1_53, all_1_5_5, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.65 | (778) all_127_0_52 = 0 | all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (11) with all_127_0_52, all_16_1_11, all_127_1_53, all_1_2_2, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.51/8.65 | (779) all_127_0_52 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (11) with all_16_1_11, all_127_0_52, all_1_2_2, all_127_1_53, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.51/8.65 | (780) all_127_0_52 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (33) with all_127_0_52, all_16_1_11, all_1_2_2, all_127_1_53, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.51/8.65 | (781) all_127_0_52 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (33) with all_16_1_11, all_127_0_52, all_127_1_53, all_1_2_2, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 31.51/8.65 | (782) all_127_0_52 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (11) with all_127_0_52, all_1_4_4, all_127_1_53, all_1_5_5, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 31.51/8.65 | (783) all_127_0_52 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (11) with all_1_4_4, all_127_0_52, all_1_5_5, all_127_1_53, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 31.51/8.65 | (784) all_127_0_52 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (33) with all_127_0_52, all_1_4_4, all_1_5_5, all_127_1_53, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 31.51/8.65 | (785) all_127_0_52 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (33) with all_1_4_4, all_127_0_52, all_127_1_53, all_1_5_5, all_1_9_9, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 31.51/8.65 | (786) all_127_0_52 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (11) with all_127_0_52, all_98_1_41, all_127_1_53, all_1_2_2, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_98_1_41, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.65 | (787) all_127_0_52 = 0 | all_98_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (11) with all_98_1_41, all_127_0_52, all_1_2_2, all_127_1_53, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_98_1_41, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.65 | (788) all_127_0_52 = 0 | all_98_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (33) with all_127_0_52, all_98_1_41, all_1_2_2, all_127_1_53, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_98_1_41, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.65 | (789) all_127_0_52 = 0 | all_98_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (33) with all_98_1_41, all_127_0_52, all_127_1_53, all_1_2_2, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_98_1_41, apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, yields:
% 31.51/8.65 | (790) all_127_0_52 = 0 | all_98_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (25) with all_222_2_78, all_1_5_5, all_1_2_2, all_1_6_6 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = 0, distinct_lines(all_1_2_2, all_1_5_5) = all_222_2_78, yields:
% 31.51/8.65 | (791) all_222_2_78 = 0 | apart_point_and_line(all_1_6_6, all_1_5_5) = 0
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (30) with 0, all_1_6_6, all_1_6_6, all_1_7_7 and discharging atoms distinct_points(all_1_6_6, all_1_7_7) = 0, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 31.51/8.65 | (792) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_7_7, all_1_6_6) = v0 & apart_point_and_line(all_1_6_6, v0) = v1 & distinct_points(all_1_6_6, all_1_6_6) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (21) with 0, all_1_6_6, all_1_7_7, all_1_6_6 and discharging atoms distinct_points(all_1_6_6, all_1_7_7) = 0, yields:
% 31.51/8.65 | (793) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_6_6, all_1_7_7) = v0 & apart_point_and_line(all_1_6_6, v0) = v1 & distinct_points(all_1_6_6, all_1_6_6) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (36) with 0, all_1_5_5, all_1_6_6, all_1_6_6, all_1_7_7 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, distinct_points(all_1_6_6, all_1_7_7) = 0, yields:
% 31.51/8.65 | (794) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_points(all_1_6_6, all_1_6_6) = v2 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (45) with 0, all_152_1_69, all_1_6_6, all_1_7_7, all_1_6_6 and discharging atoms line_connecting(all_1_6_6, all_1_7_7) = all_152_1_69, distinct_points(all_1_6_6, all_1_7_7) = 0, yields:
% 31.51/8.65 | (795) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_152_1_69) = v1 & distinct_points(all_1_6_6, all_1_6_6) = v2 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (44) with all_152_0_68, all_152_0_68, all_152_1_69, all_152_1_69, all_1_7_7, all_1_6_6 and discharging atoms apart_point_and_line(all_1_7_7, all_152_1_69) = all_152_0_68, distinct_points(all_1_6_6, all_1_7_7) = 0, yields:
% 31.51/8.65 | (796) all_152_0_68 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_152_1_69) = v2 & apart_point_and_line(all_1_6_6, all_152_1_69) = v1 & distinct_lines(all_152_1_69, all_152_1_69) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (21) with 0, all_1_6_6, all_1_8_8, all_1_6_6 and discharging atoms distinct_points(all_1_6_6, all_1_8_8) = 0, yields:
% 31.51/8.65 | (797) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_6_6, all_1_8_8) = v0 & apart_point_and_line(all_1_6_6, v0) = v1 & distinct_points(all_1_6_6, all_1_6_6) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (21) with 0, all_1_6_6, all_1_9_9, all_1_6_6 and discharging atoms distinct_points(all_1_6_6, all_1_9_9) = 0, yields:
% 31.51/8.65 | (798) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_6_6, all_1_9_9) = v0 & apart_point_and_line(all_1_6_6, v0) = v1 & distinct_points(all_1_6_6, all_1_6_6) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (44) with all_16_1_11, all_127_0_52, all_1_2_2, all_127_1_53, all_1_9_9, all_1_6_6 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, distinct_points(all_1_6_6, all_1_9_9) = 0, yields:
% 31.51/8.65 | (799) all_127_0_52 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v1 & apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (44) with all_1_4_4, all_127_0_52, all_1_5_5, all_127_1_53, all_1_9_9, all_1_6_6 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, distinct_points(all_1_6_6, all_1_9_9) = 0, yields:
% 31.51/8.65 | (800) all_127_0_52 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v1 & apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (44) with all_127_0_52, all_1_4_4, all_127_1_53, all_1_5_5, all_1_9_9, all_1_6_6 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, distinct_points(all_1_6_6, all_1_9_9) = 0, yields:
% 31.51/8.65 | (801) all_127_0_52 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_127_1_53) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (44) with all_127_0_52, all_127_0_52, all_127_1_53, all_127_1_53, all_1_9_9, all_1_6_6 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, distinct_points(all_1_6_6, all_1_9_9) = 0, yields:
% 31.51/8.65 | (802) all_127_0_52 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v2 & apart_point_and_line(all_1_6_6, all_127_1_53) = v1 & distinct_lines(all_127_1_53, all_127_1_53) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (30) with all_297_3_137, all_1_8_8, all_1_6_6, all_1_7_7 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = 0, distinct_points(all_1_8_8, all_1_7_7) = all_297_3_137, yields:
% 31.51/8.65 | (803) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_7_7, all_1_6_6) = v0 & apart_point_and_line(all_1_8_8, v0) = v1 & distinct_points(all_1_8_8, all_1_6_6) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_297_3_137 = 0)))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (44) with all_16_1_11, all_127_0_52, all_1_2_2, all_127_1_53, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 31.51/8.65 | (804) all_127_0_52 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v1 & apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (44) with all_1_4_4, all_127_0_52, all_1_5_5, all_127_1_53, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 31.51/8.65 | (805) all_127_0_52 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v1 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.65 |
% 31.51/8.65 | Instantiating formula (44) with all_127_0_52, all_16_1_11, all_127_1_53, all_1_2_2, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 31.51/8.66 | (806) all_127_0_52 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_127_1_53) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.66 |
% 31.51/8.66 | Instantiating formula (44) with all_127_0_52, all_1_4_4, all_127_1_53, all_1_5_5, all_1_9_9, all_1_8_8 and discharging atoms apart_point_and_line(all_1_9_9, all_127_1_53) = all_127_0_52, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 31.51/8.66 | (807) all_127_0_52 = 0 | all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_127_1_53) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.66 |
% 31.51/8.66 | Instantiating formula (30) with all_222_3_79, all_1_9_9, all_1_6_6, all_1_7_7 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = 0, distinct_points(all_1_9_9, all_1_7_7) = all_222_3_79, yields:
% 31.51/8.66 | (808) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_7_7, all_1_6_6) = v0 & apart_point_and_line(all_1_9_9, v0) = v1 & distinct_points(all_1_9_9, all_1_6_6) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_222_3_79 = 0)))
% 31.51/8.66 |
% 31.51/8.66 | Instantiating (793) with all_385_0_160, all_385_1_161, all_385_2_162 yields:
% 31.51/8.66 | (809) line_connecting(all_1_6_6, all_1_7_7) = all_385_2_162 & apart_point_and_line(all_1_6_6, all_385_2_162) = all_385_1_161 & distinct_points(all_1_6_6, all_1_6_6) = all_385_0_160 & ( ~ (all_385_1_161 = 0) | all_385_0_160 = 0)
% 31.51/8.66 |
% 31.51/8.66 | Applying alpha-rule on (809) yields:
% 31.51/8.66 | (810) line_connecting(all_1_6_6, all_1_7_7) = all_385_2_162
% 31.51/8.66 | (811) apart_point_and_line(all_1_6_6, all_385_2_162) = all_385_1_161
% 31.51/8.66 | (812) distinct_points(all_1_6_6, all_1_6_6) = all_385_0_160
% 31.51/8.66 | (813) ~ (all_385_1_161 = 0) | all_385_0_160 = 0
% 31.51/8.66 |
% 31.51/8.66 | Instantiating (792) with all_387_0_163, all_387_1_164, all_387_2_165 yields:
% 31.51/8.66 | (814) line_connecting(all_1_7_7, all_1_6_6) = all_387_2_165 & apart_point_and_line(all_1_6_6, all_387_2_165) = all_387_1_164 & distinct_points(all_1_6_6, all_1_6_6) = all_387_0_163 & ( ~ (all_387_1_164 = 0) | all_387_0_163 = 0)
% 31.51/8.66 |
% 31.51/8.66 | Applying alpha-rule on (814) yields:
% 31.51/8.66 | (815) line_connecting(all_1_7_7, all_1_6_6) = all_387_2_165
% 31.51/8.66 | (816) apart_point_and_line(all_1_6_6, all_387_2_165) = all_387_1_164
% 31.51/8.66 | (817) distinct_points(all_1_6_6, all_1_6_6) = all_387_0_163
% 31.51/8.66 | (818) ~ (all_387_1_164 = 0) | all_387_0_163 = 0
% 31.51/8.66 |
% 31.51/8.66 | Instantiating (808) with all_395_0_175, all_395_1_176, all_395_2_177 yields:
% 31.51/8.66 | (819) line_connecting(all_1_7_7, all_1_6_6) = all_395_2_177 & apart_point_and_line(all_1_9_9, all_395_2_177) = all_395_1_176 & distinct_points(all_1_9_9, all_1_6_6) = all_395_0_175 & ( ~ (all_395_1_176 = 0) | (all_395_0_175 = 0 & all_222_3_79 = 0))
% 31.51/8.66 |
% 31.51/8.66 | Applying alpha-rule on (819) yields:
% 31.51/8.66 | (820) line_connecting(all_1_7_7, all_1_6_6) = all_395_2_177
% 31.51/8.66 | (821) apart_point_and_line(all_1_9_9, all_395_2_177) = all_395_1_176
% 31.51/8.66 | (822) distinct_points(all_1_9_9, all_1_6_6) = all_395_0_175
% 31.51/8.66 | (823) ~ (all_395_1_176 = 0) | (all_395_0_175 = 0 & all_222_3_79 = 0)
% 31.51/8.66 |
% 31.51/8.66 | Instantiating (803) with all_429_0_226, all_429_1_227, all_429_2_228 yields:
% 31.51/8.66 | (824) line_connecting(all_1_7_7, all_1_6_6) = all_429_2_228 & apart_point_and_line(all_1_8_8, all_429_2_228) = all_429_1_227 & distinct_points(all_1_8_8, all_1_6_6) = all_429_0_226 & ( ~ (all_429_1_227 = 0) | (all_429_0_226 = 0 & all_297_3_137 = 0))
% 31.51/8.66 |
% 31.51/8.66 | Applying alpha-rule on (824) yields:
% 31.51/8.66 | (825) line_connecting(all_1_7_7, all_1_6_6) = all_429_2_228
% 31.51/8.66 | (826) apart_point_and_line(all_1_8_8, all_429_2_228) = all_429_1_227
% 31.51/8.66 | (827) distinct_points(all_1_8_8, all_1_6_6) = all_429_0_226
% 31.51/8.66 | (828) ~ (all_429_1_227 = 0) | (all_429_0_226 = 0 & all_297_3_137 = 0)
% 31.51/8.66 |
% 31.51/8.66 | Instantiating (798) with all_441_0_244, all_441_1_245, all_441_2_246 yields:
% 31.51/8.66 | (829) line_connecting(all_1_6_6, all_1_9_9) = all_441_2_246 & apart_point_and_line(all_1_6_6, all_441_2_246) = all_441_1_245 & distinct_points(all_1_6_6, all_1_6_6) = all_441_0_244 & ( ~ (all_441_1_245 = 0) | all_441_0_244 = 0)
% 31.51/8.66 |
% 31.51/8.66 | Applying alpha-rule on (829) yields:
% 31.51/8.66 | (830) line_connecting(all_1_6_6, all_1_9_9) = all_441_2_246
% 31.51/8.66 | (831) apart_point_and_line(all_1_6_6, all_441_2_246) = all_441_1_245
% 31.51/8.66 | (832) distinct_points(all_1_6_6, all_1_6_6) = all_441_0_244
% 31.51/8.66 | (833) ~ (all_441_1_245 = 0) | all_441_0_244 = 0
% 31.51/8.66 |
% 31.51/8.66 | Instantiating (797) with all_445_0_250, all_445_1_251, all_445_2_252 yields:
% 31.51/8.66 | (834) line_connecting(all_1_6_6, all_1_8_8) = all_445_2_252 & apart_point_and_line(all_1_6_6, all_445_2_252) = all_445_1_251 & distinct_points(all_1_6_6, all_1_6_6) = all_445_0_250 & ( ~ (all_445_1_251 = 0) | all_445_0_250 = 0)
% 31.51/8.66 |
% 31.51/8.66 | Applying alpha-rule on (834) yields:
% 31.51/8.66 | (835) line_connecting(all_1_6_6, all_1_8_8) = all_445_2_252
% 31.51/8.66 | (836) apart_point_and_line(all_1_6_6, all_445_2_252) = all_445_1_251
% 31.51/8.66 | (837) distinct_points(all_1_6_6, all_1_6_6) = all_445_0_250
% 31.51/8.66 | (838) ~ (all_445_1_251 = 0) | all_445_0_250 = 0
% 31.51/8.66 |
% 31.51/8.66 | Instantiating (795) with all_463_0_277, all_463_1_278, all_463_2_279 yields:
% 31.51/8.66 | (839) apart_point_and_line(all_1_6_6, all_152_1_69) = all_463_1_278 & distinct_points(all_1_6_6, all_1_6_6) = all_463_0_277 & distinct_points(all_1_6_6, all_1_7_7) = all_463_2_279 & ( ~ (all_463_1_278 = 0) | ~ (all_463_2_279 = 0) | all_463_0_277 = 0)
% 31.51/8.66 |
% 31.51/8.66 | Applying alpha-rule on (839) yields:
% 31.51/8.66 | (840) apart_point_and_line(all_1_6_6, all_152_1_69) = all_463_1_278
% 31.51/8.66 | (841) distinct_points(all_1_6_6, all_1_6_6) = all_463_0_277
% 31.51/8.66 | (842) distinct_points(all_1_6_6, all_1_7_7) = all_463_2_279
% 31.51/8.66 | (843) ~ (all_463_1_278 = 0) | ~ (all_463_2_279 = 0) | all_463_0_277 = 0
% 31.51/8.66 |
% 31.51/8.66 | Instantiating (794) with all_465_0_280, all_465_1_281, all_465_2_282 yields:
% 31.51/8.66 | (844) apart_point_and_line(all_1_6_6, all_1_5_5) = all_465_1_281 & distinct_points(all_1_6_6, all_1_6_6) = all_465_0_280 & distinct_points(all_1_7_7, all_1_6_6) = all_465_2_282 & ( ~ (all_465_1_281 = 0) | ~ (all_465_2_282 = 0) | all_465_0_280 = 0)
% 31.51/8.66 |
% 31.51/8.66 | Applying alpha-rule on (844) yields:
% 31.51/8.66 | (845) apart_point_and_line(all_1_6_6, all_1_5_5) = all_465_1_281
% 31.51/8.66 | (846) distinct_points(all_1_6_6, all_1_6_6) = all_465_0_280
% 31.51/8.66 | (847) distinct_points(all_1_7_7, all_1_6_6) = all_465_2_282
% 31.51/8.66 | (848) ~ (all_465_1_281 = 0) | ~ (all_465_2_282 = 0) | all_465_0_280 = 0
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (791), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (849) apart_point_and_line(all_1_6_6, all_1_5_5) = 0
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (559), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (850) ~ (apart_point_and_line(all_1_6_6, all_1_5_5) = all_1_0_0)
% 31.51/8.66 |
% 31.51/8.66 | From (729) and (850) follows:
% 31.51/8.66 | (851) ~ (apart_point_and_line(all_1_6_6, all_1_5_5) = 0)
% 31.51/8.66 |
% 31.51/8.66 | Using (849) and (851) yields:
% 31.51/8.66 | (203) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (853) apart_point_and_line(all_1_6_6, all_1_5_5) = all_1_0_0
% 31.51/8.66 | (854) all_132_1_56 = all_1_0_0
% 31.51/8.66 |
% 31.51/8.66 | From (729) and (853) follows:
% 31.51/8.66 | (849) apart_point_and_line(all_1_6_6, all_1_5_5) = 0
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (796), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (856) all_152_0_68 = 0
% 31.51/8.66 |
% 31.51/8.66 | Equations (856) can reduce 725 to:
% 31.51/8.66 | (93) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.66 | (859) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_152_1_69) = v2 & apart_point_and_line(all_1_6_6, all_152_1_69) = v1 & distinct_lines(all_152_1_69, all_152_1_69) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (766), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (856) all_152_0_68 = 0
% 31.51/8.66 |
% 31.51/8.66 | Equations (856) can reduce 725 to:
% 31.51/8.66 | (93) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.66 | (863) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_152_1_69) = v3 & apart_point_and_line(all_1_7_7, all_152_1_69) = v2 & distinct_lines(all_152_1_69, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (802), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (864) all_127_0_52 = 0
% 31.51/8.66 |
% 31.51/8.66 | Equations (864) can reduce 727 to:
% 31.51/8.66 | (93) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.66 | (867) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v2 & apart_point_and_line(all_1_6_6, all_127_1_53) = v1 & distinct_lines(all_127_1_53, all_127_1_53) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (801), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (864) all_127_0_52 = 0
% 31.51/8.66 |
% 31.51/8.66 | Equations (864) can reduce 727 to:
% 31.51/8.66 | (93) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.66 | (871) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_127_1_53) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (755), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (856) all_152_0_68 = 0
% 31.51/8.66 |
% 31.51/8.66 | Equations (856) can reduce 725 to:
% 31.51/8.66 | (93) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.66 | (875) all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_152_1_69) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (756), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (856) all_152_0_68 = 0
% 31.51/8.66 |
% 31.51/8.66 | Equations (856) can reduce 725 to:
% 31.51/8.66 | (93) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.66 | (879) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_152_1_69) = v2 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_8_8, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (757), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (856) all_152_0_68 = 0
% 31.51/8.66 |
% 31.51/8.66 | Equations (856) can reduce 725 to:
% 31.51/8.66 | (93) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.66 | (883) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_152_1_69) = v3 & distinct_lines(all_152_1_69, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.66 |
% 31.51/8.66 +-Applying beta-rule and splitting (758), into two cases.
% 31.51/8.66 |-Branch one:
% 31.51/8.66 | (856) all_152_0_68 = 0
% 31.51/8.66 |
% 31.51/8.66 | Equations (856) can reduce 725 to:
% 31.51/8.66 | (93) $false
% 31.51/8.66 |
% 31.51/8.66 |-The branch is then unsatisfiable
% 31.51/8.66 |-Branch two:
% 31.51/8.66 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.66 | (887) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_8_8, all_152_1_69) = v2 & distinct_lines(all_152_1_69, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (806), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (891) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_127_1_53) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (804), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (895) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v1 & apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (779), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (899) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (780), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (903) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (761), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (856) all_152_0_68 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (856) can reduce 725 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.67 | (907) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_152_1_69) = v3 & distinct_lines(all_152_1_69, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (759), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (856) all_152_0_68 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (856) can reduce 725 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.67 | (911) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_8_8, all_152_1_69) = v3 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (760), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (856) all_152_0_68 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (856) can reduce 725 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.67 | (915) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_152_1_69) = v2 & distinct_lines(all_1_2_2, all_152_1_69) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (762), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (856) all_152_0_68 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (856) can reduce 725 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.67 | (919) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_152_1_69) = v2 & distinct_lines(all_152_1_69, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (807), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (923) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_8_8, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_127_1_53) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (781), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (927) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (765), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (856) all_152_0_68 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (856) can reduce 725 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.67 | (931) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & apart_point_and_line(all_1_9_9, all_152_1_69) = v3 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (763), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (856) all_152_0_68 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (856) can reduce 725 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.67 | (935) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_152_1_69) = v3 & distinct_lines(all_1_2_2, all_152_1_69) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (764), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (856) all_152_0_68 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (856) can reduce 725 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (725) ~ (all_152_0_68 = 0)
% 31.51/8.67 | (939) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_152_1_69) = v2 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (782), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (943) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (805), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (947) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v1 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (783), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (951) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (784), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (955) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (785), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (959) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (786), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (963) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (789), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (967) all_98_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (787), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (971) all_98_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (788), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.67 |
% 31.51/8.67 | Equations (864) can reduce 727 to:
% 31.51/8.67 | (93) $false
% 31.51/8.67 |
% 31.51/8.67 |-The branch is then unsatisfiable
% 31.51/8.67 |-Branch two:
% 31.51/8.67 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.67 | (975) all_98_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.67 |
% 31.51/8.67 +-Applying beta-rule and splitting (790), into two cases.
% 31.51/8.67 |-Branch one:
% 31.51/8.67 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (979) all_98_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (771), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (983) all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (772), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (987) all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (773), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (991) all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (774), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (995) all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (777), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (999) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (769), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1003) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (767), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1007) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (768), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1011) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (770), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1015) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (775), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1019) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (776), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1023) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (778), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1027) all_1_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (799), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1031) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v1 & apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & distinct_lines(all_127_1_53, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (800), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (864) all_127_0_52 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (864) can reduce 727 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (727) ~ (all_127_0_52 = 0)
% 31.51/8.68 | (1035) all_1_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v1 & apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (939), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (102) all_1_4_4 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (102) can reduce 53 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (53) ~ (all_1_4_4 = 0)
% 31.51/8.68 | (1039) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_9_9, all_152_1_69) = v2 & distinct_lines(all_1_5_5, all_152_1_69) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (947), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (102) all_1_4_4 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (102) can reduce 53 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (53) ~ (all_1_4_4 = 0)
% 31.51/8.68 | (1043) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_127_1_53) = v1 & apart_point_and_line(all_1_8_8, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (951), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (102) all_1_4_4 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (102) can reduce 53 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (53) ~ (all_1_4_4 = 0)
% 31.51/8.68 | (1047) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (955), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (102) all_1_4_4 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (102) can reduce 53 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (53) ~ (all_1_4_4 = 0)
% 31.51/8.68 | (1051) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (959), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (102) all_1_4_4 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (102) can reduce 53 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (53) ~ (all_1_4_4 = 0)
% 31.51/8.68 | (1055) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_127_1_53, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (963), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (102) all_1_4_4 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (102) can reduce 53 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (53) ~ (all_1_4_4 = 0)
% 31.51/8.68 | (1059) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_9_9, all_127_1_53) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_127_1_53) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 31.51/8.68 |
% 31.51/8.68 +-Applying beta-rule and splitting (1035), into two cases.
% 31.51/8.68 |-Branch one:
% 31.51/8.68 | (102) all_1_4_4 = 0
% 31.51/8.68 |
% 31.51/8.68 | Equations (102) can reduce 53 to:
% 31.51/8.68 | (93) $false
% 31.51/8.68 |
% 31.51/8.68 |-The branch is then unsatisfiable
% 31.51/8.68 |-Branch two:
% 31.51/8.68 | (53) ~ (all_1_4_4 = 0)
% 31.51/8.68 | (1063) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_127_1_53) = v1 & apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & distinct_lines(all_127_1_53, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 31.51/8.68 |
% 31.51/8.68 | Instantiating (1063) with all_754_0_340, all_754_1_341, all_754_2_342 yields:
% 31.51/8.68 | (1064) apart_point_and_line(all_1_6_6, all_127_1_53) = all_754_1_341 & apart_point_and_line(all_1_6_6, all_1_5_5) = all_754_0_340 & distinct_lines(all_127_1_53, all_1_5_5) = all_754_2_342 & ( ~ (all_754_2_342 = 0) | all_754_0_340 = 0 | all_754_1_341 = 0)
% 31.51/8.68 |
% 31.51/8.68 | Applying alpha-rule on (1064) yields:
% 31.51/8.68 | (1065) apart_point_and_line(all_1_6_6, all_127_1_53) = all_754_1_341
% 31.51/8.68 | (1066) apart_point_and_line(all_1_6_6, all_1_5_5) = all_754_0_340
% 31.51/8.68 | (1067) distinct_lines(all_127_1_53, all_1_5_5) = all_754_2_342
% 31.51/8.68 | (1068) ~ (all_754_2_342 = 0) | all_754_0_340 = 0 | all_754_1_341 = 0
% 31.51/8.68 |
% 31.51/8.68 | Instantiating formula (27) with all_1_7_7, all_1_6_6, all_429_2_228, all_1_5_5 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_429_2_228, line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, yields:
% 31.51/8.68 | (1069) all_429_2_228 = all_1_5_5
% 31.51/8.68 |
% 31.51/8.68 | Instantiating formula (27) with all_1_7_7, all_1_6_6, all_395_2_177, all_429_2_228 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_429_2_228, line_connecting(all_1_7_7, all_1_6_6) = all_395_2_177, yields:
% 31.51/8.68 | (1070) all_429_2_228 = all_395_2_177
% 31.51/8.68 |
% 31.51/8.68 | Instantiating formula (27) with all_1_7_7, all_1_6_6, all_387_2_165, all_429_2_228 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_429_2_228, line_connecting(all_1_7_7, all_1_6_6) = all_387_2_165, yields:
% 31.51/8.69 | (1071) all_429_2_228 = all_387_2_165
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (9) with all_1_6_6, all_1_5_5, all_754_0_340, 0 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_754_0_340, apart_point_and_line(all_1_6_6, all_1_5_5) = 0, yields:
% 31.51/8.69 | (1072) all_754_0_340 = 0
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (9) with all_1_6_6, all_1_5_5, all_754_0_340, all_387_1_164 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_754_0_340, yields:
% 31.51/8.69 | (1073) all_754_0_340 = all_387_1_164 | ~ (apart_point_and_line(all_1_6_6, all_1_5_5) = all_387_1_164)
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (9) with all_1_6_6, all_1_5_5, all_465_1_281, all_754_0_340 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_754_0_340, apart_point_and_line(all_1_6_6, all_1_5_5) = all_465_1_281, yields:
% 31.51/8.69 | (1074) all_754_0_340 = all_465_1_281
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (43) with all_1_6_6 yields:
% 31.51/8.69 | (1075) ~ (distinct_points(all_1_6_6, all_1_6_6) = 0)
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (37) with all_1_6_6, all_1_6_6, all_463_0_277, all_465_0_280 and discharging atoms distinct_points(all_1_6_6, all_1_6_6) = all_465_0_280, distinct_points(all_1_6_6, all_1_6_6) = all_463_0_277, yields:
% 31.51/8.69 | (1076) all_465_0_280 = all_463_0_277
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (37) with all_1_6_6, all_1_6_6, all_445_0_250, all_465_0_280 and discharging atoms distinct_points(all_1_6_6, all_1_6_6) = all_465_0_280, distinct_points(all_1_6_6, all_1_6_6) = all_445_0_250, yields:
% 31.51/8.69 | (1077) all_465_0_280 = all_445_0_250
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (37) with all_1_6_6, all_1_6_6, all_441_0_244, all_463_0_277 and discharging atoms distinct_points(all_1_6_6, all_1_6_6) = all_463_0_277, distinct_points(all_1_6_6, all_1_6_6) = all_441_0_244, yields:
% 31.51/8.69 | (1078) all_463_0_277 = all_441_0_244
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (37) with all_1_6_6, all_1_6_6, all_387_0_163, all_465_0_280 and discharging atoms distinct_points(all_1_6_6, all_1_6_6) = all_465_0_280, distinct_points(all_1_6_6, all_1_6_6) = all_387_0_163, yields:
% 31.51/8.69 | (1079) all_465_0_280 = all_387_0_163
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (37) with all_1_6_6, all_1_6_6, all_385_0_160, all_465_0_280 and discharging atoms distinct_points(all_1_6_6, all_1_6_6) = all_465_0_280, distinct_points(all_1_6_6, all_1_6_6) = all_385_0_160, yields:
% 31.51/8.69 | (1080) all_465_0_280 = all_385_0_160
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1072,1074) yields a new equation:
% 31.51/8.69 | (1081) all_465_1_281 = 0
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1080,1077) yields a new equation:
% 31.51/8.69 | (1082) all_445_0_250 = all_385_0_160
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1076,1077) yields a new equation:
% 31.51/8.69 | (1083) all_463_0_277 = all_445_0_250
% 31.51/8.69 |
% 31.51/8.69 | Simplifying 1083 yields:
% 31.51/8.69 | (1084) all_463_0_277 = all_445_0_250
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1079,1077) yields a new equation:
% 31.51/8.69 | (1085) all_445_0_250 = all_387_0_163
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1084,1078) yields a new equation:
% 31.51/8.69 | (1086) all_445_0_250 = all_441_0_244
% 31.51/8.69 |
% 31.51/8.69 | Simplifying 1086 yields:
% 31.51/8.69 | (1087) all_445_0_250 = all_441_0_244
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1085,1087) yields a new equation:
% 31.51/8.69 | (1088) all_441_0_244 = all_387_0_163
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1082,1087) yields a new equation:
% 31.51/8.69 | (1089) all_441_0_244 = all_385_0_160
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1088,1089) yields a new equation:
% 31.51/8.69 | (1090) all_387_0_163 = all_385_0_160
% 31.51/8.69 |
% 31.51/8.69 | Simplifying 1090 yields:
% 31.51/8.69 | (1091) all_387_0_163 = all_385_0_160
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1069,1070) yields a new equation:
% 31.51/8.69 | (1092) all_395_2_177 = all_1_5_5
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1071,1070) yields a new equation:
% 31.51/8.69 | (1093) all_395_2_177 = all_387_2_165
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1092,1093) yields a new equation:
% 31.51/8.69 | (1094) all_387_2_165 = all_1_5_5
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1081,1074) yields a new equation:
% 31.51/8.69 | (1072) all_754_0_340 = 0
% 31.51/8.69 |
% 31.51/8.69 | From (1094) and (816) follows:
% 31.51/8.69 | (1096) apart_point_and_line(all_1_6_6, all_1_5_5) = all_387_1_164
% 31.51/8.69 |
% 31.51/8.69 | From (1091) and (817) follows:
% 31.51/8.69 | (812) distinct_points(all_1_6_6, all_1_6_6) = all_385_0_160
% 31.51/8.69 |
% 31.51/8.69 +-Applying beta-rule and splitting (1073), into two cases.
% 31.51/8.69 |-Branch one:
% 31.51/8.69 | (1098) ~ (apart_point_and_line(all_1_6_6, all_1_5_5) = all_387_1_164)
% 31.51/8.69 |
% 31.51/8.69 | Using (1096) and (1098) yields:
% 31.51/8.69 | (203) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1096) apart_point_and_line(all_1_6_6, all_1_5_5) = all_387_1_164
% 31.51/8.69 | (1101) all_754_0_340 = all_387_1_164
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1072,1101) yields a new equation:
% 31.51/8.69 | (1102) all_387_1_164 = 0
% 31.51/8.69 |
% 31.51/8.69 +-Applying beta-rule and splitting (818), into two cases.
% 31.51/8.69 |-Branch one:
% 31.51/8.69 | (1103) ~ (all_387_1_164 = 0)
% 31.51/8.69 |
% 31.51/8.69 | Equations (1102) can reduce 1103 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1102) all_387_1_164 = 0
% 31.51/8.69 | (1106) all_387_0_163 = 0
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1091,1106) yields a new equation:
% 31.51/8.69 | (1107) all_385_0_160 = 0
% 31.51/8.69 |
% 31.51/8.69 | Simplifying 1107 yields:
% 31.51/8.69 | (1108) all_385_0_160 = 0
% 31.51/8.69 |
% 31.51/8.69 | From (1108) and (812) follows:
% 31.51/8.69 | (1109) distinct_points(all_1_6_6, all_1_6_6) = 0
% 31.51/8.69 |
% 31.51/8.69 | Using (1109) and (1075) yields:
% 31.51/8.69 | (203) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (851) ~ (apart_point_and_line(all_1_6_6, all_1_5_5) = 0)
% 31.51/8.69 | (1112) all_222_2_78 = 0
% 31.51/8.69 |
% 31.51/8.69 | Equations (1112) can reduce 724 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1114) ~ (distinct_points(all_1_6_6, all_1_9_9) = 0)
% 31.51/8.69 | (281) all_16_1_11 = 0
% 31.51/8.69 |
% 31.51/8.69 | Equations (281) can reduce 206 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1117) ~ (all_1_0_0 = 0)
% 31.51/8.69 | (1118) all_1_1_1 = 0
% 31.51/8.69 |
% 31.51/8.69 | Equations (1118) can reduce 728 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (864) all_127_0_52 = 0
% 31.51/8.69 | (1121) ~ (all_127_2_54 = 0)
% 31.51/8.69 |
% 31.51/8.69 | Equations (696) can reduce 1121 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1123) apart_point_and_line(all_1_7_7, all_1_2_2) = 0
% 31.51/8.69 | (1124) all_18_1_14 = 0 | distinct_lines(all_1_2_2, all_1_5_5) = 0
% 31.51/8.69 |
% 31.51/8.69 +-Applying beta-rule and splitting (1124), into two cases.
% 31.51/8.69 |-Branch one:
% 31.51/8.69 | (1125) distinct_lines(all_1_2_2, all_1_5_5) = 0
% 31.51/8.69 |
% 31.51/8.69 | Instantiating formula (6) with all_1_2_2, all_1_5_5, 0, all_222_2_78 and discharging atoms distinct_lines(all_1_2_2, all_1_5_5) = all_222_2_78, distinct_lines(all_1_2_2, all_1_5_5) = 0, yields:
% 31.51/8.69 | (1112) all_222_2_78 = 0
% 31.51/8.69 |
% 31.51/8.69 | Equations (1112) can reduce 724 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1128) ~ (distinct_lines(all_1_2_2, all_1_5_5) = 0)
% 31.51/8.69 | (272) all_18_1_14 = 0
% 31.51/8.69 |
% 31.51/8.69 | Equations (272) can reduce 212 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (856) all_152_0_68 = 0
% 31.51/8.69 | (1132) ~ (all_152_2_70 = 0)
% 31.51/8.69 |
% 31.51/8.69 | Equations (603) can reduce 1132 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1134) all_227_2_82 = 0
% 31.51/8.69 | (1135) ~ (all_227_3_83 = 0) | all_227_0_80 = 0 | all_227_1_81 = 0
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1134,680) yields a new equation:
% 31.51/8.69 | (1112) all_222_2_78 = 0
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1112,701) yields a new equation:
% 31.51/8.69 | (1137) all_282_2_124 = 0
% 31.51/8.69 |
% 31.51/8.69 +-Applying beta-rule and splitting (516), into two cases.
% 31.51/8.69 |-Branch one:
% 31.51/8.69 | (1138) ~ (all_282_2_124 = 0)
% 31.51/8.69 |
% 31.51/8.69 | Equations (1137) can reduce 1138 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1137) all_282_2_124 = 0
% 31.51/8.69 | (1141) ~ (all_282_3_125 = 0) | all_282_0_122 = 0 | all_282_1_123 = 0
% 31.51/8.69 |
% 31.51/8.69 +-Applying beta-rule and splitting (1141), into two cases.
% 31.51/8.69 |-Branch one:
% 31.51/8.69 | (1142) ~ (all_282_3_125 = 0)
% 31.51/8.69 |
% 31.51/8.69 | Equations (611) can reduce 1142 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (611) all_282_3_125 = 0
% 31.51/8.69 | (1145) all_282_0_122 = 0 | all_282_1_123 = 0
% 31.51/8.69 |
% 31.51/8.69 +-Applying beta-rule and splitting (1145), into two cases.
% 31.51/8.69 |-Branch one:
% 31.51/8.69 | (1146) all_282_0_122 = 0
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (703,1146) yields a new equation:
% 31.51/8.69 | (1147) all_98_1_41 = 0
% 31.51/8.69 |
% 31.51/8.69 | Simplifying 1147 yields:
% 31.51/8.69 | (1148) all_98_1_41 = 0
% 31.51/8.69 |
% 31.51/8.69 | Equations (1148) can reduce 721 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.69 |-Branch two:
% 31.51/8.69 | (1150) ~ (all_282_0_122 = 0)
% 31.51/8.69 | (1151) all_282_1_123 = 0
% 31.51/8.69 |
% 31.51/8.69 | Combining equations (1151,702) yields a new equation:
% 31.51/8.69 | (102) all_1_4_4 = 0
% 31.51/8.69 |
% 31.51/8.69 | Equations (102) can reduce 53 to:
% 31.51/8.69 | (93) $false
% 31.51/8.69 |
% 31.51/8.69 |-The branch is then unsatisfiable
% 31.51/8.70 |-Branch two:
% 31.51/8.70 | (1154) all_100_1_44 = 0
% 31.51/8.70 | (1155) all_100_0_43 = 0 & all_28_3_25 = 0
% 31.51/8.70 |
% 31.51/8.70 | Applying alpha-rule on (1155) yields:
% 31.51/8.70 | (686) all_100_0_43 = 0
% 31.51/8.70 | (1157) all_28_3_25 = 0
% 31.51/8.70 |
% 31.51/8.70 | Equations (1157) can reduce 214 to:
% 31.51/8.70 | (93) $false
% 31.51/8.70 |
% 31.51/8.70 |-The branch is then unsatisfiable
% 31.51/8.70 |-Branch two:
% 31.51/8.70 | (1159) ~ (distinct_points(all_1_8_8, all_1_9_9) = 0)
% 31.51/8.70 | (257) all_16_0_10 = 0
% 31.51/8.70 |
% 31.51/8.70 | Equations (257) can reduce 189 to:
% 31.51/8.70 | (93) $false
% 31.51/8.70 |
% 31.51/8.70 |-The branch is then unsatisfiable
% 31.51/8.70 |-Branch two:
% 31.51/8.70 | (1162) ~ (distinct_points(all_1_6_6, all_1_7_7) = 0)
% 31.51/8.70 | (295) all_18_0_13 = 0
% 31.51/8.70 |
% 31.51/8.70 | Equations (295) can reduce 188 to:
% 31.51/8.70 | (93) $false
% 31.51/8.70 |
% 31.51/8.70 |-The branch is then unsatisfiable
% 31.51/8.70 |-Branch two:
% 31.51/8.70 | (1165) all_22_1_20 = 0
% 31.51/8.70 | (1166) ~ (all_22_2_21 = 0) | all_22_0_19 = 0
% 31.51/8.70 |
% 31.51/8.70 +-Applying beta-rule and splitting (1166), into two cases.
% 31.51/8.70 |-Branch one:
% 31.51/8.70 | (1167) ~ (all_22_2_21 = 0)
% 31.51/8.70 |
% 31.51/8.70 | Equations (162) can reduce 1167 to:
% 31.51/8.70 | (93) $false
% 31.51/8.70 |
% 31.51/8.70 |-The branch is then unsatisfiable
% 31.51/8.70 |-Branch two:
% 31.51/8.70 | (162) all_22_2_21 = 0
% 31.51/8.70 | (1170) all_22_0_19 = 0
% 31.51/8.70 |
% 31.51/8.70 | Combining equations (164,1170) yields a new equation:
% 31.51/8.70 | (1171) all_18_0_13 = 0
% 31.51/8.70 |
% 31.51/8.70 | Simplifying 1171 yields:
% 31.51/8.70 | (295) all_18_0_13 = 0
% 31.51/8.70 |
% 31.51/8.70 | Equations (295) can reduce 188 to:
% 31.51/8.70 | (93) $false
% 31.51/8.70 |
% 31.51/8.70 |-The branch is then unsatisfiable
% 31.51/8.70 |-Branch two:
% 31.51/8.70 | (1174) all_20_1_17 = 0
% 31.51/8.70 | (1175) all_20_0_16 = 0
% 31.51/8.70 |
% 31.51/8.70 | Combining equations (1175,185) yields a new equation:
% 31.51/8.70 | (257) all_16_0_10 = 0
% 31.51/8.70 |
% 31.51/8.70 | Equations (257) can reduce 189 to:
% 31.51/8.70 | (93) $false
% 31.51/8.70 |
% 31.51/8.70 |-The branch is then unsatisfiable
% 31.51/8.70 % SZS output end Proof for theBenchmark
% 31.51/8.70
% 31.51/8.70 8099ms
%------------------------------------------------------------------------------