TSTP Solution File: GEO196+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO196+1 : 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 03:48:32 EDT 2022
% Result : Theorem 6.04s 2.11s
% Output : Proof 27.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO196+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 18:11:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.59 ___ / __ \_____(_)___ ________ __________
% 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic
% 0.59/0.60 (ePrincess v.1.0)
% 0.59/0.60
% 0.59/0.60 (c) Philipp Rümmer, 2009-2015
% 0.59/0.60 (c) Peter Backeman, 2014-2015
% 0.59/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.60 Bug reports to peter@backeman.se
% 0.59/0.60
% 0.59/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.60
% 0.59/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/0.91 Prover 0: Preprocessing ...
% 1.85/1.04 Prover 0: Warning: ignoring some quantifiers
% 1.85/1.06 Prover 0: Constructing countermodel ...
% 3.16/1.42 Prover 0: gave up
% 3.16/1.42 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.16/1.44 Prover 1: Preprocessing ...
% 3.63/1.53 Prover 1: Constructing countermodel ...
% 3.63/1.59 Prover 1: gave up
% 3.63/1.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.63/1.62 Prover 2: Preprocessing ...
% 4.38/1.76 Prover 2: Warning: ignoring some quantifiers
% 4.38/1.77 Prover 2: Constructing countermodel ...
% 6.04/2.11 Prover 2: proved (519ms)
% 6.04/2.11
% 6.04/2.11 No countermodel exists, formula is valid
% 6.04/2.11 % SZS status Theorem for theBenchmark
% 6.04/2.11
% 6.04/2.11 Generating proof ... Warning: ignoring some quantifiers
% 25.71/8.41 found it (size 771)
% 25.71/8.41
% 25.71/8.41 % SZS output start Proof for theBenchmark
% 25.71/8.41 Assumed formulas after preprocessing and simplification:
% 25.71/8.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & ~ (v5 = 0) & intersection_point(v2, v3) = v7 & intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v3) = v6 & apart_point_and_line(v4, v2) = v5 & convergent_lines(v2, v3) = 0 & convergent_lines(v0, v1) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v11, v12) = v14) | ~ (distinct_points(v10, v11) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v10, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v10, v13) = v14) | ~ (distinct_lines(v12, v13) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v12) = v15) | ~ (apart_point_and_line(v10, v13) = v14) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v12) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v12, v13) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v10, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_points(v10, v11) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v11, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v12, v11) = v14) | ~ (distinct_points(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (convergent_lines(v11, v12) = v14) | ~ (convergent_lines(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (convergent_lines(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (distinct_lines(v11, v12) = v14) | ~ (distinct_lines(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & distinct_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (distinct_points(v11, v12) = v14) | ~ (distinct_points(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & distinct_points(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v12, v11) = v13) | ~ (apart_point_and_line(v10, v11) = 0) | distinct_points(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v12) = v13) | ~ (apart_point_and_line(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = 0) | ~ (distinct_lines(v11, v12) = v13) | apart_point_and_line(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = 0) | ~ (distinct_points(v10, v12) = v13) | apart_point_and_line(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v11, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v11) = 0) | ~ (distinct_lines(v11, v12) = v13) | convergent_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_lines(v11, v12) = v13) | ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_lines(v10, v12) = v13) | ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_points(v11, v12) = v13) | ~ (distinct_points(v10, v11) = 0) | distinct_points(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_points(v10, v12) = v13) | ~ (distinct_points(v10, v11) = 0) | distinct_points(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (intersection_point(v13, v12) = v11) | ~ (intersection_point(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (line_connecting(v13, v12) = v11) | ~ (line_connecting(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (apart_point_and_line(v13, v12) = v11) | ~ (apart_point_and_line(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (convergent_lines(v13, v12) = v11) | ~ (convergent_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (distinct_lines(v13, v12) = v11) | ~ (distinct_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (distinct_points(v13, v12) = v11) | ~ (distinct_points(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (distinct_lines(v12, v13) = 0) | ~ (distinct_points(v10, v11) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v11, v13) = 0) | (v14 = 0 & apart_point_and_line(v11, v12) = 0) | (v14 = 0 & apart_point_and_line(v10, v13) = 0) | (v14 = 0 & apart_point_and_line(v10, v12) = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v11) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v11, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v10, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v11) = v13)) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v10) = v13)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v11, v12) = v13)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v10, v12) = v13)) & ! [v10] : ~ (convergent_lines(v10, v10) = 0) & ! [v10] : ~ (distinct_lines(v10, v10) = 0) & ! [v10] : ~ (distinct_points(v10, v10) = 0) & ? [v10] : ? [v11] : ? [v12] : intersection_point(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : line_connecting(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : apart_point_and_line(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : convergent_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : distinct_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : distinct_points(v11, v10) = v12 & ((v9 = 0 & apart_point_and_line(v7, v1) = 0) | (v8 = 0 & apart_point_and_line(v7, v0) = 0)))
% 26.05/8.46 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 26.05/8.46 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5 & apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3 & apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4 & convergent_lines(all_0_7_7, all_0_6_6) = 0 & convergent_lines(all_0_9_9, all_0_8_8) = 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] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ((all_0_0_0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_0_1_1 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0))
% 26.05/8.48 |
% 26.05/8.48 | Applying alpha-rule on (1) yields:
% 26.05/8.48 | (2) ! [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)
% 26.05/8.48 | (3) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 26.05/8.48 | (4) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 26.05/8.48 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 26.05/8.48 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 26.05/8.48 | (7) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 26.05/8.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 26.05/8.48 | (9) (all_0_0_0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_0_1_1 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0)
% 26.05/8.48 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 26.05/8.48 | (11) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 26.05/8.48 | (12) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 26.05/8.48 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 26.05/8.49 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 26.05/8.49 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 26.05/8.49 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 26.05/8.49 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 26.05/8.49 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 26.05/8.49 | (19) ~ (all_0_3_3 = 0)
% 26.05/8.49 | (20) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 26.05/8.49 | (21) ! [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)
% 26.05/8.49 | (22) ! [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)
% 26.05/8.49 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 26.05/8.49 | (24) convergent_lines(all_0_9_9, all_0_8_8) = 0
% 26.21/8.49 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 26.21/8.49 | (26) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 26.21/8.49 | (27) apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3
% 26.21/8.49 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 26.21/8.49 | (29) ! [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))
% 26.21/8.49 | (30) intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5
% 26.21/8.49 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 26.21/8.49 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 26.21/8.49 | (33) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 26.21/8.49 | (34) ! [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))
% 26.21/8.49 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 26.21/8.49 | (36) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 26.21/8.49 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 26.21/8.49 | (38) intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2
% 26.21/8.49 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 26.21/8.49 | (40) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 26.21/8.49 | (41) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 26.21/8.49 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 26.21/8.49 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 26.21/8.50 | (44) ! [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))
% 26.21/8.50 | (45) ~ (all_0_4_4 = 0)
% 26.21/8.50 | (46) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 26.21/8.50 | (47) ! [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))
% 26.21/8.50 | (48) apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4
% 26.21/8.50 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 26.21/8.50 | (50) convergent_lines(all_0_7_7, all_0_6_6) = 0
% 26.21/8.50 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 26.21/8.50 | (52) ! [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)
% 26.21/8.50 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 26.21/8.50 | (54) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 26.21/8.50 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 26.21/8.50 | (56) ! [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))
% 26.21/8.50 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 26.21/8.50 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 26.21/8.50 |
% 26.21/8.50 | Instantiating formula (10) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 26.21/8.50 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = v0))
% 26.21/8.50 |
% 26.21/8.50 | Instantiating formula (55) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 26.21/8.50 | (60) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = v0))
% 26.21/8.50 |
% 26.21/8.50 | Instantiating formula (10) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields:
% 26.21/8.50 | (61) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = v0))
% 26.21/8.50 |
% 26.21/8.50 | Instantiating formula (55) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields:
% 26.21/8.50 | (62) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = v0))
% 26.21/8.50 |
% 26.21/8.50 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_0_6_6, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.21/8.50 | (63) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.50 |
% 26.21/8.50 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_0_7_7, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.21/8.50 | (64) all_0_3_3 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.51 |
% 26.21/8.51 | Instantiating formula (8) with all_0_3_3, all_0_4_4, all_0_6_6, all_0_7_7, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.21/8.51 | (65) all_0_3_3 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.51 |
% 26.21/8.51 | Instantiating formula (8) with all_0_4_4, all_0_4_4, all_0_7_7, all_0_7_7, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.21/8.51 | (66) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.51 |
% 26.21/8.51 | Instantiating formula (20) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 26.21/8.51 | (67) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(v0, all_0_6_6) = v1)
% 26.21/8.51 |
% 26.21/8.51 | Instantiating formula (7) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 26.21/8.51 | (68) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(v0, all_0_7_7) = v1)
% 26.21/8.51 |
% 26.21/8.51 | Instantiating formula (20) with all_0_8_8, all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = 0, yields:
% 26.21/8.51 | (69) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(v0, all_0_8_8) = v1)
% 26.21/8.51 |
% 26.21/8.51 | Instantiating formula (7) with all_0_8_8, all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = 0, yields:
% 26.21/8.51 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(v0, all_0_9_9) = v1)
% 26.21/8.51 |
% 26.21/8.51 | Instantiating (70) with all_20_0_28, all_20_1_29 yields:
% 26.21/8.51 | (71) ~ (all_20_0_28 = 0) & intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29 & apart_point_and_line(all_20_1_29, all_0_9_9) = all_20_0_28
% 26.21/8.51 |
% 26.21/8.51 | Applying alpha-rule on (71) yields:
% 26.21/8.51 | (72) ~ (all_20_0_28 = 0)
% 26.21/8.51 | (73) intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29
% 26.21/8.51 | (74) apart_point_and_line(all_20_1_29, all_0_9_9) = all_20_0_28
% 26.21/8.51 |
% 26.21/8.51 | Instantiating (62) with all_22_0_30 yields:
% 26.21/8.51 | (75) ( ~ (all_22_0_30 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30) | ( ~ (all_22_0_30 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30)
% 26.21/8.51 |
% 26.21/8.51 | Instantiating (61) with all_23_0_31 yields:
% 26.21/8.51 | (76) ( ~ (all_23_0_31 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31) | ( ~ (all_23_0_31 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31)
% 26.21/8.51 |
% 26.21/8.51 | Instantiating (59) with all_24_0_32 yields:
% 26.21/8.51 | (77) ( ~ (all_24_0_32 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32) | ( ~ (all_24_0_32 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32)
% 26.21/8.51 |
% 26.21/8.51 | Instantiating (60) with all_25_0_33 yields:
% 26.21/8.51 | (78) ( ~ (all_25_0_33 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33) | ( ~ (all_25_0_33 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33)
% 26.21/8.51 |
% 26.21/8.51 | Instantiating (69) with all_26_0_34, all_26_1_35 yields:
% 26.21/8.51 | (79) ~ (all_26_0_34 = 0) & intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35 & apart_point_and_line(all_26_1_35, all_0_8_8) = all_26_0_34
% 26.21/8.51 |
% 26.21/8.51 | Applying alpha-rule on (79) yields:
% 26.21/8.51 | (80) ~ (all_26_0_34 = 0)
% 26.21/8.51 | (81) intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35
% 26.21/8.51 | (82) apart_point_and_line(all_26_1_35, all_0_8_8) = all_26_0_34
% 26.21/8.51 |
% 26.21/8.51 | Instantiating (67) with all_28_0_36, all_28_1_37 yields:
% 26.21/8.51 | (83) ~ (all_28_0_36 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37 & apart_point_and_line(all_28_1_37, all_0_6_6) = all_28_0_36
% 26.21/8.51 |
% 26.21/8.51 | Applying alpha-rule on (83) yields:
% 26.21/8.51 | (84) ~ (all_28_0_36 = 0)
% 26.21/8.51 | (85) intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37
% 26.21/8.51 | (86) apart_point_and_line(all_28_1_37, all_0_6_6) = all_28_0_36
% 26.21/8.51 |
% 26.21/8.51 | Instantiating (68) with all_30_0_38, all_30_1_39 yields:
% 26.21/8.51 | (87) ~ (all_30_0_38 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39 & apart_point_and_line(all_30_1_39, all_0_7_7) = all_30_0_38
% 26.21/8.51 |
% 26.21/8.51 | Applying alpha-rule on (87) yields:
% 26.21/8.51 | (88) ~ (all_30_0_38 = 0)
% 26.21/8.51 | (89) intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39
% 26.21/8.51 | (90) apart_point_and_line(all_30_1_39, all_0_7_7) = all_30_0_38
% 26.21/8.51 |
% 26.21/8.51 +-Applying beta-rule and splitting (75), into two cases.
% 26.21/8.51 |-Branch one:
% 26.21/8.51 | (91) ~ (all_22_0_30 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30
% 26.21/8.51 |
% 26.21/8.51 | Applying alpha-rule on (91) yields:
% 26.21/8.51 | (92) ~ (all_22_0_30 = 0)
% 26.21/8.51 | (93) apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30
% 26.21/8.51 |
% 26.21/8.51 +-Applying beta-rule and splitting (76), into two cases.
% 26.21/8.51 |-Branch one:
% 26.21/8.51 | (94) ~ (all_23_0_31 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31
% 26.21/8.51 |
% 26.21/8.51 | Applying alpha-rule on (94) yields:
% 26.21/8.51 | (95) ~ (all_23_0_31 = 0)
% 26.21/8.51 | (96) apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31
% 26.21/8.51 |
% 26.21/8.51 +-Applying beta-rule and splitting (77), into two cases.
% 26.21/8.51 |-Branch one:
% 26.21/8.51 | (97) ~ (all_24_0_32 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32
% 26.21/8.51 |
% 26.21/8.51 | Applying alpha-rule on (97) yields:
% 26.21/8.51 | (98) ~ (all_24_0_32 = 0)
% 26.21/8.51 | (99) apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32
% 26.21/8.51 |
% 26.21/8.51 +-Applying beta-rule and splitting (66), into two cases.
% 26.21/8.51 |-Branch one:
% 26.21/8.51 | (100) all_0_4_4 = 0
% 26.21/8.51 |
% 26.21/8.51 | Equations (100) can reduce 45 to:
% 26.21/8.51 | (101) $false
% 26.21/8.51 |
% 26.21/8.51 |-The branch is then unsatisfiable
% 26.21/8.51 |-Branch two:
% 26.21/8.51 | (45) ~ (all_0_4_4 = 0)
% 26.21/8.51 | (103) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52 |
% 26.21/8.52 +-Applying beta-rule and splitting (78), into two cases.
% 26.21/8.52 |-Branch one:
% 26.21/8.52 | (104) ~ (all_25_0_33 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33
% 26.21/8.52 |
% 26.21/8.52 | Applying alpha-rule on (104) yields:
% 26.21/8.52 | (105) ~ (all_25_0_33 = 0)
% 26.21/8.52 | (106) apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33
% 26.21/8.52 |
% 26.21/8.52 +-Applying beta-rule and splitting (63), into two cases.
% 26.21/8.52 |-Branch one:
% 26.21/8.52 | (107) all_0_3_3 = 0
% 26.21/8.52 |
% 26.21/8.52 | Equations (107) can reduce 19 to:
% 26.21/8.52 | (101) $false
% 26.21/8.52 |
% 26.21/8.52 |-The branch is then unsatisfiable
% 26.21/8.52 |-Branch two:
% 26.21/8.52 | (19) ~ (all_0_3_3 = 0)
% 26.21/8.52 | (110) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52 |
% 26.21/8.52 +-Applying beta-rule and splitting (64), into two cases.
% 26.21/8.52 |-Branch one:
% 26.21/8.52 | (107) all_0_3_3 = 0
% 26.21/8.52 |
% 26.21/8.52 | Equations (107) can reduce 19 to:
% 26.21/8.52 | (101) $false
% 26.21/8.52 |
% 26.21/8.52 |-The branch is then unsatisfiable
% 26.21/8.52 |-Branch two:
% 26.21/8.52 | (19) ~ (all_0_3_3 = 0)
% 26.21/8.52 | (114) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52 |
% 26.21/8.52 +-Applying beta-rule and splitting (65), into two cases.
% 26.21/8.52 |-Branch one:
% 26.21/8.52 | (107) all_0_3_3 = 0
% 26.21/8.52 |
% 26.21/8.52 | Equations (107) can reduce 19 to:
% 26.21/8.52 | (101) $false
% 26.21/8.52 |
% 26.21/8.52 |-The branch is then unsatisfiable
% 26.21/8.52 |-Branch two:
% 26.21/8.52 | (19) ~ (all_0_3_3 = 0)
% 26.21/8.52 | (118) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52 |
% 26.21/8.52 +-Applying beta-rule and splitting (114), into two cases.
% 26.21/8.52 |-Branch one:
% 26.21/8.52 | (100) all_0_4_4 = 0
% 26.21/8.52 |
% 26.21/8.52 | Equations (100) can reduce 45 to:
% 26.21/8.52 | (101) $false
% 26.21/8.52 |
% 26.21/8.52 |-The branch is then unsatisfiable
% 26.21/8.52 |-Branch two:
% 26.21/8.52 | (45) ~ (all_0_4_4 = 0)
% 26.21/8.52 | (122) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52 |
% 26.21/8.52 +-Applying beta-rule and splitting (118), into two cases.
% 26.21/8.52 |-Branch one:
% 26.21/8.52 | (100) all_0_4_4 = 0
% 26.21/8.52 |
% 26.21/8.52 | Equations (100) can reduce 45 to:
% 26.21/8.52 | (101) $false
% 26.21/8.52 |
% 26.21/8.52 |-The branch is then unsatisfiable
% 26.21/8.52 |-Branch two:
% 26.21/8.52 | (45) ~ (all_0_4_4 = 0)
% 26.21/8.52 | (126) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52 |
% 26.21/8.52 | Instantiating formula (39) with all_0_7_7, all_0_6_6, all_30_1_39, all_0_2_2 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39, intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 26.21/8.52 | (127) all_30_1_39 = all_0_2_2
% 26.21/8.52 |
% 26.21/8.52 | Instantiating formula (39) with all_0_7_7, all_0_6_6, all_28_1_37, all_30_1_39 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39, intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37, yields:
% 26.21/8.52 | (128) all_30_1_39 = all_28_1_37
% 26.21/8.52 |
% 26.21/8.52 | Instantiating formula (39) with all_0_9_9, all_0_8_8, all_26_1_35, all_0_5_5 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35, intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields:
% 26.21/8.52 | (129) all_26_1_35 = all_0_5_5
% 26.21/8.52 |
% 26.21/8.52 | Instantiating formula (39) with all_0_9_9, all_0_8_8, all_20_1_29, all_26_1_35 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35, intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29, yields:
% 26.21/8.52 | (130) all_26_1_35 = all_20_1_29
% 26.21/8.52 |
% 26.21/8.52 | Combining equations (127,128) yields a new equation:
% 26.21/8.52 | (131) all_28_1_37 = all_0_2_2
% 26.21/8.52 |
% 26.21/8.52 | Combining equations (130,129) yields a new equation:
% 26.21/8.52 | (132) all_20_1_29 = all_0_5_5
% 26.21/8.52 |
% 26.21/8.52 | Simplifying 132 yields:
% 26.21/8.52 | (133) all_20_1_29 = all_0_5_5
% 26.21/8.52 |
% 26.21/8.52 | Combining equations (131,128) yields a new equation:
% 26.21/8.52 | (127) all_30_1_39 = all_0_2_2
% 26.21/8.52 |
% 26.21/8.52 | From (127) and (90) follows:
% 26.21/8.52 | (135) apart_point_and_line(all_0_2_2, all_0_7_7) = all_30_0_38
% 26.21/8.52 |
% 26.21/8.52 | From (131) and (86) follows:
% 26.21/8.52 | (136) apart_point_and_line(all_0_2_2, all_0_6_6) = all_28_0_36
% 26.21/8.52 |
% 26.21/8.52 | From (129) and (82) follows:
% 26.21/8.52 | (137) apart_point_and_line(all_0_5_5, all_0_8_8) = all_26_0_34
% 26.21/8.52 |
% 26.21/8.52 | From (133) and (74) follows:
% 26.21/8.52 | (138) apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28
% 26.21/8.52 |
% 26.21/8.52 | Instantiating formula (25) with all_0_2_2, all_0_6_6, all_28_0_36, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_28_0_36, apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, yields:
% 26.21/8.52 | (139) all_28_0_36 = all_24_0_32
% 26.21/8.52 |
% 26.21/8.52 | Instantiating formula (25) with all_0_2_2, all_0_7_7, all_30_0_38, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_30_0_38, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields:
% 26.21/8.52 | (140) all_30_0_38 = all_25_0_33
% 26.21/8.52 |
% 26.21/8.52 | Instantiating formula (25) with all_0_5_5, all_0_8_8, all_26_0_34, all_23_0_31 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_26_0_34, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.21/8.52 | (141) all_26_0_34 = all_23_0_31
% 26.21/8.52 |
% 26.21/8.52 | Instantiating formula (25) with all_0_5_5, all_0_9_9, all_20_0_28, all_22_0_30 and discharging atoms apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.21/8.53 | (142) all_22_0_30 = all_20_0_28
% 26.21/8.53 |
% 26.21/8.53 | Equations (140) can reduce 88 to:
% 26.21/8.53 | (105) ~ (all_25_0_33 = 0)
% 26.21/8.53 |
% 26.21/8.53 | Equations (139) can reduce 84 to:
% 26.21/8.53 | (98) ~ (all_24_0_32 = 0)
% 26.21/8.53 |
% 26.21/8.53 | Equations (141) can reduce 80 to:
% 26.21/8.53 | (95) ~ (all_23_0_31 = 0)
% 26.21/8.53 |
% 26.21/8.53 | Equations (142) can reduce 92 to:
% 26.21/8.53 | (72) ~ (all_20_0_28 = 0)
% 26.21/8.53 |
% 26.21/8.53 | From (139) and (136) follows:
% 26.21/8.53 | (99) apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32
% 26.21/8.53 |
% 26.21/8.53 | From (140) and (135) follows:
% 26.21/8.53 | (106) apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33
% 26.21/8.53 |
% 26.21/8.53 | From (141) and (137) follows:
% 26.21/8.53 | (96) apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31
% 26.21/8.53 |
% 26.21/8.53 | From (142) and (93) follows:
% 26.21/8.53 | (138) apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28
% 26.21/8.53 |
% 26.21/8.53 | Instantiating formula (8) with all_24_0_32, all_0_3_3, all_0_6_6, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.21/8.53 | (151) all_24_0_32 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.21/8.53 |
% 26.21/8.53 | Instantiating formula (8) with all_0_3_3, all_24_0_32, all_0_6_6, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.21/8.53 | (152) all_24_0_32 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.40/8.53 |
% 26.40/8.53 | Instantiating formula (8) with all_24_0_32, all_0_4_4, all_0_6_6, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.40/8.53 | (153) all_24_0_32 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.40/8.53 |
% 26.40/8.53 | Instantiating formula (8) with all_0_4_4, all_24_0_32, all_0_7_7, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.40/8.53 | (154) all_24_0_32 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.40/8.53 |
% 26.40/8.53 | Instantiating formula (58) with all_24_0_32, all_0_4_4, all_0_7_7, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.40/8.53 | (155) all_24_0_32 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.40/8.53 |
% 26.40/8.53 | Instantiating formula (58) with all_0_4_4, all_24_0_32, all_0_6_6, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.40/8.53 | (156) all_24_0_32 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.40/8.53 |
% 26.40/8.53 | Instantiating formula (8) with all_24_0_32, all_24_0_32, all_0_6_6, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, yields:
% 26.40/8.53 | (157) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.40/8.53 |
% 26.40/8.53 | Instantiating formula (8) with all_25_0_33, all_0_3_3, all_0_7_7, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.40/8.53 | (158) all_25_0_33 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.40/8.53 |
% 26.40/8.53 | Instantiating formula (8) with all_0_3_3, all_25_0_33, all_0_6_6, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.40/8.53 | (159) all_25_0_33 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.40/8.53 |
% 26.40/8.53 | Instantiating formula (58) with all_25_0_33, all_0_3_3, all_0_6_6, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.40/8.53 | (160) all_25_0_33 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.40/8.54 |
% 26.40/8.54 | Instantiating formula (58) with all_0_3_3, all_25_0_33, all_0_7_7, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.40/8.54 | (161) all_25_0_33 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_25_0_33, all_0_4_4, all_0_7_7, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.45/8.54 | (162) all_25_0_33 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_0_4_4, all_25_0_33, all_0_7_7, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.45/8.54 | (163) all_25_0_33 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_25_0_33, all_24_0_32, all_0_7_7, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields:
% 26.45/8.54 | (164) all_25_0_33 = 0 | all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_24_0_32, all_25_0_33, all_0_6_6, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields:
% 26.45/8.54 | (165) all_25_0_33 = 0 | all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_25_0_33, all_25_0_33, all_0_7_7, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields:
% 26.45/8.54 | (166) all_25_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_23_0_31, all_0_3_3, all_0_8_8, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54 | (167) all_23_0_31 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_0_3_3, all_23_0_31, all_0_6_6, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54 | (168) all_23_0_31 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_23_0_31, all_0_4_4, all_0_8_8, all_0_7_7, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54 | (169) all_23_0_31 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_0_4_4, all_23_0_31, all_0_7_7, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54 | (170) all_23_0_31 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_23_0_31, all_24_0_32, all_0_8_8, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54 | (171) all_24_0_32 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (8) with all_24_0_32, all_23_0_31, all_0_6_6, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54 | (172) all_24_0_32 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.54 |
% 26.45/8.54 | Instantiating formula (58) with all_23_0_31, all_24_0_32, all_0_6_6, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55 | (173) all_24_0_32 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (58) with all_24_0_32, all_23_0_31, all_0_8_8, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55 | (174) all_24_0_32 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (8) with all_23_0_31, all_25_0_33, all_0_8_8, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55 | (175) all_25_0_33 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (8) with all_25_0_33, all_23_0_31, all_0_7_7, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55 | (176) all_25_0_33 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (58) with all_23_0_31, all_25_0_33, all_0_7_7, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55 | (177) all_25_0_33 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (58) with all_25_0_33, all_23_0_31, all_0_8_8, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55 | (178) all_25_0_33 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (8) with all_23_0_31, all_23_0_31, all_0_8_8, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55 | (179) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (8) with all_20_0_28, all_0_3_3, all_0_9_9, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55 | (180) all_20_0_28 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (8) with all_0_3_3, all_20_0_28, all_0_6_6, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55 | (181) all_20_0_28 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (8) with all_20_0_28, all_0_4_4, all_0_9_9, all_0_7_7, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55 | (182) all_20_0_28 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (8) with all_0_4_4, all_20_0_28, all_0_7_7, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55 | (183) all_20_0_28 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55 |
% 26.45/8.55 | Instantiating formula (8) with all_20_0_28, all_24_0_32, all_0_9_9, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55 | (184) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (8) with all_24_0_32, all_20_0_28, all_0_6_6, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (185) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (58) with all_20_0_28, all_24_0_32, all_0_6_6, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (186) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (58) with all_24_0_32, all_20_0_28, all_0_9_9, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (187) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (8) with all_20_0_28, all_25_0_33, all_0_9_9, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (188) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (8) with all_25_0_33, all_20_0_28, all_0_7_7, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (189) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (58) with all_20_0_28, all_25_0_33, all_0_7_7, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (190) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (58) with all_25_0_33, all_20_0_28, all_0_9_9, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (191) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (8) with all_20_0_28, all_23_0_31, all_0_9_9, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (192) all_23_0_31 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (8) with all_23_0_31, all_20_0_28, all_0_8_8, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (193) all_23_0_31 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.56 |
% 26.45/8.56 | Instantiating formula (8) with all_20_0_28, all_20_0_28, all_0_9_9, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56 | (194) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.56 |
% 26.45/8.56 +-Applying beta-rule and splitting (9), into two cases.
% 26.45/8.56 |-Branch one:
% 26.45/8.56 | (195) all_0_0_0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0
% 26.45/8.56 |
% 26.45/8.56 | Applying alpha-rule on (195) yields:
% 26.45/8.56 | (196) all_0_0_0 = 0
% 26.45/8.56 | (197) apart_point_and_line(all_0_2_2, all_0_8_8) = 0
% 26.45/8.56 |
% 26.45/8.56 +-Applying beta-rule and splitting (166), into two cases.
% 26.45/8.56 |-Branch one:
% 26.45/8.56 | (198) all_25_0_33 = 0
% 26.45/8.56 |
% 26.45/8.56 | Equations (198) can reduce 105 to:
% 26.45/8.56 | (101) $false
% 26.45/8.56 |
% 26.45/8.56 |-The branch is then unsatisfiable
% 26.45/8.56 |-Branch two:
% 26.45/8.56 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.56 | (201) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.56 |
% 26.45/8.56 +-Applying beta-rule and splitting (157), into two cases.
% 26.45/8.56 |-Branch one:
% 26.45/8.56 | (202) all_24_0_32 = 0
% 26.45/8.56 |
% 26.45/8.56 | Equations (202) can reduce 98 to:
% 26.45/8.56 | (101) $false
% 26.45/8.56 |
% 26.45/8.56 |-The branch is then unsatisfiable
% 26.45/8.56 |-Branch two:
% 26.45/8.56 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.56 | (205) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.56 |
% 26.45/8.56 +-Applying beta-rule and splitting (179), into two cases.
% 26.45/8.56 |-Branch one:
% 26.45/8.56 | (206) all_23_0_31 = 0
% 26.45/8.56 |
% 26.45/8.56 | Equations (206) can reduce 95 to:
% 26.45/8.56 | (101) $false
% 26.45/8.56 |
% 26.45/8.56 |-The branch is then unsatisfiable
% 26.45/8.56 |-Branch two:
% 26.45/8.56 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.56 | (209) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.56 |
% 26.45/8.56 +-Applying beta-rule and splitting (194), into two cases.
% 26.45/8.56 |-Branch one:
% 26.45/8.56 | (210) all_20_0_28 = 0
% 26.45/8.56 |
% 26.45/8.56 | Equations (210) can reduce 72 to:
% 26.45/8.56 | (101) $false
% 26.45/8.56 |
% 26.45/8.56 |-The branch is then unsatisfiable
% 26.45/8.56 |-Branch two:
% 26.45/8.56 | (72) ~ (all_20_0_28 = 0)
% 26.45/8.56 | (213) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (181), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (210) all_20_0_28 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (210) can reduce 72 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (72) ~ (all_20_0_28 = 0)
% 26.45/8.57 | (217) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (182), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (210) all_20_0_28 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (210) can reduce 72 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (72) ~ (all_20_0_28 = 0)
% 26.45/8.57 | (221) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (187), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (202) all_24_0_32 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (202) can reduce 98 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.57 | (225) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (188), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (198) all_25_0_33 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (198) can reduce 105 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.57 | (229) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (191), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (198) all_25_0_33 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (198) can reduce 105 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.57 | (233) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (151), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (202) all_24_0_32 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (202) can reduce 98 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.57 | (237) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (163), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (198) all_25_0_33 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (198) can reduce 105 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.57 | (241) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (164), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (198) all_25_0_33 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (198) can reduce 105 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.57 | (245) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (192), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (206) all_23_0_31 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (206) can reduce 95 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.57 | (249) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (152), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (202) all_24_0_32 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (202) can reduce 98 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.57 | (253) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (153), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (202) all_24_0_32 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (202) can reduce 98 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.57 | (257) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (154), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (202) all_24_0_32 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (202) can reduce 98 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.57 | (261) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (158), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (198) all_25_0_33 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (198) can reduce 105 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.57 | (265) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (155), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (202) all_24_0_32 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (202) can reduce 98 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.57 | (269) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57 |
% 26.45/8.57 +-Applying beta-rule and splitting (183), into two cases.
% 26.45/8.57 |-Branch one:
% 26.45/8.57 | (210) all_20_0_28 = 0
% 26.45/8.57 |
% 26.45/8.57 | Equations (210) can reduce 72 to:
% 26.45/8.57 | (101) $false
% 26.45/8.57 |
% 26.45/8.57 |-The branch is then unsatisfiable
% 26.45/8.57 |-Branch two:
% 26.45/8.57 | (72) ~ (all_20_0_28 = 0)
% 26.45/8.57 | (273) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (171), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (202) all_24_0_32 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (202) can reduce 98 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.58 | (277) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (184), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (202) all_24_0_32 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (202) can reduce 98 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.58 | (281) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (156), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (202) all_24_0_32 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (202) can reduce 98 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.58 | (285) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (185), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (202) all_24_0_32 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (202) can reduce 98 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.58 | (289) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (186), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (202) all_24_0_32 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (202) can reduce 98 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.58 | (293) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (189), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (198) all_25_0_33 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (198) can reduce 105 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.58 | (297) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (190), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (198) all_25_0_33 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (198) can reduce 105 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.58 | (301) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (172), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (202) all_24_0_32 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (202) can reduce 98 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.58 | (305) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (175), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (198) all_25_0_33 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (198) can reduce 105 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.58 | (309) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (176), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (198) all_25_0_33 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (198) can reduce 105 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.58 | (313) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (177), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (198) all_25_0_33 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (198) can reduce 105 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.58 | (317) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (178), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (198) all_25_0_33 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (198) can reduce 105 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.58 | (321) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (180), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (210) all_20_0_28 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (210) can reduce 72 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (72) ~ (all_20_0_28 = 0)
% 26.45/8.58 | (325) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (193), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (206) all_23_0_31 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (206) can reduce 95 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.58 | (329) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (167), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (206) all_23_0_31 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (206) can reduce 95 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.58 | (333) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (168), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (206) all_23_0_31 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (206) can reduce 95 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.58 | (337) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58 |
% 26.45/8.58 +-Applying beta-rule and splitting (169), into two cases.
% 26.45/8.58 |-Branch one:
% 26.45/8.58 | (206) all_23_0_31 = 0
% 26.45/8.58 |
% 26.45/8.58 | Equations (206) can reduce 95 to:
% 26.45/8.58 | (101) $false
% 26.45/8.58 |
% 26.45/8.58 |-The branch is then unsatisfiable
% 26.45/8.58 |-Branch two:
% 26.45/8.58 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.58 | (341) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (170), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (206) all_23_0_31 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (206) can reduce 95 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.59 | (345) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (173), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (202) all_24_0_32 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (202) can reduce 98 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.59 | (349) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (174), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (202) all_24_0_32 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (202) can reduce 98 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.59 | (353) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (159), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (198) all_25_0_33 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (198) can reduce 105 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.59 | (357) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (160), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (198) all_25_0_33 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (198) can reduce 105 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.59 | (361) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (161), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (198) all_25_0_33 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (198) can reduce 105 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.59 | (365) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (162), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (198) all_25_0_33 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (198) can reduce 105 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.59 | (369) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (165), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (198) all_25_0_33 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (198) can reduce 105 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (105) ~ (all_25_0_33 = 0)
% 26.45/8.59 | (373) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (217), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (107) all_0_3_3 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (107) can reduce 19 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.59 | (377) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (221), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (100) all_0_4_4 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (100) can reduce 45 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.59 | (381) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (237), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (107) all_0_3_3 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (107) can reduce 19 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.59 | (385) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (241), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (100) all_0_4_4 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (100) can reduce 45 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.59 | (389) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (245), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (202) all_24_0_32 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (202) can reduce 98 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (98) ~ (all_24_0_32 = 0)
% 26.45/8.59 | (393) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (253), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (107) all_0_3_3 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (107) can reduce 19 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.59 | (397) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (257), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (100) all_0_4_4 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (100) can reduce 45 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.59 | (401) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (261), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (100) all_0_4_4 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (100) can reduce 45 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.59 | (405) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59 |
% 26.45/8.59 | Instantiating (405) with all_272_0_59 yields:
% 26.45/8.59 | (406) (all_272_0_59 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_59 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_272_0_59 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59) | ( ~ (all_272_0_59 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_272_0_59)
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (265), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (107) all_0_3_3 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (107) can reduce 19 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.59 | (410) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59 |
% 26.45/8.59 | Instantiating (410) with all_276_0_60 yields:
% 26.45/8.59 | (411) (all_276_0_60 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_60 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_276_0_60 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60) | ( ~ (all_276_0_60 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_276_0_60)
% 26.45/8.59 |
% 26.45/8.59 +-Applying beta-rule and splitting (269), into two cases.
% 26.45/8.59 |-Branch one:
% 26.45/8.59 | (100) all_0_4_4 = 0
% 26.45/8.59 |
% 26.45/8.59 | Equations (100) can reduce 45 to:
% 26.45/8.59 | (101) $false
% 26.45/8.59 |
% 26.45/8.59 |-The branch is then unsatisfiable
% 26.45/8.59 |-Branch two:
% 26.45/8.59 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.59 | (415) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60 |
% 26.45/8.60 | Instantiating (415) with all_280_0_61 yields:
% 26.45/8.60 | (416) (all_280_0_61 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_61 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_280_0_61 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61) | ( ~ (all_280_0_61 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_280_0_61)
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (273), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (100) all_0_4_4 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (100) can reduce 45 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.60 | (420) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (277), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (206) all_23_0_31 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (206) can reduce 95 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.60 | (424) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (285), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (100) all_0_4_4 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (100) can reduce 45 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.60 | (428) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (305), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (206) all_23_0_31 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (206) can reduce 95 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.60 | (432) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (309), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (206) all_23_0_31 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (206) can reduce 95 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.60 | (436) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (313), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (206) all_23_0_31 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (206) can reduce 95 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.60 | (440) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (317), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (206) all_23_0_31 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (206) can reduce 95 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.60 | (444) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (321), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (206) all_23_0_31 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (206) can reduce 95 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.60 | (448) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (325), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (107) all_0_3_3 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (107) can reduce 19 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.60 | (452) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (333), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (107) all_0_3_3 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (107) can reduce 19 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.60 | (456) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (337), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (107) all_0_3_3 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (107) can reduce 19 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.60 | (460) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (341), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (100) all_0_4_4 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (100) can reduce 45 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.60 | (464) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (345), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (100) all_0_4_4 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (100) can reduce 45 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (45) ~ (all_0_4_4 = 0)
% 26.45/8.60 | (468) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (349), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (206) all_23_0_31 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (206) can reduce 95 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.60 | (472) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (353), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (206) all_23_0_31 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (206) can reduce 95 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (95) ~ (all_23_0_31 = 0)
% 26.45/8.60 | (476) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (357), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (107) all_0_3_3 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (107) can reduce 19 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.60 | (480) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (361), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (107) all_0_3_3 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (107) can reduce 19 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.60 | (484) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60 |
% 26.45/8.60 +-Applying beta-rule and splitting (365), into two cases.
% 26.45/8.60 |-Branch one:
% 26.45/8.60 | (107) all_0_3_3 = 0
% 26.45/8.60 |
% 26.45/8.60 | Equations (107) can reduce 19 to:
% 26.45/8.60 | (101) $false
% 26.45/8.60 |
% 26.45/8.60 |-The branch is then unsatisfiable
% 26.45/8.60 |-Branch two:
% 26.45/8.60 | (19) ~ (all_0_3_3 = 0)
% 26.45/8.60 | (488) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60 |
% 26.45/8.60 | Instantiating (488) with all_376_0_85 yields:
% 26.45/8.60 | (489) (all_376_0_85 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_85 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_376_0_85 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85) | ( ~ (all_376_0_85 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_376_0_85)
% 26.78/8.60 |
% 26.78/8.60 +-Applying beta-rule and splitting (369), into two cases.
% 26.78/8.60 |-Branch one:
% 26.78/8.60 | (100) all_0_4_4 = 0
% 26.78/8.60 |
% 26.78/8.60 | Equations (100) can reduce 45 to:
% 26.78/8.60 | (101) $false
% 26.78/8.60 |
% 26.78/8.60 |-The branch is then unsatisfiable
% 26.78/8.60 |-Branch two:
% 26.78/8.60 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.60 | (493) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.60 |
% 26.78/8.60 +-Applying beta-rule and splitting (373), into two cases.
% 26.78/8.60 |-Branch one:
% 26.78/8.60 | (202) all_24_0_32 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (202) can reduce 98 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.61 | (497) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (2) with all_23_0_31, all_0_5_5, all_0_8_8, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = 0, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.78/8.61 | (498) all_23_0_31 = 0 | distinct_points(all_0_2_2, all_0_5_5) = 0
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (498), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (499) distinct_points(all_0_2_2, all_0_5_5) = 0
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (489), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (500) (all_376_0_85 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_85 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_376_0_85 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85)
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (500), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (501) (all_376_0_85 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_85 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (501), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (502) all_376_0_85 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (502) yields:
% 26.78/8.61 | (503) all_376_0_85 = 0
% 26.78/8.61 | (504) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (25) with all_0_2_2, all_0_6_6, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 26.78/8.61 | (202) all_24_0_32 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (202) can reduce 98 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (507) all_376_0_85 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (507) yields:
% 26.78/8.61 | (503) all_376_0_85 = 0
% 26.78/8.61 | (509) apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (25) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields:
% 26.78/8.61 | (100) all_0_4_4 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (100) can reduce 45 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (512) ~ (all_376_0_85 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (512) yields:
% 26.78/8.61 | (513) ~ (all_376_0_85 = 0)
% 26.78/8.61 | (514) distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (406), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (515) (all_272_0_59 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_59 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_272_0_59 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59)
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (515), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (516) (all_272_0_59 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_59 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0)
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (516), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (517) all_272_0_59 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (517) yields:
% 26.78/8.61 | (518) all_272_0_59 = 0
% 26.78/8.61 | (519) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (25) with all_0_2_2, all_0_7_7, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 26.78/8.61 | (198) all_25_0_33 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (198) can reduce 105 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (522) all_272_0_59 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (522) yields:
% 26.78/8.61 | (518) all_272_0_59 = 0
% 26.78/8.61 | (524) apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (25) with all_0_5_5, all_0_6_6, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields:
% 26.78/8.61 | (107) all_0_3_3 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (107) can reduce 19 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (527) ~ (all_272_0_59 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (527) yields:
% 26.78/8.61 | (528) ~ (all_272_0_59 = 0)
% 26.78/8.61 | (529) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (28) with all_0_6_6, all_0_7_7, all_272_0_59, all_376_0_85 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59, yields:
% 26.78/8.61 | (530) all_376_0_85 = all_272_0_59
% 26.78/8.61 |
% 26.78/8.61 | From (530) and (514) follows:
% 26.78/8.61 | (529) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (411), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (532) (all_276_0_60 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_60 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_276_0_60 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60)
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (532), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (533) (all_276_0_60 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_60 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (533), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (534) all_276_0_60 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (534) yields:
% 26.78/8.61 | (535) all_276_0_60 = 0
% 26.78/8.61 | (504) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (25) with all_0_2_2, all_0_6_6, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 26.78/8.61 | (202) all_24_0_32 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (202) can reduce 98 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (539) all_276_0_60 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (539) yields:
% 26.78/8.61 | (535) all_276_0_60 = 0
% 26.78/8.61 | (509) apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (25) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields:
% 26.78/8.61 | (100) all_0_4_4 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (100) can reduce 45 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (544) ~ (all_276_0_60 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (544) yields:
% 26.78/8.61 | (545) ~ (all_276_0_60 = 0)
% 26.78/8.61 | (546) distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (28) with all_0_6_6, all_0_7_7, all_276_0_60, all_272_0_59 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59, yields:
% 26.78/8.61 | (547) all_276_0_60 = all_272_0_59
% 26.78/8.61 |
% 26.78/8.61 | From (547) and (546) follows:
% 26.78/8.61 | (529) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (416), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (549) (all_280_0_61 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_61 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_280_0_61 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61)
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (549), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (550) (all_280_0_61 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_61 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0)
% 26.78/8.61 |
% 26.78/8.61 +-Applying beta-rule and splitting (550), into two cases.
% 26.78/8.61 |-Branch one:
% 26.78/8.61 | (551) all_280_0_61 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (551) yields:
% 26.78/8.61 | (552) all_280_0_61 = 0
% 26.78/8.61 | (519) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (25) with all_0_2_2, all_0_7_7, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 26.78/8.61 | (198) all_25_0_33 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (198) can reduce 105 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (556) all_280_0_61 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (556) yields:
% 26.78/8.61 | (552) all_280_0_61 = 0
% 26.78/8.61 | (524) apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (25) with all_0_5_5, all_0_6_6, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields:
% 26.78/8.61 | (107) all_0_3_3 = 0
% 26.78/8.61 |
% 26.78/8.61 | Equations (107) can reduce 19 to:
% 26.78/8.61 | (101) $false
% 26.78/8.61 |
% 26.78/8.61 |-The branch is then unsatisfiable
% 26.78/8.61 |-Branch two:
% 26.78/8.61 | (561) ~ (all_280_0_61 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61
% 26.78/8.61 |
% 26.78/8.61 | Applying alpha-rule on (561) yields:
% 26.78/8.61 | (562) ~ (all_280_0_61 = 0)
% 26.78/8.61 | (563) distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61
% 26.78/8.61 |
% 26.78/8.61 | Instantiating formula (28) with all_0_6_6, all_0_7_7, all_280_0_61, all_272_0_59 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59, yields:
% 26.78/8.62 | (564) all_280_0_61 = all_272_0_59
% 26.78/8.62 |
% 26.78/8.62 | Equations (564) can reduce 562 to:
% 26.78/8.62 | (528) ~ (all_272_0_59 = 0)
% 26.78/8.62 |
% 26.78/8.62 | From (564) and (563) follows:
% 26.78/8.62 | (529) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.62 |
% 26.78/8.62 | Instantiating formula (17) with all_272_0_59, all_0_7_7, all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59, yields:
% 26.78/8.62 | (567) all_272_0_59 = 0 | convergent_lines(all_0_7_7, all_0_7_7) = 0
% 26.78/8.62 |
% 26.78/8.62 +-Applying beta-rule and splitting (567), into two cases.
% 26.78/8.62 |-Branch one:
% 26.78/8.62 | (568) convergent_lines(all_0_7_7, all_0_7_7) = 0
% 26.78/8.62 |
% 26.78/8.62 | Instantiating formula (4) with all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_7_7) = 0, yields:
% 26.78/8.62 | (569) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (570) ~ (convergent_lines(all_0_7_7, all_0_7_7) = 0)
% 26.78/8.62 | (518) all_272_0_59 = 0
% 26.78/8.62 |
% 26.78/8.62 | Equations (518) can reduce 528 to:
% 26.78/8.62 | (101) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (573) ~ (all_280_0_61 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_280_0_61
% 26.78/8.62 |
% 26.78/8.62 | Applying alpha-rule on (573) yields:
% 26.78/8.62 | (562) ~ (all_280_0_61 = 0)
% 26.78/8.62 | (575) distinct_points(all_0_5_5, all_0_2_2) = all_280_0_61
% 26.78/8.62 |
% 26.78/8.62 | Instantiating formula (32) with all_280_0_61, all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_2_2) = all_280_0_61, yields:
% 26.78/8.62 | (576) all_280_0_61 = 0 | distinct_points(all_0_2_2, all_0_2_2) = 0
% 26.78/8.62 |
% 26.78/8.62 +-Applying beta-rule and splitting (576), into two cases.
% 26.78/8.62 |-Branch one:
% 26.78/8.62 | (577) distinct_points(all_0_2_2, all_0_2_2) = 0
% 26.78/8.62 |
% 26.78/8.62 | Instantiating formula (26) with all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_2_2) = 0, yields:
% 26.78/8.62 | (569) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (579) ~ (distinct_points(all_0_2_2, all_0_2_2) = 0)
% 26.78/8.62 | (552) all_280_0_61 = 0
% 26.78/8.62 |
% 26.78/8.62 | Equations (552) can reduce 562 to:
% 26.78/8.62 | (101) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (582) ~ (all_276_0_60 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_276_0_60
% 26.78/8.62 |
% 26.78/8.62 | Applying alpha-rule on (582) yields:
% 26.78/8.62 | (545) ~ (all_276_0_60 = 0)
% 26.78/8.62 | (584) distinct_points(all_0_5_5, all_0_2_2) = all_276_0_60
% 26.78/8.62 |
% 26.78/8.62 | Instantiating formula (32) with all_276_0_60, all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_2_2) = all_276_0_60, yields:
% 26.78/8.62 | (585) all_276_0_60 = 0 | distinct_points(all_0_2_2, all_0_2_2) = 0
% 26.78/8.62 |
% 26.78/8.62 +-Applying beta-rule and splitting (585), into two cases.
% 26.78/8.62 |-Branch one:
% 26.78/8.62 | (577) distinct_points(all_0_2_2, all_0_2_2) = 0
% 26.78/8.62 |
% 26.78/8.62 | Instantiating formula (26) with all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_2_2) = 0, yields:
% 26.78/8.62 | (569) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (579) ~ (distinct_points(all_0_2_2, all_0_2_2) = 0)
% 26.78/8.62 | (535) all_276_0_60 = 0
% 26.78/8.62 |
% 26.78/8.62 | Equations (535) can reduce 545 to:
% 26.78/8.62 | (101) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (591) ~ (all_272_0_59 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_272_0_59
% 26.78/8.62 |
% 26.78/8.62 | Applying alpha-rule on (591) yields:
% 26.78/8.62 | (528) ~ (all_272_0_59 = 0)
% 26.78/8.62 | (593) distinct_points(all_0_2_2, all_0_5_5) = all_272_0_59
% 26.78/8.62 |
% 26.78/8.62 | Instantiating formula (35) with all_0_2_2, all_0_5_5, 0, all_272_0_59 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = all_272_0_59, distinct_points(all_0_2_2, all_0_5_5) = 0, yields:
% 26.78/8.62 | (518) all_272_0_59 = 0
% 26.78/8.62 |
% 26.78/8.62 | Equations (518) can reduce 528 to:
% 26.78/8.62 | (101) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (596) ~ (all_376_0_85 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_376_0_85
% 26.78/8.62 |
% 26.78/8.62 | Applying alpha-rule on (596) yields:
% 26.78/8.62 | (513) ~ (all_376_0_85 = 0)
% 26.78/8.62 | (598) distinct_points(all_0_2_2, all_0_5_5) = all_376_0_85
% 26.78/8.62 |
% 26.78/8.62 | Instantiating formula (35) with all_0_2_2, all_0_5_5, 0, all_376_0_85 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = all_376_0_85, distinct_points(all_0_2_2, all_0_5_5) = 0, yields:
% 26.78/8.62 | (503) all_376_0_85 = 0
% 26.78/8.62 |
% 26.78/8.62 | Equations (503) can reduce 513 to:
% 26.78/8.62 | (101) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (601) ~ (distinct_points(all_0_2_2, all_0_5_5) = 0)
% 26.78/8.62 | (206) all_23_0_31 = 0
% 26.78/8.62 |
% 26.78/8.62 | Equations (206) can reduce 95 to:
% 26.78/8.62 | (101) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (604) all_0_1_1 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0
% 26.78/8.62 |
% 26.78/8.62 | Applying alpha-rule on (604) yields:
% 26.78/8.62 | (605) all_0_1_1 = 0
% 26.78/8.62 | (606) apart_point_and_line(all_0_2_2, all_0_9_9) = 0
% 26.78/8.62 |
% 26.78/8.62 +-Applying beta-rule and splitting (166), into two cases.
% 26.78/8.62 |-Branch one:
% 26.78/8.62 | (198) all_25_0_33 = 0
% 26.78/8.62 |
% 26.78/8.62 | Equations (198) can reduce 105 to:
% 26.78/8.62 | (101) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.62 | (201) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.62 |
% 26.78/8.62 +-Applying beta-rule and splitting (157), into two cases.
% 26.78/8.62 |-Branch one:
% 26.78/8.62 | (202) all_24_0_32 = 0
% 26.78/8.62 |
% 26.78/8.62 | Equations (202) can reduce 98 to:
% 26.78/8.62 | (101) $false
% 26.78/8.62 |
% 26.78/8.62 |-The branch is then unsatisfiable
% 26.78/8.62 |-Branch two:
% 26.78/8.62 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.62 | (205) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.62 |
% 26.78/8.62 +-Applying beta-rule and splitting (179), into two cases.
% 26.78/8.62 |-Branch one:
% 26.78/8.63 | (206) all_23_0_31 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (206) can reduce 95 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (95) ~ (all_23_0_31 = 0)
% 26.78/8.63 | (209) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (194), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (210) all_20_0_28 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (210) can reduce 72 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.63 | (213) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (181), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (210) all_20_0_28 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (210) can reduce 72 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.63 | (217) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (182), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (210) all_20_0_28 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (210) can reduce 72 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.63 | (221) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (187), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (225) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (188), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (198) all_25_0_33 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (198) can reduce 105 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.63 | (229) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (191), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (198) all_25_0_33 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (198) can reduce 105 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.63 | (233) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (151), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (237) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (163), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (198) all_25_0_33 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (198) can reduce 105 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.63 | (241) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (164), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (198) all_25_0_33 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (198) can reduce 105 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.63 | (245) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (192), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (206) all_23_0_31 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (206) can reduce 95 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (95) ~ (all_23_0_31 = 0)
% 26.78/8.63 | (249) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (152), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (253) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (153), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (257) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (154), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (261) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (158), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (198) all_25_0_33 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (198) can reduce 105 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.63 | (265) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (155), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (269) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (183), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (210) all_20_0_28 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (210) can reduce 72 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.63 | (273) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (171), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (277) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (184), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (281) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (156), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (285) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (185), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (289) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (186), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (202) all_24_0_32 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (202) can reduce 98 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.63 | (293) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (189), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (198) all_25_0_33 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (198) can reduce 105 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.63 | (297) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63 |
% 26.78/8.63 +-Applying beta-rule and splitting (190), into two cases.
% 26.78/8.63 |-Branch one:
% 26.78/8.63 | (198) all_25_0_33 = 0
% 26.78/8.63 |
% 26.78/8.63 | Equations (198) can reduce 105 to:
% 26.78/8.63 | (101) $false
% 26.78/8.63 |
% 26.78/8.63 |-The branch is then unsatisfiable
% 26.78/8.63 |-Branch two:
% 26.78/8.63 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.63 | (301) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (172), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (202) all_24_0_32 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (202) can reduce 98 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.64 | (305) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (175), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (309) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (176), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (313) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (177), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (317) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (178), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (321) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (180), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (210) all_20_0_28 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (210) can reduce 72 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.64 | (325) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (193), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (206) all_23_0_31 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (206) can reduce 95 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (95) ~ (all_23_0_31 = 0)
% 26.78/8.64 | (329) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (167), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (206) all_23_0_31 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (206) can reduce 95 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (95) ~ (all_23_0_31 = 0)
% 26.78/8.64 | (333) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (168), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (206) all_23_0_31 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (206) can reduce 95 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (95) ~ (all_23_0_31 = 0)
% 26.78/8.64 | (337) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (169), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (206) all_23_0_31 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (206) can reduce 95 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (95) ~ (all_23_0_31 = 0)
% 26.78/8.64 | (341) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (170), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (206) all_23_0_31 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (206) can reduce 95 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (95) ~ (all_23_0_31 = 0)
% 26.78/8.64 | (345) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (173), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (202) all_24_0_32 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (202) can reduce 98 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.64 | (349) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (174), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (202) all_24_0_32 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (202) can reduce 98 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.64 | (353) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (159), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (357) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (160), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (361) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (161), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (365) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (162), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (369) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (165), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (198) all_25_0_33 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (198) can reduce 105 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (105) ~ (all_25_0_33 = 0)
% 26.78/8.64 | (373) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (217), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (107) all_0_3_3 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (107) can reduce 19 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.64 | (377) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (221), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (100) all_0_4_4 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (100) can reduce 45 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.64 | (381) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (225), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (210) all_20_0_28 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (210) can reduce 72 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.64 | (794) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64 |
% 26.78/8.64 +-Applying beta-rule and splitting (229), into two cases.
% 26.78/8.64 |-Branch one:
% 26.78/8.64 | (210) all_20_0_28 = 0
% 26.78/8.64 |
% 26.78/8.64 | Equations (210) can reduce 72 to:
% 26.78/8.64 | (101) $false
% 26.78/8.64 |
% 26.78/8.64 |-The branch is then unsatisfiable
% 26.78/8.64 |-Branch two:
% 26.78/8.64 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.64 | (798) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (233), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (210) all_20_0_28 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (210) can reduce 72 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.65 | (802) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (237), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (107) all_0_3_3 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (107) can reduce 19 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.65 | (385) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (241), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (100) all_0_4_4 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (100) can reduce 45 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.65 | (389) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (245), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (202) all_24_0_32 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (202) can reduce 98 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.65 | (393) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (249), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (210) all_20_0_28 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (210) can reduce 72 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.65 | (818) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (253), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (107) all_0_3_3 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (107) can reduce 19 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.65 | (397) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (257), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (100) all_0_4_4 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (100) can reduce 45 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.65 | (401) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (261), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (100) all_0_4_4 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (100) can reduce 45 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.65 | (405) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 | Instantiating (405) with all_272_0_417 yields:
% 26.78/8.65 | (831) (all_272_0_417 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_417 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_272_0_417 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417) | ( ~ (all_272_0_417 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_272_0_417)
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (265), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (107) all_0_3_3 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (107) can reduce 19 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.65 | (410) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65 |
% 26.78/8.65 | Instantiating (410) with all_276_0_418 yields:
% 26.78/8.65 | (836) (all_276_0_418 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_418 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_276_0_418 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418) | ( ~ (all_276_0_418 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_276_0_418)
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (269), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (100) all_0_4_4 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (100) can reduce 45 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.65 | (415) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65 |
% 26.78/8.65 | Instantiating (415) with all_280_0_419 yields:
% 26.78/8.65 | (841) (all_280_0_419 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_419 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_280_0_419 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419) | ( ~ (all_280_0_419 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_280_0_419)
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (273), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (100) all_0_4_4 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (100) can reduce 45 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.65 | (420) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (281), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (210) all_20_0_28 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (210) can reduce 72 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.65 | (849) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (285), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (100) all_0_4_4 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (100) can reduce 45 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.65 | (428) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (289), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (210) all_20_0_28 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (210) can reduce 72 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.65 | (857) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (293), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (210) all_20_0_28 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (210) can reduce 72 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.65 | (861) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (297), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (210) all_20_0_28 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (210) can reduce 72 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.65 | (865) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (301), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (210) all_20_0_28 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (210) can reduce 72 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.65 | (869) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (325), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (107) all_0_3_3 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (107) can reduce 19 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.65 | (452) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (329), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (210) all_20_0_28 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (210) can reduce 72 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (72) ~ (all_20_0_28 = 0)
% 26.78/8.65 | (877) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.65 +-Applying beta-rule and splitting (333), into two cases.
% 26.78/8.65 |-Branch one:
% 26.78/8.65 | (107) all_0_3_3 = 0
% 26.78/8.65 |
% 26.78/8.65 | Equations (107) can reduce 19 to:
% 26.78/8.65 | (101) $false
% 26.78/8.65 |
% 26.78/8.65 |-The branch is then unsatisfiable
% 26.78/8.65 |-Branch two:
% 26.78/8.65 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.65 | (456) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65 |
% 26.78/8.66 +-Applying beta-rule and splitting (337), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (107) all_0_3_3 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (107) can reduce 19 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.66 | (460) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (341), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (100) all_0_4_4 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (100) can reduce 45 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.66 | (464) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (345), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (100) all_0_4_4 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (100) can reduce 45 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.66 | (468) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (357), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (107) all_0_3_3 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (107) can reduce 19 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.66 | (480) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (361), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (107) all_0_3_3 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (107) can reduce 19 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.66 | (484) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (365), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (107) all_0_3_3 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (107) can reduce 19 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (19) ~ (all_0_3_3 = 0)
% 26.78/8.66 | (488) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.66 |
% 26.78/8.66 | Instantiating (488) with all_376_0_443 yields:
% 26.78/8.66 | (906) (all_376_0_443 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_443 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_376_0_443 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443) | ( ~ (all_376_0_443 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_376_0_443)
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (369), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (100) all_0_4_4 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (100) can reduce 45 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (45) ~ (all_0_4_4 = 0)
% 26.78/8.66 | (493) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (373), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (202) all_24_0_32 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (202) can reduce 98 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (98) ~ (all_24_0_32 = 0)
% 26.78/8.66 | (497) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.66 |
% 26.78/8.66 | Instantiating formula (2) with all_20_0_28, all_0_5_5, all_0_9_9, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = 0, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.78/8.66 | (915) all_20_0_28 = 0 | distinct_points(all_0_2_2, all_0_5_5) = 0
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (915), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (499) distinct_points(all_0_2_2, all_0_5_5) = 0
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (831), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (917) (all_272_0_417 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_417 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_272_0_417 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417)
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (917), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (918) (all_272_0_417 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_417 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0)
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (918), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (919) all_272_0_417 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.66 |
% 26.78/8.66 | Applying alpha-rule on (919) yields:
% 26.78/8.66 | (920) all_272_0_417 = 0
% 26.78/8.66 | (519) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.66 |
% 26.78/8.66 | Instantiating formula (25) with all_0_2_2, all_0_7_7, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 26.78/8.66 | (198) all_25_0_33 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (198) can reduce 105 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (924) all_272_0_417 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.66 |
% 26.78/8.66 | Applying alpha-rule on (924) yields:
% 26.78/8.66 | (920) all_272_0_417 = 0
% 26.78/8.66 | (524) apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.66 |
% 26.78/8.66 | Instantiating formula (25) with all_0_5_5, all_0_6_6, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields:
% 26.78/8.66 | (107) all_0_3_3 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (107) can reduce 19 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (929) ~ (all_272_0_417 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 26.78/8.66 |
% 26.78/8.66 | Applying alpha-rule on (929) yields:
% 26.78/8.66 | (930) ~ (all_272_0_417 = 0)
% 26.78/8.66 | (931) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (906), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (932) (all_376_0_443 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_443 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_376_0_443 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443)
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (932), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (933) (all_376_0_443 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_443 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (933), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (934) all_376_0_443 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.66 |
% 26.78/8.66 | Applying alpha-rule on (934) yields:
% 26.78/8.66 | (935) all_376_0_443 = 0
% 26.78/8.66 | (504) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.66 |
% 26.78/8.66 | Instantiating formula (25) with all_0_2_2, all_0_6_6, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 26.78/8.66 | (202) all_24_0_32 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (202) can reduce 98 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (939) all_376_0_443 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.66 |
% 26.78/8.66 | Applying alpha-rule on (939) yields:
% 26.78/8.66 | (935) all_376_0_443 = 0
% 26.78/8.66 | (509) apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.66 |
% 26.78/8.66 | Instantiating formula (25) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields:
% 26.78/8.66 | (100) all_0_4_4 = 0
% 26.78/8.66 |
% 26.78/8.66 | Equations (100) can reduce 45 to:
% 26.78/8.66 | (101) $false
% 26.78/8.66 |
% 26.78/8.66 |-The branch is then unsatisfiable
% 26.78/8.66 |-Branch two:
% 26.78/8.66 | (944) ~ (all_376_0_443 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443
% 26.78/8.66 |
% 26.78/8.66 | Applying alpha-rule on (944) yields:
% 26.78/8.66 | (945) ~ (all_376_0_443 = 0)
% 26.78/8.66 | (946) distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443
% 26.78/8.66 |
% 26.78/8.66 | Instantiating formula (28) with all_0_6_6, all_0_7_7, all_272_0_417, all_376_0_443 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417, yields:
% 26.78/8.66 | (947) all_376_0_443 = all_272_0_417
% 26.78/8.66 |
% 26.78/8.66 | From (947) and (946) follows:
% 26.78/8.66 | (931) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (836), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (949) (all_276_0_418 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_418 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_276_0_418 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418)
% 26.78/8.66 |
% 26.78/8.66 +-Applying beta-rule and splitting (949), into two cases.
% 26.78/8.66 |-Branch one:
% 26.78/8.66 | (950) (all_276_0_418 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_418 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)
% 26.78/8.67 |
% 26.78/8.67 +-Applying beta-rule and splitting (950), into two cases.
% 26.78/8.67 |-Branch one:
% 26.78/8.67 | (951) all_276_0_418 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.67 |
% 26.78/8.67 | Applying alpha-rule on (951) yields:
% 26.78/8.67 | (952) all_276_0_418 = 0
% 27.04/8.67 | (504) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (25) with all_0_2_2, all_0_6_6, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 27.04/8.67 | (202) all_24_0_32 = 0
% 27.04/8.67 |
% 27.04/8.67 | Equations (202) can reduce 98 to:
% 27.04/8.67 | (101) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (956) all_276_0_418 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 27.04/8.67 |
% 27.04/8.67 | Applying alpha-rule on (956) yields:
% 27.04/8.67 | (952) all_276_0_418 = 0
% 27.04/8.67 | (509) apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (25) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields:
% 27.04/8.67 | (100) all_0_4_4 = 0
% 27.04/8.67 |
% 27.04/8.67 | Equations (100) can reduce 45 to:
% 27.04/8.67 | (101) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (961) ~ (all_276_0_418 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418
% 27.04/8.67 |
% 27.04/8.67 | Applying alpha-rule on (961) yields:
% 27.04/8.67 | (962) ~ (all_276_0_418 = 0)
% 27.04/8.67 | (963) distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (28) with all_0_6_6, all_0_7_7, all_276_0_418, all_272_0_417 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417, yields:
% 27.04/8.67 | (964) all_276_0_418 = all_272_0_417
% 27.04/8.67 |
% 27.04/8.67 | From (964) and (963) follows:
% 27.04/8.67 | (931) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 27.04/8.67 |
% 27.04/8.67 +-Applying beta-rule and splitting (841), into two cases.
% 27.04/8.67 |-Branch one:
% 27.04/8.67 | (966) (all_280_0_419 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_419 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_280_0_419 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419)
% 27.04/8.67 |
% 27.04/8.67 +-Applying beta-rule and splitting (966), into two cases.
% 27.04/8.67 |-Branch one:
% 27.04/8.67 | (967) (all_280_0_419 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_419 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0)
% 27.04/8.67 |
% 27.04/8.67 +-Applying beta-rule and splitting (967), into two cases.
% 27.04/8.67 |-Branch one:
% 27.04/8.67 | (968) all_280_0_419 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 27.04/8.67 |
% 27.04/8.67 | Applying alpha-rule on (968) yields:
% 27.04/8.67 | (969) all_280_0_419 = 0
% 27.04/8.67 | (519) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (25) with all_0_2_2, all_0_7_7, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 27.04/8.67 | (198) all_25_0_33 = 0
% 27.04/8.67 |
% 27.04/8.67 | Equations (198) can reduce 105 to:
% 27.04/8.67 | (101) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (973) all_280_0_419 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 27.04/8.67 |
% 27.04/8.67 | Applying alpha-rule on (973) yields:
% 27.04/8.67 | (969) all_280_0_419 = 0
% 27.04/8.67 | (524) apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (25) with all_0_5_5, all_0_6_6, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields:
% 27.04/8.67 | (107) all_0_3_3 = 0
% 27.04/8.67 |
% 27.04/8.67 | Equations (107) can reduce 19 to:
% 27.04/8.67 | (101) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (978) ~ (all_280_0_419 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419
% 27.04/8.67 |
% 27.04/8.67 | Applying alpha-rule on (978) yields:
% 27.04/8.67 | (979) ~ (all_280_0_419 = 0)
% 27.04/8.67 | (980) distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (28) with all_0_6_6, all_0_7_7, all_280_0_419, all_272_0_417 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417, yields:
% 27.04/8.67 | (981) all_280_0_419 = all_272_0_417
% 27.04/8.67 |
% 27.04/8.67 | Equations (981) can reduce 979 to:
% 27.04/8.67 | (930) ~ (all_272_0_417 = 0)
% 27.04/8.67 |
% 27.04/8.67 | From (981) and (980) follows:
% 27.04/8.67 | (931) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (17) with all_272_0_417, all_0_7_7, all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417, yields:
% 27.04/8.67 | (984) all_272_0_417 = 0 | convergent_lines(all_0_7_7, all_0_7_7) = 0
% 27.04/8.67 |
% 27.04/8.67 +-Applying beta-rule and splitting (984), into two cases.
% 27.04/8.67 |-Branch one:
% 27.04/8.67 | (568) convergent_lines(all_0_7_7, all_0_7_7) = 0
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (4) with all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_7_7) = 0, yields:
% 27.04/8.67 | (569) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (570) ~ (convergent_lines(all_0_7_7, all_0_7_7) = 0)
% 27.04/8.67 | (920) all_272_0_417 = 0
% 27.04/8.67 |
% 27.04/8.67 | Equations (920) can reduce 930 to:
% 27.04/8.67 | (101) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (990) ~ (all_280_0_419 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_280_0_419
% 27.04/8.67 |
% 27.04/8.67 | Applying alpha-rule on (990) yields:
% 27.04/8.67 | (979) ~ (all_280_0_419 = 0)
% 27.04/8.67 | (992) distinct_points(all_0_5_5, all_0_2_2) = all_280_0_419
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (32) with all_280_0_419, all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_2_2) = all_280_0_419, yields:
% 27.04/8.67 | (993) all_280_0_419 = 0 | distinct_points(all_0_2_2, all_0_2_2) = 0
% 27.04/8.67 |
% 27.04/8.67 +-Applying beta-rule and splitting (993), into two cases.
% 27.04/8.67 |-Branch one:
% 27.04/8.67 | (577) distinct_points(all_0_2_2, all_0_2_2) = 0
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (26) with all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_2_2) = 0, yields:
% 27.04/8.67 | (569) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (579) ~ (distinct_points(all_0_2_2, all_0_2_2) = 0)
% 27.04/8.67 | (969) all_280_0_419 = 0
% 27.04/8.67 |
% 27.04/8.67 | Equations (969) can reduce 979 to:
% 27.04/8.67 | (101) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (999) ~ (all_276_0_418 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_276_0_418
% 27.04/8.67 |
% 27.04/8.67 | Applying alpha-rule on (999) yields:
% 27.04/8.67 | (962) ~ (all_276_0_418 = 0)
% 27.04/8.67 | (1001) distinct_points(all_0_5_5, all_0_2_2) = all_276_0_418
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (32) with all_276_0_418, all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_2_2) = all_276_0_418, yields:
% 27.04/8.67 | (1002) all_276_0_418 = 0 | distinct_points(all_0_2_2, all_0_2_2) = 0
% 27.04/8.67 |
% 27.04/8.67 +-Applying beta-rule and splitting (1002), into two cases.
% 27.04/8.67 |-Branch one:
% 27.04/8.67 | (577) distinct_points(all_0_2_2, all_0_2_2) = 0
% 27.04/8.67 |
% 27.04/8.67 | Instantiating formula (26) with all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_2_2) = 0, yields:
% 27.04/8.67 | (569) $false
% 27.04/8.67 |
% 27.04/8.67 |-The branch is then unsatisfiable
% 27.04/8.67 |-Branch two:
% 27.04/8.67 | (579) ~ (distinct_points(all_0_2_2, all_0_2_2) = 0)
% 27.04/8.67 | (952) all_276_0_418 = 0
% 27.04/8.68 |
% 27.04/8.68 | Equations (952) can reduce 962 to:
% 27.04/8.68 | (101) $false
% 27.04/8.68 |
% 27.04/8.68 |-The branch is then unsatisfiable
% 27.04/8.68 |-Branch two:
% 27.04/8.68 | (1008) ~ (all_376_0_443 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_376_0_443
% 27.04/8.68 |
% 27.04/8.68 | Applying alpha-rule on (1008) yields:
% 27.04/8.68 | (945) ~ (all_376_0_443 = 0)
% 27.04/8.68 | (1010) distinct_points(all_0_2_2, all_0_5_5) = all_376_0_443
% 27.04/8.68 |
% 27.04/8.68 | Instantiating formula (35) with all_0_2_2, all_0_5_5, 0, all_376_0_443 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = all_376_0_443, distinct_points(all_0_2_2, all_0_5_5) = 0, yields:
% 27.04/8.68 | (935) all_376_0_443 = 0
% 27.04/8.68 |
% 27.04/8.68 | Equations (935) can reduce 945 to:
% 27.04/8.68 | (101) $false
% 27.04/8.68 |
% 27.04/8.68 |-The branch is then unsatisfiable
% 27.04/8.68 |-Branch two:
% 27.04/8.68 | (1013) ~ (all_272_0_417 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_272_0_417
% 27.04/8.68 |
% 27.04/8.68 | Applying alpha-rule on (1013) yields:
% 27.04/8.68 | (930) ~ (all_272_0_417 = 0)
% 27.04/8.68 | (1015) distinct_points(all_0_2_2, all_0_5_5) = all_272_0_417
% 27.04/8.68 |
% 27.04/8.68 | Instantiating formula (35) with all_0_2_2, all_0_5_5, 0, all_272_0_417 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = all_272_0_417, distinct_points(all_0_2_2, all_0_5_5) = 0, yields:
% 27.04/8.68 | (920) all_272_0_417 = 0
% 27.04/8.68 |
% 27.04/8.68 | Equations (920) can reduce 930 to:
% 27.04/8.68 | (101) $false
% 27.04/8.68 |
% 27.04/8.68 |-The branch is then unsatisfiable
% 27.04/8.68 |-Branch two:
% 27.04/8.68 | (601) ~ (distinct_points(all_0_2_2, all_0_5_5) = 0)
% 27.04/8.68 | (210) all_20_0_28 = 0
% 27.04/8.68 |
% 27.04/8.68 | Equations (210) can reduce 72 to:
% 27.04/8.68 | (101) $false
% 27.04/8.68 |
% 27.04/8.68 |-The branch is then unsatisfiable
% 27.04/8.68 |-Branch two:
% 27.04/8.68 | (1021) ~ (all_25_0_33 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33
% 27.04/8.68 |
% 27.04/8.68 | Applying alpha-rule on (1021) yields:
% 27.04/8.68 | (105) ~ (all_25_0_33 = 0)
% 27.04/8.68 | (1023) convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33
% 27.04/8.68 |
% 27.04/8.68 | Instantiating formula (5) with all_0_7_7, all_0_6_6, all_25_0_33, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33, convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 27.04/8.68 | (198) all_25_0_33 = 0
% 27.04/8.68 |
% 27.04/8.68 | Equations (198) can reduce 105 to:
% 27.04/8.68 | (101) $false
% 27.04/8.68 |
% 27.04/8.68 |-The branch is then unsatisfiable
% 27.04/8.68 |-Branch two:
% 27.04/8.68 | (1026) ~ (all_24_0_32 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32
% 27.04/8.68 |
% 27.04/8.68 | Applying alpha-rule on (1026) yields:
% 27.04/8.68 | (98) ~ (all_24_0_32 = 0)
% 27.04/8.68 | (1028) convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32
% 27.04/8.68 |
% 27.04/8.68 | Instantiating formula (5) with all_0_7_7, all_0_6_6, all_24_0_32, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32, convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 27.04/8.68 | (202) all_24_0_32 = 0
% 27.04/8.68 |
% 27.04/8.68 | Equations (202) can reduce 98 to:
% 27.04/8.68 | (101) $false
% 27.04/8.68 |
% 27.04/8.68 |-The branch is then unsatisfiable
% 27.04/8.68 |-Branch two:
% 27.04/8.68 | (1031) ~ (all_23_0_31 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31
% 27.04/8.68 |
% 27.04/8.68 | Applying alpha-rule on (1031) yields:
% 27.04/8.68 | (95) ~ (all_23_0_31 = 0)
% 27.04/8.68 | (1033) convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31
% 27.04/8.68 |
% 27.04/8.68 | Instantiating formula (5) with all_0_9_9, all_0_8_8, all_23_0_31, 0 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31, convergent_lines(all_0_9_9, all_0_8_8) = 0, yields:
% 27.04/8.68 | (206) all_23_0_31 = 0
% 27.04/8.68 |
% 27.04/8.68 | Equations (206) can reduce 95 to:
% 27.04/8.68 | (101) $false
% 27.04/8.68 |
% 27.04/8.68 |-The branch is then unsatisfiable
% 27.04/8.68 |-Branch two:
% 27.04/8.68 | (1036) ~ (all_22_0_30 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30
% 27.04/8.68 |
% 27.04/8.68 | Applying alpha-rule on (1036) yields:
% 27.04/8.68 | (92) ~ (all_22_0_30 = 0)
% 27.04/8.68 | (1038) convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30
% 27.04/8.68 |
% 27.04/8.68 | Instantiating formula (5) with all_0_9_9, all_0_8_8, all_22_0_30, 0 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30, convergent_lines(all_0_9_9, all_0_8_8) = 0, yields:
% 27.04/8.68 | (1039) all_22_0_30 = 0
% 27.04/8.68 |
% 27.04/8.68 | Equations (1039) can reduce 92 to:
% 27.04/8.68 | (101) $false
% 27.04/8.68 |
% 27.04/8.68 |-The branch is then unsatisfiable
% 27.04/8.68 % SZS output end Proof for theBenchmark
% 27.04/8.68
% 27.04/8.68 8077ms
%------------------------------------------------------------------------------