TSTP Solution File: GEO187+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:23 EDT 2022
% Result : Theorem 5.11s 1.87s
% Output : Proof 19.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n005.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 20:44:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.50/0.60 ____ _
% 0.50/0.60 ___ / __ \_____(_)___ ________ __________
% 0.50/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.60
% 0.50/0.60 A Theorem Prover for First-Order Logic
% 0.50/0.60 (ePrincess v.1.0)
% 0.50/0.60
% 0.50/0.60 (c) Philipp Rümmer, 2009-2015
% 0.50/0.60 (c) Peter Backeman, 2014-2015
% 0.50/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.60 Bug reports to peter@backeman.se
% 0.50/0.60
% 0.50/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.60
% 0.50/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/0.95 Prover 0: Preprocessing ...
% 2.00/1.09 Prover 0: Warning: ignoring some quantifiers
% 2.00/1.11 Prover 0: Constructing countermodel ...
% 2.87/1.34 Prover 0: gave up
% 2.87/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.99/1.37 Prover 1: Preprocessing ...
% 3.27/1.46 Prover 1: Constructing countermodel ...
% 3.39/1.52 Prover 1: gave up
% 3.39/1.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.61/1.54 Prover 2: Preprocessing ...
% 4.09/1.66 Prover 2: Warning: ignoring some quantifiers
% 4.09/1.66 Prover 2: Constructing countermodel ...
% 5.11/1.86 Prover 2: proved (347ms)
% 5.11/1.87
% 5.11/1.87 No countermodel exists, formula is valid
% 5.11/1.87 % SZS status Theorem for theBenchmark
% 5.11/1.87
% 5.11/1.87 Generating proof ... Warning: ignoring some quantifiers
% 18.56/5.06 found it (size 840)
% 18.56/5.06
% 18.56/5.06 % SZS output start Proof for theBenchmark
% 18.56/5.06 Assumed formulas after preprocessing and simplification:
% 18.56/5.06 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & ~ (v5 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) = v7 & apart_point_and_line(v1, v4) = v6 & apart_point_and_line(v0, v4) = v5 & distinct_points(v2, v3) = 0 & distinct_points(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(v3, v7) = 0) | (v8 = 0 & apart_point_and_line(v2, v7) = 0)))
% 18.88/5.12 | 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:
% 18.88/5.12 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5 & line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2 & apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3 & apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4 & distinct_points(all_0_7_7, all_0_6_6) = 0 & distinct_points(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_6_6, all_0_2_2) = 0) | (all_0_1_1 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0))
% 18.88/5.15 |
% 18.88/5.15 | Applying alpha-rule on (1) yields:
% 18.88/5.15 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 18.88/5.15 | (3) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 18.88/5.15 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 18.88/5.15 | (5) ! [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)))
% 18.88/5.15 | (6) ! [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))
% 19.07/5.15 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 19.07/5.15 | (8) ! [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)))
% 19.07/5.15 | (9) (all_0_0_0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_0_1_1 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0)
% 19.07/5.15 | (10) ! [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)))
% 19.07/5.15 | (11) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 19.07/5.15 | (12) ! [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)))
% 19.07/5.15 | (13) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 19.07/5.15 | (14) line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5
% 19.07/5.15 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 19.07/5.15 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 19.07/5.15 | (17) ! [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)
% 19.07/5.15 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 19.07/5.15 | (19) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 19.07/5.15 | (20) ~ (all_0_3_3 = 0)
% 19.07/5.15 | (21) ! [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))
% 19.07/5.15 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 19.07/5.15 | (23) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 19.07/5.15 | (24) ! [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)))
% 19.07/5.16 | (25) ! [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))
% 19.07/5.16 | (26) line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2
% 19.07/5.16 | (27) apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3
% 19.07/5.16 | (28) distinct_points(all_0_9_9, all_0_8_8) = 0
% 19.07/5.16 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 19.07/5.16 | (30) ! [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))
% 19.07/5.16 | (31) ! [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))
% 19.07/5.16 | (32) ! [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)
% 19.07/5.16 | (33) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 19.07/5.16 | (34) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 19.07/5.16 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 19.07/5.16 | (36) ! [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)))
% 19.07/5.16 | (37) ! [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)))
% 19.07/5.16 | (38) ! [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)))
% 19.07/5.16 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((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)))
% 19.07/5.16 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 19.07/5.16 | (41) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 19.07/5.16 | (42) ! [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)
% 19.07/5.16 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 19.07/5.16 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 19.07/5.16 | (45) ! [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)))
% 19.07/5.16 | (46) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 19.07/5.16 | (47) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 19.07/5.16 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 19.07/5.16 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 19.07/5.17 | (50) ~ (all_0_4_4 = 0)
% 19.07/5.17 | (51) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 19.07/5.17 | (52) ! [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))
% 19.07/5.17 | (53) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 19.07/5.17 | (54) ! [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)))
% 19.07/5.17 | (55) distinct_points(all_0_7_7, all_0_6_6) = 0
% 19.07/5.17 | (56) apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4
% 19.07/5.17 | (57) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 19.07/5.17 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (12) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 19.07/5.17 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (45) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 19.07/5.17 | (60) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (12) with all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields:
% 19.07/5.17 | (61) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (45) with all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields:
% 19.07/5.17 | (62) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (10) with all_0_3_3, all_0_3_3, all_0_5_5, all_0_5_5, all_0_8_8, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, yields:
% 19.07/5.17 | (63) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (10) with all_0_4_4, all_0_3_3, all_0_5_5, all_0_5_5, all_0_9_9, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.17 | (64) all_0_3_3 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.17 | (65) all_0_3_3 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5, all_0_9_9, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.17 | (66) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (46) with all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 19.07/5.17 | (67) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(all_0_6_6, v0) = v1)
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (53) with all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 19.07/5.17 | (68) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(all_0_7_7, v0) = v1)
% 19.07/5.17 |
% 19.07/5.17 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_0_5_5, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.18 | (69) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 19.07/5.18 |
% 19.07/5.18 | Instantiating formula (54) with all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.18 | (70) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 19.07/5.18 |
% 19.07/5.18 | Instantiating formula (46) with all_0_8_8, all_0_9_9 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.18 | (71) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(all_0_8_8, v0) = v1)
% 19.07/5.18 |
% 19.07/5.18 | Instantiating formula (53) with all_0_8_8, all_0_9_9 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.18 | (72) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(all_0_9_9, v0) = v1)
% 19.07/5.18 |
% 19.07/5.18 | Instantiating (72) with all_20_0_28, all_20_1_29 yields:
% 19.07/5.18 | (73) ~ (all_20_0_28 = 0) & line_connecting(all_0_9_9, all_0_8_8) = all_20_1_29 & apart_point_and_line(all_0_9_9, all_20_1_29) = all_20_0_28
% 19.07/5.18 |
% 19.07/5.18 | Applying alpha-rule on (73) yields:
% 19.07/5.18 | (74) ~ (all_20_0_28 = 0)
% 19.07/5.18 | (75) line_connecting(all_0_9_9, all_0_8_8) = all_20_1_29
% 19.07/5.18 | (76) apart_point_and_line(all_0_9_9, all_20_1_29) = all_20_0_28
% 19.07/5.18 |
% 19.07/5.18 | Instantiating (71) with all_22_0_30, all_22_1_31 yields:
% 19.07/5.18 | (77) ~ (all_22_0_30 = 0) & line_connecting(all_0_9_9, all_0_8_8) = all_22_1_31 & apart_point_and_line(all_0_8_8, all_22_1_31) = all_22_0_30
% 19.07/5.18 |
% 19.07/5.18 | Applying alpha-rule on (77) yields:
% 19.07/5.18 | (78) ~ (all_22_0_30 = 0)
% 19.07/5.18 | (79) line_connecting(all_0_9_9, all_0_8_8) = all_22_1_31
% 19.07/5.18 | (80) apart_point_and_line(all_0_8_8, all_22_1_31) = all_22_0_30
% 19.07/5.18 |
% 19.07/5.18 | Instantiating (62) with all_24_0_32 yields:
% 19.07/5.18 | (81) ( ~ (all_24_0_32 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = all_24_0_32) | ( ~ (all_24_0_32 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_24_0_32)
% 19.07/5.18 |
% 19.07/5.18 | Instantiating (68) with all_25_0_33, all_25_1_34 yields:
% 19.07/5.18 | (82) ~ (all_25_0_33 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_25_1_34 & apart_point_and_line(all_0_7_7, all_25_1_34) = all_25_0_33
% 19.07/5.18 |
% 19.07/5.18 | Applying alpha-rule on (82) yields:
% 19.07/5.18 | (83) ~ (all_25_0_33 = 0)
% 19.07/5.18 | (84) line_connecting(all_0_7_7, all_0_6_6) = all_25_1_34
% 19.07/5.18 | (85) apart_point_and_line(all_0_7_7, all_25_1_34) = all_25_0_33
% 19.07/5.18 |
% 19.07/5.18 | Instantiating (67) with all_27_0_35, all_27_1_36 yields:
% 19.07/5.18 | (86) ~ (all_27_0_35 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_27_1_36 & apart_point_and_line(all_0_6_6, all_27_1_36) = all_27_0_35
% 19.07/5.18 |
% 19.07/5.18 | Applying alpha-rule on (86) yields:
% 19.07/5.18 | (87) ~ (all_27_0_35 = 0)
% 19.07/5.18 | (88) line_connecting(all_0_7_7, all_0_6_6) = all_27_1_36
% 19.07/5.18 | (89) apart_point_and_line(all_0_6_6, all_27_1_36) = all_27_0_35
% 19.07/5.18 |
% 19.07/5.18 | Instantiating (61) with all_29_0_37 yields:
% 19.07/5.18 | (90) ( ~ (all_29_0_37 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = all_29_0_37) | ( ~ (all_29_0_37 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_29_0_37)
% 19.07/5.18 |
% 19.07/5.18 | Instantiating (59) with all_30_0_38 yields:
% 19.07/5.18 | (91) ( ~ (all_30_0_38 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = all_30_0_38) | ( ~ (all_30_0_38 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_30_0_38)
% 19.07/5.18 |
% 19.07/5.18 | Instantiating (60) with all_31_0_39 yields:
% 19.07/5.18 | (92) ( ~ (all_31_0_39 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = all_31_0_39) | ( ~ (all_31_0_39 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_31_0_39)
% 19.07/5.18 |
% 19.07/5.18 +-Applying beta-rule and splitting (91), into two cases.
% 19.07/5.18 |-Branch one:
% 19.07/5.18 | (93) ~ (all_30_0_38 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = all_30_0_38
% 19.07/5.18 |
% 19.07/5.18 | Applying alpha-rule on (93) yields:
% 19.07/5.18 | (94) ~ (all_30_0_38 = 0)
% 19.07/5.18 | (95) apart_point_and_line(all_0_6_6, all_0_5_5) = all_30_0_38
% 19.07/5.18 |
% 19.07/5.18 +-Applying beta-rule and splitting (69), into two cases.
% 19.07/5.18 |-Branch one:
% 19.07/5.18 | (96) all_0_3_3 = 0
% 19.07/5.18 |
% 19.07/5.18 | Equations (96) can reduce 20 to:
% 19.07/5.18 | (97) $false
% 19.07/5.18 |
% 19.07/5.18 |-The branch is then unsatisfiable
% 19.07/5.18 |-Branch two:
% 19.07/5.18 | (20) ~ (all_0_3_3 = 0)
% 19.07/5.18 | (99) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 19.07/5.18 |
% 19.07/5.18 +-Applying beta-rule and splitting (70), into two cases.
% 19.07/5.18 |-Branch one:
% 19.07/5.18 | (100) all_0_4_4 = 0
% 19.07/5.18 |
% 19.07/5.18 | Equations (100) can reduce 50 to:
% 19.07/5.18 | (97) $false
% 19.07/5.18 |
% 19.07/5.18 |-The branch is then unsatisfiable
% 19.07/5.18 |-Branch two:
% 19.07/5.18 | (50) ~ (all_0_4_4 = 0)
% 19.07/5.18 | (103) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 19.07/5.18 |
% 19.07/5.18 +-Applying beta-rule and splitting (63), into two cases.
% 19.07/5.18 |-Branch one:
% 19.07/5.18 | (96) all_0_3_3 = 0
% 19.07/5.18 |
% 19.07/5.18 | Equations (96) can reduce 20 to:
% 19.07/5.18 | (97) $false
% 19.07/5.18 |
% 19.07/5.18 |-The branch is then unsatisfiable
% 19.07/5.18 |-Branch two:
% 19.07/5.18 | (20) ~ (all_0_3_3 = 0)
% 19.07/5.18 | (107) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.07/5.18 |
% 19.07/5.18 +-Applying beta-rule and splitting (65), into two cases.
% 19.07/5.18 |-Branch one:
% 19.07/5.18 | (96) all_0_3_3 = 0
% 19.07/5.19 |
% 19.07/5.19 | Equations (96) can reduce 20 to:
% 19.07/5.19 | (97) $false
% 19.07/5.19 |
% 19.07/5.19 |-The branch is then unsatisfiable
% 19.07/5.19 |-Branch two:
% 19.07/5.19 | (20) ~ (all_0_3_3 = 0)
% 19.07/5.19 | (111) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.07/5.19 |
% 19.07/5.19 +-Applying beta-rule and splitting (64), into two cases.
% 19.07/5.19 |-Branch one:
% 19.07/5.19 | (96) all_0_3_3 = 0
% 19.07/5.19 |
% 19.07/5.19 | Equations (96) can reduce 20 to:
% 19.07/5.19 | (97) $false
% 19.07/5.19 |
% 19.07/5.19 |-The branch is then unsatisfiable
% 19.07/5.19 |-Branch two:
% 19.07/5.19 | (20) ~ (all_0_3_3 = 0)
% 19.07/5.19 | (115) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.07/5.19 |
% 19.07/5.19 +-Applying beta-rule and splitting (90), into two cases.
% 19.07/5.19 |-Branch one:
% 19.07/5.19 | (116) ~ (all_29_0_37 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = all_29_0_37
% 19.07/5.19 |
% 19.07/5.19 | Applying alpha-rule on (116) yields:
% 19.07/5.19 | (117) ~ (all_29_0_37 = 0)
% 19.07/5.19 | (118) apart_point_and_line(all_0_8_8, all_0_2_2) = all_29_0_37
% 19.07/5.19 |
% 19.07/5.19 +-Applying beta-rule and splitting (81), into two cases.
% 19.07/5.19 |-Branch one:
% 19.07/5.19 | (119) ~ (all_24_0_32 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = all_24_0_32
% 19.07/5.19 |
% 19.07/5.19 | Applying alpha-rule on (119) yields:
% 19.07/5.19 | (120) ~ (all_24_0_32 = 0)
% 19.07/5.19 | (121) apart_point_and_line(all_0_9_9, all_0_2_2) = all_24_0_32
% 19.07/5.19 |
% 19.07/5.19 +-Applying beta-rule and splitting (66), into two cases.
% 19.07/5.19 |-Branch one:
% 19.07/5.19 | (100) all_0_4_4 = 0
% 19.07/5.19 |
% 19.07/5.19 | Equations (100) can reduce 50 to:
% 19.07/5.19 | (97) $false
% 19.07/5.19 |
% 19.07/5.19 |-The branch is then unsatisfiable
% 19.07/5.19 |-Branch two:
% 19.07/5.19 | (50) ~ (all_0_4_4 = 0)
% 19.07/5.19 | (125) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.07/5.19 |
% 19.07/5.19 +-Applying beta-rule and splitting (115), into two cases.
% 19.07/5.19 |-Branch one:
% 19.07/5.19 | (100) all_0_4_4 = 0
% 19.07/5.19 |
% 19.07/5.19 | Equations (100) can reduce 50 to:
% 19.07/5.19 | (97) $false
% 19.07/5.19 |
% 19.07/5.19 |-The branch is then unsatisfiable
% 19.07/5.19 |-Branch two:
% 19.07/5.19 | (50) ~ (all_0_4_4 = 0)
% 19.07/5.19 | (129) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.07/5.19 |
% 19.07/5.19 +-Applying beta-rule and splitting (92), into two cases.
% 19.07/5.19 |-Branch one:
% 19.07/5.19 | (130) ~ (all_31_0_39 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = all_31_0_39
% 19.07/5.19 |
% 19.07/5.19 | Applying alpha-rule on (130) yields:
% 19.07/5.19 | (131) ~ (all_31_0_39 = 0)
% 19.07/5.19 | (132) apart_point_and_line(all_0_7_7, all_0_5_5) = all_31_0_39
% 19.07/5.19 |
% 19.07/5.19 | Instantiating formula (40) with all_0_7_7, all_0_6_6, all_27_1_36, all_0_5_5 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_27_1_36, line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 19.07/5.19 | (133) all_27_1_36 = all_0_5_5
% 19.07/5.19 |
% 19.07/5.19 | Instantiating formula (40) with all_0_7_7, all_0_6_6, all_25_1_34, all_27_1_36 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_27_1_36, line_connecting(all_0_7_7, all_0_6_6) = all_25_1_34, yields:
% 19.07/5.19 | (134) all_27_1_36 = all_25_1_34
% 19.07/5.19 |
% 19.07/5.19 | Instantiating formula (40) with all_0_9_9, all_0_8_8, all_22_1_31, all_0_2_2 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_22_1_31, line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields:
% 19.07/5.19 | (135) all_22_1_31 = all_0_2_2
% 19.07/5.19 |
% 19.07/5.19 | Instantiating formula (40) with all_0_9_9, all_0_8_8, all_20_1_29, all_22_1_31 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_22_1_31, line_connecting(all_0_9_9, all_0_8_8) = all_20_1_29, yields:
% 19.07/5.19 | (136) all_22_1_31 = all_20_1_29
% 19.07/5.19 |
% 19.07/5.19 | Combining equations (133,134) yields a new equation:
% 19.07/5.19 | (137) all_25_1_34 = all_0_5_5
% 19.07/5.19 |
% 19.07/5.19 | Combining equations (136,135) yields a new equation:
% 19.07/5.19 | (138) all_20_1_29 = all_0_2_2
% 19.07/5.19 |
% 19.07/5.19 | Simplifying 138 yields:
% 19.07/5.19 | (139) all_20_1_29 = all_0_2_2
% 19.07/5.19 |
% 19.07/5.19 | Combining equations (137,134) yields a new equation:
% 19.07/5.19 | (133) all_27_1_36 = all_0_5_5
% 19.07/5.19 |
% 19.07/5.19 | From (133) and (89) follows:
% 19.07/5.19 | (141) apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35
% 19.07/5.19 |
% 19.07/5.19 | From (137) and (85) follows:
% 19.07/5.19 | (142) apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33
% 19.07/5.19 |
% 19.07/5.19 | From (135) and (80) follows:
% 19.07/5.19 | (143) apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30
% 19.07/5.19 |
% 19.07/5.19 | From (139) and (76) follows:
% 19.07/5.19 | (144) apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28
% 19.07/5.19 |
% 19.07/5.19 | Instantiating formula (44) with all_0_6_6, all_0_5_5, all_27_0_35, all_30_0_38 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_30_0_38, apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, yields:
% 19.07/5.19 | (145) all_30_0_38 = all_27_0_35
% 19.07/5.19 |
% 19.07/5.19 | Instantiating formula (44) with all_0_7_7, all_0_5_5, all_25_0_33, all_31_0_39 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_31_0_39, apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, yields:
% 19.07/5.19 | (146) all_31_0_39 = all_25_0_33
% 19.07/5.19 |
% 19.07/5.19 | Instantiating formula (44) with all_0_8_8, all_0_2_2, all_22_0_30, all_29_0_37 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_29_0_37, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.20 | (147) all_29_0_37 = all_22_0_30
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (44) with all_0_9_9, all_0_2_2, all_20_0_28, all_24_0_32 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_24_0_32, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.20 | (148) all_24_0_32 = all_20_0_28
% 19.07/5.20 |
% 19.07/5.20 | Equations (146) can reduce 131 to:
% 19.07/5.20 | (83) ~ (all_25_0_33 = 0)
% 19.07/5.20 |
% 19.07/5.20 | Equations (145) can reduce 94 to:
% 19.07/5.20 | (87) ~ (all_27_0_35 = 0)
% 19.07/5.20 |
% 19.07/5.20 | Equations (147) can reduce 117 to:
% 19.07/5.20 | (78) ~ (all_22_0_30 = 0)
% 19.07/5.20 |
% 19.07/5.20 | Equations (148) can reduce 120 to:
% 19.07/5.20 | (74) ~ (all_20_0_28 = 0)
% 19.07/5.20 |
% 19.07/5.20 | From (145) and (95) follows:
% 19.07/5.20 | (141) apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35
% 19.07/5.20 |
% 19.07/5.20 | From (146) and (132) follows:
% 19.07/5.20 | (142) apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33
% 19.07/5.20 |
% 19.07/5.20 | From (147) and (118) follows:
% 19.07/5.20 | (143) apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30
% 19.07/5.20 |
% 19.07/5.20 | From (148) and (121) follows:
% 19.07/5.20 | (144) apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_27_0_35, all_0_3_3, all_0_5_5, all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, yields:
% 19.07/5.20 | (157) all_27_0_35 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_0_3_3, all_27_0_35, all_0_5_5, all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, yields:
% 19.07/5.20 | (158) all_27_0_35 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_27_0_35, all_0_4_4, all_0_5_5, all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.20 | (159) all_27_0_35 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_0_4_4, all_27_0_35, all_0_5_5, all_0_5_5, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.20 | (160) all_27_0_35 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_27_0_35, all_27_0_35, all_0_5_5, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, yields:
% 19.07/5.20 | (161) all_27_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_25_0_33, all_0_3_3, all_0_5_5, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, yields:
% 19.07/5.20 | (162) all_25_0_33 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_0_3_3, all_25_0_33, all_0_5_5, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, yields:
% 19.07/5.20 | (163) all_25_0_33 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_25_0_33, all_0_4_4, all_0_5_5, all_0_5_5, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.20 | (164) all_25_0_33 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_0_4_4, all_25_0_33, all_0_5_5, all_0_5_5, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.20 | (165) all_25_0_33 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.07/5.20 |
% 19.07/5.20 | Instantiating formula (10) with all_25_0_33, all_27_0_35, all_0_5_5, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, yields:
% 19.07/5.21 | (166) all_27_0_35 = 0 | all_25_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (10) with all_25_0_33, all_25_0_33, all_0_5_5, all_0_5_5, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, yields:
% 19.07/5.21 | (167) all_25_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (8) with all_22_0_30, all_0_3_3, all_0_2_2, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.21 | (168) all_22_0_30 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (8) with all_0_3_3, all_22_0_30, all_0_5_5, all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.21 | (169) all_22_0_30 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (10) with all_22_0_30, all_0_3_3, all_0_2_2, all_0_5_5, all_0_8_8, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, yields:
% 19.07/5.21 | (170) all_22_0_30 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (10) with all_0_3_3, all_22_0_30, all_0_5_5, all_0_2_2, all_0_8_8, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, yields:
% 19.07/5.21 | (171) all_22_0_30 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (10) with all_22_0_30, all_0_4_4, all_0_2_2, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.21 | (172) all_22_0_30 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (10) with all_0_4_4, all_22_0_30, all_0_5_5, all_0_2_2, all_0_9_9, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.21 | (173) all_22_0_30 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (5) with all_22_0_30, all_0_4_4, all_0_5_5, all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.21 | (174) all_22_0_30 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (5) with all_0_4_4, all_22_0_30, all_0_2_2, all_0_5_5, all_0_9_9, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.21 | (175) all_22_0_30 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (10) with all_22_0_30, all_27_0_35, all_0_2_2, all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.21 | (176) all_27_0_35 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.07/5.21 |
% 19.07/5.21 | Instantiating formula (10) with all_27_0_35, all_22_0_30, all_0_5_5, all_0_2_2, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.21 | (177) all_27_0_35 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.07/5.21 |
% 19.07/5.22 | Instantiating formula (5) with all_22_0_30, all_27_0_35, all_0_5_5, all_0_2_2, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.22 | (178) all_27_0_35 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (5) with all_27_0_35, all_22_0_30, all_0_2_2, all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.22 | (179) all_27_0_35 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (10) with all_22_0_30, all_25_0_33, all_0_2_2, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.22 | (180) all_25_0_33 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (10) with all_25_0_33, all_22_0_30, all_0_5_5, all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.22 | (181) all_25_0_33 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (5) with all_22_0_30, all_25_0_33, all_0_5_5, all_0_2_2, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.22 | (182) all_25_0_33 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (5) with all_25_0_33, all_22_0_30, all_0_2_2, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.22 | (183) all_25_0_33 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (8) with all_22_0_30, all_22_0_30, all_0_2_2, all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.22 | (184) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (10) with all_22_0_30, all_22_0_30, all_0_2_2, all_0_2_2, all_0_8_8, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields:
% 19.07/5.22 | (185) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (10) with all_20_0_28, all_0_3_3, all_0_2_2, all_0_5_5, all_0_9_9, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.22 | (186) all_20_0_28 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (10) with all_0_3_3, all_20_0_28, all_0_5_5, all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.22 | (187) all_20_0_28 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (5) with all_20_0_28, all_0_3_3, all_0_5_5, all_0_2_2, all_0_9_9, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.22 | (188) all_20_0_28 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (5) with all_0_3_3, all_20_0_28, all_0_2_2, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.22 | (189) all_20_0_28 = 0 | all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.07/5.22 |
% 19.07/5.22 | Instantiating formula (54) with all_20_0_28, all_0_4_4, all_0_2_2, all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.23 | (190) all_20_0_28 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (54) with all_0_4_4, all_20_0_28, all_0_5_5, all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.07/5.23 | (191) all_20_0_28 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (10) with all_20_0_28, all_0_4_4, all_0_2_2, all_0_5_5, all_0_9_9, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.23 | (192) all_20_0_28 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (10) with all_0_4_4, all_20_0_28, all_0_5_5, all_0_2_2, all_0_9_9, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, yields:
% 19.07/5.23 | (193) all_20_0_28 = 0 | all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (10) with all_20_0_28, all_27_0_35, all_0_2_2, all_0_5_5, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.23 | (194) all_27_0_35 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (10) with all_27_0_35, all_20_0_28, all_0_5_5, all_0_2_2, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.23 | (195) all_27_0_35 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (5) with all_20_0_28, all_27_0_35, all_0_5_5, all_0_2_2, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.23 | (196) all_27_0_35 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (5) with all_27_0_35, all_20_0_28, all_0_2_2, all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.23 | (197) all_27_0_35 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (10) with all_20_0_28, all_25_0_33, all_0_2_2, all_0_5_5, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.23 | (198) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (10) with all_25_0_33, all_20_0_28, all_0_5_5, all_0_2_2, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.23 | (199) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (5) with all_20_0_28, all_25_0_33, all_0_5_5, all_0_2_2, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.23 | (200) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.07/5.23 |
% 19.07/5.23 | Instantiating formula (5) with all_25_0_33, all_20_0_28, all_0_2_2, all_0_5_5, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.07/5.23 | (201) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.48/5.23 |
% 19.48/5.23 | Instantiating formula (10) with all_20_0_28, all_22_0_30, all_0_2_2, all_0_2_2, all_0_9_9, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.48/5.23 | (202) all_22_0_30 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.23 |
% 19.48/5.23 | Instantiating formula (10) with all_22_0_30, all_20_0_28, all_0_2_2, all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.48/5.23 | (203) all_22_0_30 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.23 |
% 19.48/5.23 | Instantiating formula (54) with all_20_0_28, all_20_0_28, all_0_2_2, all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.48/5.23 | (204) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 19.48/5.23 |
% 19.48/5.23 | Instantiating formula (10) with all_20_0_28, all_20_0_28, all_0_2_2, all_0_2_2, all_0_9_9, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields:
% 19.48/5.23 | (205) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (9), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (206) all_0_0_0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 19.48/5.24 |
% 19.48/5.24 | Applying alpha-rule on (206) yields:
% 19.48/5.24 | (207) all_0_0_0 = 0
% 19.48/5.24 | (208) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (185), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (209) all_22_0_30 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (209) can reduce 78 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.24 | (212) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (204), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (213) all_20_0_28 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (213) can reduce 74 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.24 | (216) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (205), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (213) all_20_0_28 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (213) can reduce 74 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.24 | (220) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (161), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (221) all_27_0_35 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (221) can reduce 87 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.24 | (224) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (167), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (225) all_25_0_33 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (225) can reduce 83 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.24 | (228) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (184), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (209) all_22_0_30 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (209) can reduce 78 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.24 | (232) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (169), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (209) all_22_0_30 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (209) can reduce 78 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.24 | (236) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (157), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (221) all_27_0_35 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (221) can reduce 87 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.24 | (240) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (160), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (221) all_27_0_35 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (221) can reduce 87 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.24 | (244) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (165), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (225) all_25_0_33 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (225) can reduce 83 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.24 | (248) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (158), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (221) all_27_0_35 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (221) can reduce 87 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.24 | (252) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (159), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (221) all_27_0_35 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (221) can reduce 87 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.24 | (256) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (171), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (209) all_22_0_30 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (209) can reduce 78 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.24 | (260) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.48/5.24 |
% 19.48/5.24 +-Applying beta-rule and splitting (166), into two cases.
% 19.48/5.24 |-Branch one:
% 19.48/5.24 | (221) all_27_0_35 = 0
% 19.48/5.24 |
% 19.48/5.24 | Equations (221) can reduce 87 to:
% 19.48/5.24 | (97) $false
% 19.48/5.24 |
% 19.48/5.24 |-The branch is then unsatisfiable
% 19.48/5.24 |-Branch two:
% 19.48/5.24 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.24 | (264) all_25_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (202), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (209) all_22_0_30 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (209) can reduce 78 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.25 | (268) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (170), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (209) all_22_0_30 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (209) can reduce 78 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.25 | (272) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (172), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (209) all_22_0_30 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (209) can reduce 78 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.25 | (276) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (173), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (209) all_22_0_30 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (209) can reduce 78 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.25 | (280) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (201), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (225) all_25_0_33 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (225) can reduce 83 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.25 | (284) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (187), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (213) all_20_0_28 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (213) can reduce 74 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.25 | (288) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (175), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (209) all_22_0_30 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (209) can reduce 78 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.25 | (292) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (174), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (209) all_22_0_30 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (209) can reduce 78 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.25 | (296) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (162), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (225) all_25_0_33 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (225) can reduce 83 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.25 | (300) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (168), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (209) all_22_0_30 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (209) can reduce 78 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.25 | (304) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (163), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (225) all_25_0_33 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (225) can reduce 83 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.25 | (308) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (181), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (225) all_25_0_33 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (225) can reduce 83 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.25 | (312) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (177), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (221) all_27_0_35 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (221) can reduce 87 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.25 | (316) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (179), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (221) all_27_0_35 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (221) can reduce 87 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.25 | (320) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (164), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (225) all_25_0_33 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (225) can reduce 83 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.25 | (324) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (188), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (213) all_20_0_28 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (213) can reduce 74 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.25 | (328) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.25 |
% 19.48/5.25 +-Applying beta-rule and splitting (197), into two cases.
% 19.48/5.25 |-Branch one:
% 19.48/5.25 | (221) all_27_0_35 = 0
% 19.48/5.25 |
% 19.48/5.25 | Equations (221) can reduce 87 to:
% 19.48/5.25 | (97) $false
% 19.48/5.25 |
% 19.48/5.25 |-The branch is then unsatisfiable
% 19.48/5.25 |-Branch two:
% 19.48/5.25 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.25 | (332) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (203), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (209) all_22_0_30 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (209) can reduce 78 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.26 | (336) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (198), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (225) all_25_0_33 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (225) can reduce 83 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.26 | (340) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (193), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (213) all_20_0_28 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (213) can reduce 74 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.26 | (344) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (176), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (221) all_27_0_35 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (221) can reduce 87 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.26 | (348) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (182), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (225) all_25_0_33 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (225) can reduce 83 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.26 | (352) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (194), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (221) all_27_0_35 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (221) can reduce 87 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.26 | (356) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (178), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (221) all_27_0_35 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (221) can reduce 87 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.26 | (360) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (180), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (225) all_25_0_33 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (225) can reduce 83 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.26 | (364) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (183), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (225) all_25_0_33 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (225) can reduce 83 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.26 | (368) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (195), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (221) all_27_0_35 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (221) can reduce 87 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.26 | (372) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (196), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (221) all_27_0_35 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (221) can reduce 87 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (87) ~ (all_27_0_35 = 0)
% 19.48/5.26 | (376) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (199), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (225) all_25_0_33 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (225) can reduce 83 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.26 | (380) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (200), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (225) all_25_0_33 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (225) can reduce 83 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (83) ~ (all_25_0_33 = 0)
% 19.48/5.26 | (384) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (186), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (213) all_20_0_28 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (213) can reduce 74 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.26 | (388) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (191), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (213) all_20_0_28 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (213) can reduce 74 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.26 | (392) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (189), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (213) all_20_0_28 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (213) can reduce 74 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.26 | (396) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (190), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (213) all_20_0_28 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (213) can reduce 74 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.26 | (400) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (192), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (213) all_20_0_28 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (213) can reduce 74 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.26 | (404) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (248), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (100) all_0_4_4 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (100) can reduce 50 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.26 | (408) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.48/5.26 |
% 19.48/5.26 +-Applying beta-rule and splitting (288), into two cases.
% 19.48/5.26 |-Branch one:
% 19.48/5.26 | (96) all_0_3_3 = 0
% 19.48/5.26 |
% 19.48/5.26 | Equations (96) can reduce 20 to:
% 19.48/5.26 | (97) $false
% 19.48/5.26 |
% 19.48/5.26 |-The branch is then unsatisfiable
% 19.48/5.26 |-Branch two:
% 19.48/5.26 | (20) ~ (all_0_3_3 = 0)
% 19.48/5.26 | (412) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.27 |
% 19.48/5.27 | Instantiating (412) with all_262_0_208 yields:
% 19.48/5.27 | (413) (all_262_0_208 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_262_0_208 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (all_262_0_208 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_208) | ( ~ (all_262_0_208 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_262_0_208)
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (348), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (209) all_22_0_30 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (209) can reduce 78 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.27 | (417) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (380), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (213) all_20_0_28 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (213) can reduce 74 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.27 | (421) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (384), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (213) all_20_0_28 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (213) can reduce 74 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.27 | (425) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (400), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (100) all_0_4_4 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (100) can reduce 50 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.27 | (429) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (252), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (96) all_0_3_3 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (96) can reduce 20 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (20) ~ (all_0_3_3 = 0)
% 19.48/5.27 | (433) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (260), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (96) all_0_3_3 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (96) can reduce 20 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (20) ~ (all_0_3_3 = 0)
% 19.48/5.27 | (437) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (268), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (213) all_20_0_28 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (213) can reduce 74 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.27 | (441) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (276), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (100) all_0_4_4 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (100) can reduce 50 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.27 | (445) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (296), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (100) all_0_4_4 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (100) can reduce 50 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.27 | (449) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.27 |
% 19.48/5.27 | Instantiating (449) with all_302_0_253 yields:
% 19.48/5.27 | (450) (all_302_0_253 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_302_0_253 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (all_302_0_253 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_253) | ( ~ (all_302_0_253 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_302_0_253)
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (300), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (96) all_0_3_3 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (96) can reduce 20 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (20) ~ (all_0_3_3 = 0)
% 19.48/5.27 | (454) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (312), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (209) all_22_0_30 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (209) can reduce 78 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.27 | (458) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (316), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (209) all_22_0_30 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (209) can reduce 78 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.27 | (462) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (324), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (100) all_0_4_4 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (100) can reduce 50 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.27 | (466) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (328), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (96) all_0_3_3 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (96) can reduce 20 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (20) ~ (all_0_3_3 = 0)
% 19.48/5.27 | (470) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (340), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (213) all_20_0_28 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (213) can reduce 74 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.27 | (474) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (352), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (209) all_22_0_30 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (209) can reduce 78 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.27 | (478) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (356), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (213) all_20_0_28 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (213) can reduce 74 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.27 | (482) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (364), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (209) all_22_0_30 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (209) can reduce 78 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.27 | (486) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.48/5.27 |
% 19.48/5.27 +-Applying beta-rule and splitting (372), into two cases.
% 19.48/5.27 |-Branch one:
% 19.48/5.27 | (213) all_20_0_28 = 0
% 19.48/5.27 |
% 19.48/5.27 | Equations (213) can reduce 74 to:
% 19.48/5.27 | (97) $false
% 19.48/5.27 |
% 19.48/5.27 |-The branch is then unsatisfiable
% 19.48/5.27 |-Branch two:
% 19.48/5.27 | (74) ~ (all_20_0_28 = 0)
% 19.48/5.27 | (490) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (388), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (96) all_0_3_3 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (96) can reduce 20 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (20) ~ (all_0_3_3 = 0)
% 19.48/5.28 | (494) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (392), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (100) all_0_4_4 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (100) can reduce 50 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.28 | (498) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 19.48/5.28 |
% 19.48/5.28 | Instantiating (498) with all_350_0_265 yields:
% 19.48/5.28 | (499) (all_350_0_265 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_350_0_265 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (all_350_0_265 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_265)
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (396), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (96) all_0_3_3 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (96) can reduce 20 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (20) ~ (all_0_3_3 = 0)
% 19.48/5.28 | (503) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (413), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (504) (all_262_0_208 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_262_0_208 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (all_262_0_208 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_208)
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (504), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (505) (all_262_0_208 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_262_0_208 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0)
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (505), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (506) all_262_0_208 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 19.48/5.28 |
% 19.48/5.28 | Applying alpha-rule on (506) yields:
% 19.48/5.28 | (507) all_262_0_208 = 0
% 19.48/5.28 | (508) apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (320), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (209) all_22_0_30 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (209) can reduce 78 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.28 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (368), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (209) all_22_0_30 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (209) can reduce 78 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.28 | (516) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (360), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (209) all_22_0_30 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (209) can reduce 78 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (78) ~ (all_22_0_30 = 0)
% 19.48/5.28 | (520) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.48/5.28 |
% 19.48/5.28 | Instantiating formula (44) with all_0_8_8, all_0_2_2, 0, all_22_0_30 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_2_2) = 0, yields:
% 19.48/5.28 | (209) all_22_0_30 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (209) can reduce 78 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (523) all_262_0_208 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0
% 19.48/5.28 |
% 19.48/5.28 | Applying alpha-rule on (523) yields:
% 19.48/5.28 | (507) all_262_0_208 = 0
% 19.48/5.28 | (525) apart_point_and_line(all_0_9_9, all_0_5_5) = 0
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (292), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (100) all_0_4_4 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (100) can reduce 50 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.28 | (529) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (404), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (100) all_0_4_4 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (100) can reduce 50 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.28 | (533) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (244), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (100) all_0_4_4 = 0
% 19.48/5.28 |
% 19.48/5.28 | Equations (100) can reduce 50 to:
% 19.48/5.28 | (97) $false
% 19.48/5.28 |
% 19.48/5.28 |-The branch is then unsatisfiable
% 19.48/5.28 |-Branch two:
% 19.48/5.28 | (50) ~ (all_0_4_4 = 0)
% 19.48/5.28 | (537) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.48/5.28 |
% 19.48/5.28 +-Applying beta-rule and splitting (256), into two cases.
% 19.48/5.28 |-Branch one:
% 19.48/5.28 | (100) all_0_4_4 = 0
% 19.71/5.28 |
% 19.71/5.28 | Equations (100) can reduce 50 to:
% 19.71/5.28 | (97) $false
% 19.71/5.28 |
% 19.71/5.28 |-The branch is then unsatisfiable
% 19.71/5.28 |-Branch two:
% 19.71/5.28 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.28 | (541) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.71/5.28 |
% 19.71/5.28 +-Applying beta-rule and splitting (280), into two cases.
% 19.71/5.28 |-Branch one:
% 19.71/5.28 | (100) all_0_4_4 = 0
% 19.71/5.28 |
% 19.71/5.28 | Equations (100) can reduce 50 to:
% 19.71/5.28 | (97) $false
% 19.71/5.28 |
% 19.71/5.28 |-The branch is then unsatisfiable
% 19.71/5.28 |-Branch two:
% 19.71/5.28 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.28 | (545) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.28 |
% 19.71/5.28 +-Applying beta-rule and splitting (344), into two cases.
% 19.71/5.28 |-Branch one:
% 19.71/5.28 | (100) all_0_4_4 = 0
% 19.71/5.28 |
% 19.71/5.28 | Equations (100) can reduce 50 to:
% 19.71/5.28 | (97) $false
% 19.71/5.28 |
% 19.71/5.28 |-The branch is then unsatisfiable
% 19.71/5.28 |-Branch two:
% 19.71/5.28 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.28 | (549) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.71/5.28 |
% 19.71/5.28 | Instantiating formula (44) with all_0_9_9, all_0_5_5, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, apart_point_and_line(all_0_9_9, all_0_5_5) = 0, yields:
% 19.71/5.28 | (100) all_0_4_4 = 0
% 19.71/5.28 |
% 19.71/5.28 | Equations (100) can reduce 50 to:
% 19.71/5.28 | (97) $false
% 19.71/5.28 |
% 19.71/5.28 |-The branch is then unsatisfiable
% 19.71/5.28 |-Branch two:
% 19.71/5.28 | (552) ~ (all_262_0_208 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_208
% 19.71/5.28 |
% 19.71/5.28 | Applying alpha-rule on (552) yields:
% 19.71/5.28 | (553) ~ (all_262_0_208 = 0)
% 19.71/5.28 | (554) distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_208
% 19.71/5.28 |
% 19.71/5.28 +-Applying beta-rule and splitting (272), into two cases.
% 19.71/5.28 |-Branch one:
% 19.71/5.28 | (96) all_0_3_3 = 0
% 19.71/5.28 |
% 19.71/5.28 | Equations (96) can reduce 20 to:
% 19.71/5.28 | (97) $false
% 19.71/5.28 |
% 19.71/5.28 |-The branch is then unsatisfiable
% 19.71/5.28 |-Branch two:
% 19.71/5.28 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.28 | (558) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.71/5.28 |
% 19.71/5.28 +-Applying beta-rule and splitting (284), into two cases.
% 19.71/5.28 |-Branch one:
% 19.71/5.28 | (213) all_20_0_28 = 0
% 19.71/5.28 |
% 19.71/5.28 | Equations (213) can reduce 74 to:
% 19.71/5.28 | (97) $false
% 19.71/5.28 |
% 19.71/5.28 |-The branch is then unsatisfiable
% 19.71/5.28 |-Branch two:
% 19.71/5.28 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.28 | (562) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.71/5.28 |
% 19.71/5.28 +-Applying beta-rule and splitting (304), into two cases.
% 19.71/5.28 |-Branch one:
% 19.71/5.28 | (96) all_0_3_3 = 0
% 19.71/5.28 |
% 19.71/5.28 | Equations (96) can reduce 20 to:
% 19.71/5.28 | (97) $false
% 19.71/5.28 |
% 19.71/5.28 |-The branch is then unsatisfiable
% 19.71/5.28 |-Branch two:
% 19.71/5.28 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.28 | (566) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.71/5.28 |
% 19.71/5.29 +-Applying beta-rule and splitting (308), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (96) all_0_3_3 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (96) can reduce 20 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.29 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (320), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (209) all_22_0_30 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (209) can reduce 78 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.29 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (368), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (209) all_22_0_30 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (209) can reduce 78 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.29 | (516) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (376), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (213) all_20_0_28 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (213) can reduce 74 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.29 | (582) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (450), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (583) (all_302_0_253 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_302_0_253 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (all_302_0_253 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_253)
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (583), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (584) (all_302_0_253 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_302_0_253 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0)
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (584), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (585) all_302_0_253 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 19.71/5.29 |
% 19.71/5.29 | Applying alpha-rule on (585) yields:
% 19.71/5.29 | (586) all_302_0_253 = 0
% 19.71/5.29 | (587) apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (240), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (96) all_0_3_3 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (96) can reduce 20 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.29 | (591) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.29 |
% 19.71/5.29 | Instantiating formula (44) with all_0_8_8, all_0_5_5, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_8_8, all_0_5_5) = 0, yields:
% 19.71/5.29 | (96) all_0_3_3 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (96) can reduce 20 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (594) all_302_0_253 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0
% 19.71/5.29 |
% 19.71/5.29 | Applying alpha-rule on (594) yields:
% 19.71/5.29 | (586) all_302_0_253 = 0
% 19.71/5.29 | (596) apart_point_and_line(all_0_9_9, all_0_2_2) = 0
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (332), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (213) all_20_0_28 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (213) can reduce 74 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.29 | (600) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.71/5.29 |
% 19.71/5.29 | Instantiating formula (44) with all_0_9_9, all_0_2_2, 0, all_20_0_28 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, apart_point_and_line(all_0_9_9, all_0_2_2) = 0, yields:
% 19.71/5.29 | (213) all_20_0_28 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (213) can reduce 74 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (603) ~ (all_302_0_253 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_253
% 19.71/5.29 |
% 19.71/5.29 | Applying alpha-rule on (603) yields:
% 19.71/5.29 | (604) ~ (all_302_0_253 = 0)
% 19.71/5.29 | (605) distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_253
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (360), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (209) all_22_0_30 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (209) can reduce 78 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.29 | (520) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (240), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (96) all_0_3_3 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (96) can reduce 20 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.29 | (591) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (499), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (614) (all_350_0_265 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_350_0_265 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0)
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (614), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (615) all_350_0_265 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 19.71/5.29 |
% 19.71/5.29 | Applying alpha-rule on (615) yields:
% 19.71/5.29 | (616) all_350_0_265 = 0
% 19.71/5.29 | (508) apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 19.71/5.29 |
% 19.71/5.29 | Instantiating formula (44) with all_0_8_8, all_0_2_2, 0, all_22_0_30 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_2_2) = 0, yields:
% 19.71/5.29 | (209) all_22_0_30 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (209) can reduce 78 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (620) all_350_0_265 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 19.71/5.29 |
% 19.71/5.29 | Applying alpha-rule on (620) yields:
% 19.71/5.29 | (616) all_350_0_265 = 0
% 19.71/5.29 | (587) apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 19.71/5.29 |
% 19.71/5.29 | Instantiating formula (44) with all_0_8_8, all_0_5_5, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_8_8, all_0_5_5) = 0, yields:
% 19.71/5.29 | (96) all_0_3_3 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (96) can reduce 20 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (625) ~ (all_350_0_265 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_265
% 19.71/5.29 |
% 19.71/5.29 | Applying alpha-rule on (625) yields:
% 19.71/5.29 | (626) ~ (all_350_0_265 = 0)
% 19.71/5.29 | (627) distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_265
% 19.71/5.29 |
% 19.71/5.29 | Instantiating formula (29) with all_0_2_2, all_0_5_5, all_302_0_253, all_350_0_265 and discharging atoms distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_265, distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_253, yields:
% 19.71/5.29 | (628) all_350_0_265 = all_302_0_253
% 19.71/5.29 |
% 19.71/5.29 | Instantiating formula (29) with all_0_2_2, all_0_5_5, all_262_0_208, all_350_0_265 and discharging atoms distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_265, distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_208, yields:
% 19.71/5.29 | (629) all_350_0_265 = all_262_0_208
% 19.71/5.29 |
% 19.71/5.29 | Combining equations (629,628) yields a new equation:
% 19.71/5.29 | (630) all_302_0_253 = all_262_0_208
% 19.71/5.29 |
% 19.71/5.29 | Equations (630) can reduce 604 to:
% 19.71/5.29 | (553) ~ (all_262_0_208 = 0)
% 19.71/5.29 |
% 19.71/5.29 | From (630) and (605) follows:
% 19.71/5.29 | (554) distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_208
% 19.71/5.29 |
% 19.71/5.29 | Instantiating formula (25) with all_27_0_35, all_262_0_208, all_0_5_5, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_208, yields:
% 19.71/5.29 | (633) all_262_0_208 = 0 | all_27_0_35 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = v0)
% 19.71/5.29 |
% 19.71/5.29 | Instantiating formula (32) with all_262_0_208, all_0_5_5, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = 0, distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_208, yields:
% 19.71/5.29 | (634) all_262_0_208 = 0 | apart_point_and_line(all_0_6_6, all_0_5_5) = 0
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (634), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (635) apart_point_and_line(all_0_6_6, all_0_5_5) = 0
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (633), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (507) all_262_0_208 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (507) can reduce 553 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (553) ~ (all_262_0_208 = 0)
% 19.71/5.29 | (639) all_27_0_35 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = v0)
% 19.71/5.29 |
% 19.71/5.29 +-Applying beta-rule and splitting (639), into two cases.
% 19.71/5.29 |-Branch one:
% 19.71/5.29 | (221) all_27_0_35 = 0
% 19.71/5.29 |
% 19.71/5.29 | Equations (221) can reduce 87 to:
% 19.71/5.29 | (97) $false
% 19.71/5.29 |
% 19.71/5.29 |-The branch is then unsatisfiable
% 19.71/5.29 |-Branch two:
% 19.71/5.29 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.30 | (643) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = v0)
% 19.71/5.30 |
% 19.71/5.30 | Instantiating formula (44) with all_0_6_6, all_0_5_5, 0, all_27_0_35 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_6_6, all_0_5_5) = 0, yields:
% 19.71/5.30 | (221) all_27_0_35 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (221) can reduce 87 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (646) ~ (apart_point_and_line(all_0_6_6, all_0_5_5) = 0)
% 19.71/5.30 | (507) all_262_0_208 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (507) can reduce 553 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (649) ~ (all_302_0_253 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_302_0_253
% 19.71/5.30 |
% 19.71/5.30 | Applying alpha-rule on (649) yields:
% 19.71/5.30 | (604) ~ (all_302_0_253 = 0)
% 19.71/5.30 | (651) distinct_points(all_0_9_9, all_0_8_8) = all_302_0_253
% 19.71/5.30 |
% 19.71/5.30 | Instantiating formula (4) with all_0_9_9, all_0_8_8, all_302_0_253, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_302_0_253, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.71/5.30 | (586) all_302_0_253 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (586) can reduce 604 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (654) ~ (all_262_0_208 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_262_0_208
% 19.71/5.30 |
% 19.71/5.30 | Applying alpha-rule on (654) yields:
% 19.71/5.30 | (553) ~ (all_262_0_208 = 0)
% 19.71/5.30 | (656) distinct_points(all_0_9_9, all_0_8_8) = all_262_0_208
% 19.71/5.30 |
% 19.71/5.30 | Instantiating formula (4) with all_0_9_9, all_0_8_8, all_262_0_208, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_262_0_208, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.71/5.30 | (507) all_262_0_208 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (507) can reduce 553 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (659) all_0_1_1 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 19.71/5.30 |
% 19.71/5.30 | Applying alpha-rule on (659) yields:
% 19.71/5.30 | (660) all_0_1_1 = 0
% 19.71/5.30 | (661) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (185), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (209) all_22_0_30 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (209) can reduce 78 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.30 | (212) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (204), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (213) all_20_0_28 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (213) can reduce 74 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.30 | (216) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (205), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (213) all_20_0_28 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (213) can reduce 74 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.30 | (220) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (161), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (221) all_27_0_35 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (221) can reduce 87 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.30 | (224) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (167), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (225) all_25_0_33 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (225) can reduce 83 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.30 | (228) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (184), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (209) all_22_0_30 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (209) can reduce 78 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.30 | (232) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (169), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (209) all_22_0_30 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (209) can reduce 78 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.30 | (236) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (157), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (221) all_27_0_35 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (221) can reduce 87 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.30 | (240) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (160), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (221) all_27_0_35 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (221) can reduce 87 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.30 | (244) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (165), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (225) all_25_0_33 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (225) can reduce 83 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.30 | (248) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.71/5.30 |
% 19.71/5.30 +-Applying beta-rule and splitting (158), into two cases.
% 19.71/5.30 |-Branch one:
% 19.71/5.30 | (221) all_27_0_35 = 0
% 19.71/5.30 |
% 19.71/5.30 | Equations (221) can reduce 87 to:
% 19.71/5.30 | (97) $false
% 19.71/5.30 |
% 19.71/5.30 |-The branch is then unsatisfiable
% 19.71/5.30 |-Branch two:
% 19.71/5.30 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.30 | (252) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (159), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (221) all_27_0_35 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (221) can reduce 87 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.31 | (256) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (171), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.31 | (260) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (166), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (221) all_27_0_35 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (221) can reduce 87 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.31 | (264) all_25_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (202), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.31 | (268) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (170), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.31 | (272) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (172), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.31 | (276) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (173), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.31 | (280) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (201), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (225) all_25_0_33 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (225) can reduce 83 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.31 | (284) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (187), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (213) all_20_0_28 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (213) can reduce 74 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.31 | (288) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (175), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.31 | (292) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (174), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.31 | (296) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (162), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (225) all_25_0_33 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (225) can reduce 83 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.31 | (300) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (168), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.31 | (304) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (163), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (225) all_25_0_33 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (225) can reduce 83 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.31 | (308) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (181), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (225) all_25_0_33 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (225) can reduce 83 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.31 | (312) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (177), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (221) all_27_0_35 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (221) can reduce 87 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.31 | (316) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (179), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (221) all_27_0_35 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (221) can reduce 87 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.31 | (320) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (164), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (225) all_25_0_33 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (225) can reduce 83 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.31 | (324) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (188), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (213) all_20_0_28 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (213) can reduce 74 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.31 | (328) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (197), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (221) all_27_0_35 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (221) can reduce 87 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.31 | (332) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.71/5.31 |
% 19.71/5.31 +-Applying beta-rule and splitting (203), into two cases.
% 19.71/5.31 |-Branch one:
% 19.71/5.31 | (209) all_22_0_30 = 0
% 19.71/5.31 |
% 19.71/5.31 | Equations (209) can reduce 78 to:
% 19.71/5.31 | (97) $false
% 19.71/5.31 |
% 19.71/5.31 |-The branch is then unsatisfiable
% 19.71/5.31 |-Branch two:
% 19.71/5.31 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.32 | (336) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (198), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (225) all_25_0_33 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (225) can reduce 83 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.32 | (340) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (193), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (213) all_20_0_28 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (213) can reduce 74 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.32 | (344) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (176), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (221) all_27_0_35 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (221) can reduce 87 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.32 | (348) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (182), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (225) all_25_0_33 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (225) can reduce 83 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.32 | (352) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (194), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (221) all_27_0_35 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (221) can reduce 87 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.32 | (356) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (178), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (221) all_27_0_35 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (221) can reduce 87 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.32 | (360) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (180), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (225) all_25_0_33 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (225) can reduce 83 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.32 | (364) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (183), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (225) all_25_0_33 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (225) can reduce 83 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.32 | (368) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (195), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (221) all_27_0_35 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (221) can reduce 87 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.32 | (372) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (196), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (221) all_27_0_35 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (221) can reduce 87 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (87) ~ (all_27_0_35 = 0)
% 19.71/5.32 | (376) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (199), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (225) all_25_0_33 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (225) can reduce 83 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.32 | (380) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (200), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (225) all_25_0_33 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (225) can reduce 83 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.32 | (384) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (186), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (213) all_20_0_28 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (213) can reduce 74 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.32 | (388) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (191), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (213) all_20_0_28 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (213) can reduce 74 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.32 | (392) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (189), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (213) all_20_0_28 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (213) can reduce 74 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.32 | (396) all_0_3_3 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (190), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (213) all_20_0_28 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (213) can reduce 74 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.32 | (400) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (192), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (213) all_20_0_28 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (213) can reduce 74 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.32 | (404) all_0_4_4 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (248), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (100) all_0_4_4 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (100) can reduce 50 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.32 | (408) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.71/5.32 |
% 19.71/5.32 +-Applying beta-rule and splitting (288), into two cases.
% 19.71/5.32 |-Branch one:
% 19.71/5.32 | (96) all_0_3_3 = 0
% 19.71/5.32 |
% 19.71/5.32 | Equations (96) can reduce 20 to:
% 19.71/5.32 | (97) $false
% 19.71/5.32 |
% 19.71/5.32 |-The branch is then unsatisfiable
% 19.71/5.32 |-Branch two:
% 19.71/5.32 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.32 | (412) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.32 |
% 19.71/5.32 | Instantiating (412) with all_262_0_640 yields:
% 19.71/5.33 | (866) (all_262_0_640 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_262_0_640 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (all_262_0_640 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_640) | ( ~ (all_262_0_640 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_262_0_640)
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (348), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (209) all_22_0_30 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (209) can reduce 78 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.33 | (417) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (380), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (213) all_20_0_28 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (213) can reduce 74 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.33 | (421) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (384), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (213) all_20_0_28 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (213) can reduce 74 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.33 | (425) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (400), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (100) all_0_4_4 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (100) can reduce 50 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.33 | (429) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (252), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (96) all_0_3_3 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (96) can reduce 20 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.33 | (433) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (260), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (96) all_0_3_3 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (96) can reduce 20 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.33 | (437) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (268), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (213) all_20_0_28 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (213) can reduce 74 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.33 | (441) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (276), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (100) all_0_4_4 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (100) can reduce 50 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.33 | (445) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (296), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (100) all_0_4_4 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (100) can reduce 50 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.33 | (449) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.33 |
% 19.71/5.33 | Instantiating (449) with all_302_0_685 yields:
% 19.71/5.33 | (903) (all_302_0_685 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_302_0_685 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (all_302_0_685 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_685) | ( ~ (all_302_0_685 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_302_0_685)
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (300), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (96) all_0_3_3 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (96) can reduce 20 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.33 | (454) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (312), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (209) all_22_0_30 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (209) can reduce 78 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.33 | (458) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (316), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (209) all_22_0_30 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (209) can reduce 78 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.33 | (462) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (324), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (100) all_0_4_4 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (100) can reduce 50 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.33 | (466) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (328), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (96) all_0_3_3 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (96) can reduce 20 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.33 | (470) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (340), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (213) all_20_0_28 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (213) can reduce 74 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.33 | (474) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (352), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (209) all_22_0_30 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (209) can reduce 78 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.33 | (478) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (356), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (213) all_20_0_28 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (213) can reduce 74 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.33 | (482) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (364), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (209) all_22_0_30 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (209) can reduce 78 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.33 | (486) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (372), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (213) all_20_0_28 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (213) can reduce 74 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.33 | (490) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (388), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (96) all_0_3_3 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (96) can reduce 20 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.33 | (494) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (392), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (100) all_0_4_4 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (100) can reduce 50 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.33 | (498) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 19.71/5.33 |
% 19.71/5.33 | Instantiating (498) with all_350_0_697 yields:
% 19.71/5.33 | (952) (all_350_0_697 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_350_0_697 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (all_350_0_697 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_697)
% 19.71/5.33 |
% 19.71/5.33 +-Applying beta-rule and splitting (396), into two cases.
% 19.71/5.33 |-Branch one:
% 19.71/5.33 | (96) all_0_3_3 = 0
% 19.71/5.33 |
% 19.71/5.33 | Equations (96) can reduce 20 to:
% 19.71/5.33 | (97) $false
% 19.71/5.33 |
% 19.71/5.33 |-The branch is then unsatisfiable
% 19.71/5.33 |-Branch two:
% 19.71/5.33 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.33 | (503) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (866), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (957) (all_262_0_640 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_262_0_640 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (all_262_0_640 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_640)
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (957), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (958) (all_262_0_640 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_262_0_640 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0)
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (958), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (959) all_262_0_640 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 19.71/5.34 |
% 19.71/5.34 | Applying alpha-rule on (959) yields:
% 19.71/5.34 | (960) all_262_0_640 = 0
% 19.71/5.34 | (508) apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (320), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (209) all_22_0_30 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (209) can reduce 78 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.34 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (368), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (209) all_22_0_30 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (209) can reduce 78 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.34 | (516) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (360), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (209) all_22_0_30 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (209) can reduce 78 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.34 | (520) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.71/5.34 |
% 19.71/5.34 | Instantiating formula (44) with all_0_8_8, all_0_2_2, 0, all_22_0_30 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_2_2) = 0, yields:
% 19.71/5.34 | (209) all_22_0_30 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (209) can reduce 78 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (976) all_262_0_640 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0
% 19.71/5.34 |
% 19.71/5.34 | Applying alpha-rule on (976) yields:
% 19.71/5.34 | (960) all_262_0_640 = 0
% 19.71/5.34 | (525) apart_point_and_line(all_0_9_9, all_0_5_5) = 0
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (292), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (100) all_0_4_4 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (100) can reduce 50 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.34 | (529) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (404), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (100) all_0_4_4 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (100) can reduce 50 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.34 | (533) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (244), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (100) all_0_4_4 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (100) can reduce 50 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.34 | (537) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (256), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (100) all_0_4_4 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (100) can reduce 50 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.34 | (541) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (280), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (100) all_0_4_4 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (100) can reduce 50 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.34 | (545) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (344), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (100) all_0_4_4 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (100) can reduce 50 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (50) ~ (all_0_4_4 = 0)
% 19.71/5.34 | (549) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 19.71/5.34 |
% 19.71/5.34 | Instantiating formula (44) with all_0_9_9, all_0_5_5, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_9_9, all_0_5_5) = all_0_4_4, apart_point_and_line(all_0_9_9, all_0_5_5) = 0, yields:
% 19.71/5.34 | (100) all_0_4_4 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (100) can reduce 50 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (1005) ~ (all_262_0_640 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_640
% 19.71/5.34 |
% 19.71/5.34 | Applying alpha-rule on (1005) yields:
% 19.71/5.34 | (1006) ~ (all_262_0_640 = 0)
% 19.71/5.34 | (1007) distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_640
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (264), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (225) all_25_0_33 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (225) can reduce 83 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (83) ~ (all_25_0_33 = 0)
% 19.71/5.34 | (1011) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (272), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (96) all_0_3_3 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (96) can reduce 20 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.34 | (558) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (284), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (213) all_20_0_28 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (213) can reduce 74 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.34 | (562) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (304), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (96) all_0_3_3 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (96) can reduce 20 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.34 | (566) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (308), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (96) all_0_3_3 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (96) can reduce 20 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.34 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (320), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (209) all_22_0_30 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (209) can reduce 78 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.34 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (368), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (209) all_22_0_30 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (209) can reduce 78 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (78) ~ (all_22_0_30 = 0)
% 19.71/5.34 | (516) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (376), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (213) all_20_0_28 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (213) can reduce 74 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.34 | (582) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (903), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (1040) (all_302_0_685 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_302_0_685 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (all_302_0_685 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_685)
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (1040), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (1041) (all_302_0_685 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_302_0_685 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0)
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (1041), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (1042) all_302_0_685 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 19.71/5.34 |
% 19.71/5.34 | Applying alpha-rule on (1042) yields:
% 19.71/5.34 | (1043) all_302_0_685 = 0
% 19.71/5.34 | (587) apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 19.71/5.34 |
% 19.71/5.34 +-Applying beta-rule and splitting (240), into two cases.
% 19.71/5.34 |-Branch one:
% 19.71/5.34 | (96) all_0_3_3 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (96) can reduce 20 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.34 |-Branch two:
% 19.71/5.34 | (20) ~ (all_0_3_3 = 0)
% 19.71/5.34 | (591) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.71/5.34 |
% 19.71/5.34 | Instantiating formula (44) with all_0_8_8, all_0_5_5, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_8_8, all_0_5_5) = 0, yields:
% 19.71/5.34 | (96) all_0_3_3 = 0
% 19.71/5.34 |
% 19.71/5.34 | Equations (96) can reduce 20 to:
% 19.71/5.34 | (97) $false
% 19.71/5.34 |
% 19.71/5.34 |-The branch is then unsatisfiable
% 19.71/5.35 |-Branch two:
% 19.71/5.35 | (1051) all_302_0_685 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0
% 19.71/5.35 |
% 19.71/5.35 | Applying alpha-rule on (1051) yields:
% 19.71/5.35 | (1043) all_302_0_685 = 0
% 19.71/5.35 | (596) apart_point_and_line(all_0_9_9, all_0_2_2) = 0
% 19.71/5.35 |
% 19.71/5.35 +-Applying beta-rule and splitting (332), into two cases.
% 19.71/5.35 |-Branch one:
% 19.71/5.35 | (213) all_20_0_28 = 0
% 19.71/5.35 |
% 19.71/5.35 | Equations (213) can reduce 74 to:
% 19.71/5.35 | (97) $false
% 19.71/5.35 |
% 19.71/5.35 |-The branch is then unsatisfiable
% 19.71/5.35 |-Branch two:
% 19.71/5.35 | (74) ~ (all_20_0_28 = 0)
% 19.71/5.35 | (600) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (44) with all_0_9_9, all_0_2_2, 0, all_20_0_28 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, apart_point_and_line(all_0_9_9, all_0_2_2) = 0, yields:
% 19.99/5.35 | (213) all_20_0_28 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (213) can reduce 74 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1060) ~ (all_302_0_685 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_685
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1060) yields:
% 19.99/5.35 | (1061) ~ (all_302_0_685 = 0)
% 19.99/5.35 | (1062) distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_685
% 19.99/5.35 |
% 19.99/5.35 +-Applying beta-rule and splitting (360), into two cases.
% 19.99/5.35 |-Branch one:
% 19.99/5.35 | (209) all_22_0_30 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (209) can reduce 78 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (78) ~ (all_22_0_30 = 0)
% 19.99/5.35 | (520) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 19.99/5.35 |
% 19.99/5.35 +-Applying beta-rule and splitting (240), into two cases.
% 19.99/5.35 |-Branch one:
% 19.99/5.35 | (96) all_0_3_3 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (96) can reduce 20 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (20) ~ (all_0_3_3 = 0)
% 19.99/5.35 | (591) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 19.99/5.35 |
% 19.99/5.35 +-Applying beta-rule and splitting (952), into two cases.
% 19.99/5.35 |-Branch one:
% 19.99/5.35 | (1071) (all_350_0_697 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (all_350_0_697 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0)
% 19.99/5.35 |
% 19.99/5.35 +-Applying beta-rule and splitting (1071), into two cases.
% 19.99/5.35 |-Branch one:
% 19.99/5.35 | (1072) all_350_0_697 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1072) yields:
% 19.99/5.35 | (1073) all_350_0_697 = 0
% 19.99/5.35 | (508) apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (44) with all_0_8_8, all_0_2_2, 0, all_22_0_30 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_2_2) = 0, yields:
% 19.99/5.35 | (209) all_22_0_30 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (209) can reduce 78 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1077) all_350_0_697 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1077) yields:
% 19.99/5.35 | (1073) all_350_0_697 = 0
% 19.99/5.35 | (587) apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (44) with all_0_8_8, all_0_5_5, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = all_0_3_3, apart_point_and_line(all_0_8_8, all_0_5_5) = 0, yields:
% 19.99/5.35 | (96) all_0_3_3 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (96) can reduce 20 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1082) ~ (all_350_0_697 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_697
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1082) yields:
% 19.99/5.35 | (1083) ~ (all_350_0_697 = 0)
% 19.99/5.35 | (1084) distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_697
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (29) with all_0_2_2, all_0_5_5, all_302_0_685, all_350_0_697 and discharging atoms distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_697, distinct_lines(all_0_2_2, all_0_5_5) = all_302_0_685, yields:
% 19.99/5.35 | (1085) all_350_0_697 = all_302_0_685
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (29) with all_0_2_2, all_0_5_5, all_262_0_640, all_350_0_697 and discharging atoms distinct_lines(all_0_2_2, all_0_5_5) = all_350_0_697, distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_640, yields:
% 19.99/5.35 | (1086) all_350_0_697 = all_262_0_640
% 19.99/5.35 |
% 19.99/5.35 | Combining equations (1086,1085) yields a new equation:
% 19.99/5.35 | (1087) all_302_0_685 = all_262_0_640
% 19.99/5.35 |
% 19.99/5.35 | Equations (1087) can reduce 1061 to:
% 19.99/5.35 | (1006) ~ (all_262_0_640 = 0)
% 19.99/5.35 |
% 19.99/5.35 | From (1087) and (1062) follows:
% 19.99/5.35 | (1007) distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_640
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (25) with all_25_0_33, all_262_0_640, all_0_5_5, all_0_2_2, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_640, yields:
% 19.99/5.35 | (1090) all_262_0_640 = 0 | all_25_0_33 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_7_7, all_0_2_2) = v0)
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (32) with all_262_0_640, all_0_5_5, all_0_2_2, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = 0, distinct_lines(all_0_2_2, all_0_5_5) = all_262_0_640, yields:
% 19.99/5.35 | (1091) all_262_0_640 = 0 | apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 19.99/5.35 |
% 19.99/5.35 +-Applying beta-rule and splitting (1091), into two cases.
% 19.99/5.35 |-Branch one:
% 19.99/5.35 | (1092) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 19.99/5.35 |
% 19.99/5.35 +-Applying beta-rule and splitting (1090), into two cases.
% 19.99/5.35 |-Branch one:
% 19.99/5.35 | (960) all_262_0_640 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (960) can reduce 1006 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1006) ~ (all_262_0_640 = 0)
% 19.99/5.35 | (1096) all_25_0_33 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_7_7, all_0_2_2) = v0)
% 19.99/5.35 |
% 19.99/5.35 +-Applying beta-rule and splitting (1096), into two cases.
% 19.99/5.35 |-Branch one:
% 19.99/5.35 | (225) all_25_0_33 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (225) can reduce 83 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (83) ~ (all_25_0_33 = 0)
% 19.99/5.35 | (1100) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_7_7, all_0_2_2) = v0)
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (44) with all_0_7_7, all_0_5_5, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_25_0_33, apart_point_and_line(all_0_7_7, all_0_5_5) = 0, yields:
% 19.99/5.35 | (225) all_25_0_33 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (225) can reduce 83 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1103) ~ (apart_point_and_line(all_0_7_7, all_0_5_5) = 0)
% 19.99/5.35 | (960) all_262_0_640 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (960) can reduce 1006 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1106) ~ (all_302_0_685 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_302_0_685
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1106) yields:
% 19.99/5.35 | (1061) ~ (all_302_0_685 = 0)
% 19.99/5.35 | (1108) distinct_points(all_0_9_9, all_0_8_8) = all_302_0_685
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (4) with all_0_9_9, all_0_8_8, all_302_0_685, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_302_0_685, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.99/5.35 | (1043) all_302_0_685 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (1043) can reduce 1061 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1111) ~ (all_262_0_640 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_262_0_640
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1111) yields:
% 19.99/5.35 | (1006) ~ (all_262_0_640 = 0)
% 19.99/5.35 | (1113) distinct_points(all_0_9_9, all_0_8_8) = all_262_0_640
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (4) with all_0_9_9, all_0_8_8, all_262_0_640, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_262_0_640, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.99/5.35 | (960) all_262_0_640 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (960) can reduce 1006 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1116) ~ (all_31_0_39 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_31_0_39
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1116) yields:
% 19.99/5.35 | (131) ~ (all_31_0_39 = 0)
% 19.99/5.35 | (1118) distinct_points(all_0_7_7, all_0_6_6) = all_31_0_39
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (4) with all_0_7_7, all_0_6_6, all_31_0_39, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_31_0_39, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 19.99/5.35 | (1119) all_31_0_39 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (1119) can reduce 131 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1121) ~ (all_24_0_32 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_24_0_32
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1121) yields:
% 19.99/5.35 | (120) ~ (all_24_0_32 = 0)
% 19.99/5.35 | (1123) distinct_points(all_0_9_9, all_0_8_8) = all_24_0_32
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (4) with all_0_9_9, all_0_8_8, all_24_0_32, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_24_0_32, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.99/5.35 | (1124) all_24_0_32 = 0
% 19.99/5.35 |
% 19.99/5.35 | Equations (1124) can reduce 120 to:
% 19.99/5.35 | (97) $false
% 19.99/5.35 |
% 19.99/5.35 |-The branch is then unsatisfiable
% 19.99/5.35 |-Branch two:
% 19.99/5.35 | (1126) ~ (all_29_0_37 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_29_0_37
% 19.99/5.35 |
% 19.99/5.35 | Applying alpha-rule on (1126) yields:
% 19.99/5.35 | (117) ~ (all_29_0_37 = 0)
% 19.99/5.35 | (1128) distinct_points(all_0_9_9, all_0_8_8) = all_29_0_37
% 19.99/5.35 |
% 19.99/5.35 | Instantiating formula (4) with all_0_9_9, all_0_8_8, all_29_0_37, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_29_0_37, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 19.99/5.36 | (1129) all_29_0_37 = 0
% 19.99/5.36 |
% 19.99/5.36 | Equations (1129) can reduce 117 to:
% 19.99/5.36 | (97) $false
% 19.99/5.36 |
% 19.99/5.36 |-The branch is then unsatisfiable
% 19.99/5.36 |-Branch two:
% 19.99/5.36 | (1131) ~ (all_30_0_38 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_30_0_38
% 19.99/5.36 |
% 19.99/5.36 | Applying alpha-rule on (1131) yields:
% 19.99/5.36 | (94) ~ (all_30_0_38 = 0)
% 19.99/5.36 | (1133) distinct_points(all_0_7_7, all_0_6_6) = all_30_0_38
% 19.99/5.36 |
% 19.99/5.36 | Instantiating formula (4) with all_0_7_7, all_0_6_6, all_30_0_38, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_30_0_38, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 19.99/5.36 | (1134) all_30_0_38 = 0
% 19.99/5.36 |
% 19.99/5.36 | Equations (1134) can reduce 94 to:
% 19.99/5.36 | (97) $false
% 19.99/5.36 |
% 19.99/5.36 |-The branch is then unsatisfiable
% 19.99/5.36 % SZS output end Proof for theBenchmark
% 19.99/5.36
% 19.99/5.36 4749ms
%------------------------------------------------------------------------------