TSTP Solution File: GEO190+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO190+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 03:48:26 EDT 2022
% Result : Theorem 6.66s 2.31s
% Output : Proof 81.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO190+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 03:25:38 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.43/0.62 ____ _
% 0.43/0.62 ___ / __ \_____(_)___ ________ __________
% 0.43/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.43/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.43/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.43/0.62
% 0.43/0.62 A Theorem Prover for First-Order Logic
% 0.43/0.62 (ePrincess v.1.0)
% 0.43/0.62
% 0.43/0.62 (c) Philipp Rümmer, 2009-2015
% 0.43/0.62 (c) Peter Backeman, 2014-2015
% 0.43/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.43/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.43/0.62 Bug reports to peter@backeman.se
% 0.43/0.62
% 0.43/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.43/0.62
% 0.43/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/0.97 Prover 0: Preprocessing ...
% 2.03/1.14 Prover 0: Warning: ignoring some quantifiers
% 2.11/1.17 Prover 0: Constructing countermodel ...
% 2.98/1.45 Prover 0: gave up
% 2.98/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.08/1.48 Prover 1: Preprocessing ...
% 3.37/1.57 Prover 1: Constructing countermodel ...
% 3.50/1.62 Prover 1: gave up
% 3.50/1.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.50/1.64 Prover 2: Preprocessing ...
% 4.28/1.76 Prover 2: Warning: ignoring some quantifiers
% 4.28/1.76 Prover 2: Constructing countermodel ...
% 6.66/2.31 Prover 2: proved (692ms)
% 6.66/2.31
% 6.66/2.31 No countermodel exists, formula is valid
% 6.66/2.31 % SZS status Theorem for theBenchmark
% 6.66/2.31
% 6.66/2.31 Generating proof ... Warning: ignoring some quantifiers
% 79.85/53.47 found it (size 615)
% 79.85/53.47
% 79.85/53.47 % SZS output start Proof for theBenchmark
% 79.85/53.47 Assumed formulas after preprocessing and simplification:
% 79.85/53.47 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & line_connecting(v1, v0) = v5 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v5) = 0 & apart_point_and_line(v2, v3) = v4 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8)
% 80.10/53.53 | 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 yields:
% 80.10/53.53 | (1) ~ (all_0_1_1 = 0) & line_connecting(all_0_4_4, all_0_5_5) = all_0_0_0 & line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1 & distinct_points(all_0_4_4, all_0_3_3) = 0 & distinct_points(all_0_5_5, all_0_3_3) = 0 & distinct_points(all_0_5_5, all_0_4_4) = 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
% 80.10/53.54 |
% 80.10/53.54 | Applying alpha-rule on (1) yields:
% 80.10/53.54 | (2) ! [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)))
% 80.10/53.54 | (3) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 80.10/53.54 | (4) ! [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))
% 80.10/53.55 | (5) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 80.10/53.55 | (6) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 80.10/53.55 | (7) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 80.10/53.55 | (8) ! [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)))
% 80.10/53.55 | (9) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 80.10/53.55 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 80.10/53.55 | (11) ! [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)))
% 80.10/53.55 | (12) ! [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))
% 80.10/53.55 | (13) ! [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))
% 80.10/53.55 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 80.10/53.55 | (15) ! [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)))
% 80.10/53.55 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 80.10/53.55 | (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)
% 80.10/53.55 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 80.10/53.55 | (19) distinct_points(all_0_5_5, all_0_4_4) = 0
% 80.10/53.55 | (20) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 80.10/53.55 | (21) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 80.10/53.55 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 80.10/53.55 | (23) ! [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)))
% 80.10/53.55 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 80.10/53.55 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 80.10/53.55 | (26) apart_point_and_line(all_0_3_3, all_0_0_0) = 0
% 80.10/53.55 | (27) ! [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)))
% 80.10/53.55 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 80.10/53.55 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 80.10/53.55 | (30) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 80.10/53.55 | (31) line_connecting(all_0_4_4, all_0_5_5) = all_0_0_0
% 80.10/53.55 | (32) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 80.10/53.55 | (33) ~ (all_0_1_1 = 0)
% 80.10/53.55 | (34) ! [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)
% 80.10/53.55 | (35) ! [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)))
% 80.10/53.56 | (36) distinct_points(all_0_5_5, all_0_3_3) = 0
% 80.10/53.56 | (37) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 80.10/53.56 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 80.10/53.56 | (39) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 80.10/53.56 | (40) distinct_points(all_0_4_4, all_0_3_3) = 0
% 80.10/53.56 | (41) ! [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)))
% 80.10/53.56 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 80.10/53.56 | (43) ! [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)))
% 80.10/53.56 | (44) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 80.10/53.56 | (45) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 80.10/53.56 | (46) ! [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)))
% 80.10/53.56 | (47) ! [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))
% 80.10/53.56 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 80.10/53.56 | (49) ! [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)
% 80.10/53.56 | (50) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 80.10/53.56 | (51) apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1
% 80.10/53.56 | (52) ! [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)))
% 80.10/53.56 | (53) ! [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))
% 80.10/53.56 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 80.10/53.56 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 80.10/53.56 | (56) ! [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)
% 80.10/53.56 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 80.10/53.56 |
% 80.10/53.56 | Instantiating formula (11) with all_0_0_0, all_0_5_5, all_0_4_4 and discharging atoms line_connecting(all_0_4_4, all_0_5_5) = all_0_0_0, yields:
% 80.10/53.56 | (58) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.10/53.56 |
% 80.10/53.56 | Instantiating formula (41) with all_0_0_0, all_0_5_5, all_0_4_4 and discharging atoms line_connecting(all_0_4_4, all_0_5_5) = all_0_0_0, yields:
% 80.10/53.56 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.10/53.56 |
% 80.10/53.56 | Instantiating formula (11) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 80.10/53.56 | (60) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (41) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 80.10/53.57 | (61) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (34) with all_0_1_1, all_0_2_2, all_0_0_0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = 0, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 80.10/53.57 | (62) all_0_1_1 = 0 | distinct_lines(all_0_0_0, all_0_2_2) = 0
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (43) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.10/53.57 | (63) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (5) with all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.10/53.57 | (64) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(all_0_3_3, v0) = v1)
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (44) with all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.10/53.57 | (65) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (43) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.10/53.57 | (66) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (5) with all_0_3_3, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.10/53.57 | (67) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(all_0_3_3, v0) = v1)
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (44) with all_0_3_3, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.10/53.57 | (68) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (5) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.10/53.57 | (69) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 80.10/53.57 |
% 80.10/53.57 | Instantiating formula (44) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.10/53.57 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 80.10/53.57 |
% 80.10/53.57 | Instantiating (70) with all_20_0_24, all_20_1_25 yields:
% 80.10/53.57 | (71) ~ (all_20_0_24 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25 & apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 80.10/53.57 |
% 80.10/53.57 | Applying alpha-rule on (71) yields:
% 80.10/53.57 | (72) ~ (all_20_0_24 = 0)
% 80.10/53.57 | (73) line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25
% 80.10/53.57 | (74) apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 80.10/53.57 |
% 80.41/53.57 | Instantiating (68) with all_22_0_26, all_22_1_27 yields:
% 80.41/53.57 | (75) ~ (all_22_0_26 = 0) & line_connecting(all_0_5_5, all_0_3_3) = all_22_1_27 & apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26
% 80.41/53.57 |
% 80.41/53.57 | Applying alpha-rule on (75) yields:
% 80.41/53.57 | (76) ~ (all_22_0_26 = 0)
% 80.41/53.57 | (77) line_connecting(all_0_5_5, all_0_3_3) = all_22_1_27
% 80.41/53.57 | (78) apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26
% 80.41/53.57 |
% 80.41/53.57 | Instantiating (65) with all_24_0_28, all_24_1_29 yields:
% 80.41/53.57 | (79) ~ (all_24_0_28 = 0) & line_connecting(all_0_4_4, all_0_3_3) = all_24_1_29 & apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28
% 80.41/53.57 |
% 80.41/53.57 | Applying alpha-rule on (79) yields:
% 80.41/53.57 | (80) ~ (all_24_0_28 = 0)
% 80.41/53.57 | (81) line_connecting(all_0_4_4, all_0_3_3) = all_24_1_29
% 80.41/53.57 | (82) apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28
% 80.41/53.57 |
% 80.41/53.57 | Instantiating (67) with all_26_0_30, all_26_1_31 yields:
% 80.41/53.57 | (83) ~ (all_26_0_30 = 0) & line_connecting(all_0_5_5, all_0_3_3) = all_26_1_31 & apart_point_and_line(all_0_3_3, all_26_1_31) = all_26_0_30
% 80.41/53.57 |
% 80.41/53.57 | Applying alpha-rule on (83) yields:
% 80.41/53.57 | (84) ~ (all_26_0_30 = 0)
% 80.41/53.57 | (85) line_connecting(all_0_5_5, all_0_3_3) = all_26_1_31
% 80.41/53.57 | (86) apart_point_and_line(all_0_3_3, all_26_1_31) = all_26_0_30
% 80.41/53.57 |
% 80.41/53.57 | Instantiating (69) with all_28_0_32, all_28_1_33 yields:
% 80.41/53.57 | (87) ~ (all_28_0_32 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_28_1_33 & apart_point_and_line(all_0_4_4, all_28_1_33) = all_28_0_32
% 80.41/53.57 |
% 80.41/53.57 | Applying alpha-rule on (87) yields:
% 80.41/53.57 | (88) ~ (all_28_0_32 = 0)
% 80.41/53.57 | (89) line_connecting(all_0_5_5, all_0_4_4) = all_28_1_33
% 80.41/53.57 | (90) apart_point_and_line(all_0_4_4, all_28_1_33) = all_28_0_32
% 80.41/53.57 |
% 80.41/53.57 | Instantiating (64) with all_30_0_34, all_30_1_35 yields:
% 80.41/53.57 | (91) ~ (all_30_0_34 = 0) & line_connecting(all_0_4_4, all_0_3_3) = all_30_1_35 & apart_point_and_line(all_0_3_3, all_30_1_35) = all_30_0_34
% 80.41/53.57 |
% 80.41/53.57 | Applying alpha-rule on (91) yields:
% 80.41/53.57 | (92) ~ (all_30_0_34 = 0)
% 80.41/53.57 | (93) line_connecting(all_0_4_4, all_0_3_3) = all_30_1_35
% 80.41/53.57 | (94) apart_point_and_line(all_0_3_3, all_30_1_35) = all_30_0_34
% 80.41/53.57 |
% 80.41/53.57 | Instantiating (61) with all_32_0_36 yields:
% 80.41/53.57 | (95) ( ~ (all_32_0_36 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36) | ( ~ (all_32_0_36 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36)
% 80.41/53.57 |
% 80.41/53.57 | Instantiating (59) with all_33_0_37 yields:
% 80.41/53.57 | (96) ( ~ (all_33_0_37 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = all_33_0_37) | ( ~ (all_33_0_37 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_33_0_37)
% 80.41/53.57 |
% 80.41/53.57 | Instantiating (58) with all_34_0_38 yields:
% 80.41/53.57 | (97) ( ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_5_5, all_0_0_0) = all_34_0_38) | ( ~ (all_34_0_38 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_34_0_38)
% 80.41/53.57 |
% 80.41/53.57 | Instantiating (60) with all_35_0_39 yields:
% 80.41/53.57 | (98) ( ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39) | ( ~ (all_35_0_39 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39)
% 80.41/53.58 |
% 80.41/53.58 +-Applying beta-rule and splitting (95), into two cases.
% 80.41/53.58 |-Branch one:
% 80.41/53.58 | (99) ~ (all_32_0_36 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36
% 80.41/53.58 |
% 80.41/53.58 | Applying alpha-rule on (99) yields:
% 80.41/53.58 | (100) ~ (all_32_0_36 = 0)
% 80.41/53.58 | (101) apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36
% 80.41/53.58 |
% 80.41/53.58 +-Applying beta-rule and splitting (66), into two cases.
% 80.41/53.58 |-Branch one:
% 80.41/53.58 | (102) all_0_1_1 = 0
% 80.41/53.58 |
% 80.41/53.58 | Equations (102) can reduce 33 to:
% 80.41/53.58 | (103) $false
% 80.41/53.58 |
% 80.41/53.58 |-The branch is then unsatisfiable
% 80.41/53.58 |-Branch two:
% 80.41/53.58 | (33) ~ (all_0_1_1 = 0)
% 80.41/53.58 | (105) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 80.41/53.58 |
% 80.41/53.58 +-Applying beta-rule and splitting (63), into two cases.
% 80.41/53.58 |-Branch one:
% 80.41/53.58 | (102) all_0_1_1 = 0
% 80.41/53.58 |
% 80.41/53.58 | Equations (102) can reduce 33 to:
% 80.41/53.58 | (103) $false
% 80.41/53.58 |
% 80.41/53.58 |-The branch is then unsatisfiable
% 80.41/53.58 |-Branch two:
% 80.41/53.58 | (33) ~ (all_0_1_1 = 0)
% 80.41/53.58 | (109) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 80.41/53.58 |
% 80.41/53.58 +-Applying beta-rule and splitting (62), into two cases.
% 80.41/53.58 |-Branch one:
% 80.41/53.58 | (110) distinct_lines(all_0_0_0, all_0_2_2) = 0
% 80.41/53.58 |
% 80.41/53.58 +-Applying beta-rule and splitting (98), into two cases.
% 80.41/53.58 |-Branch one:
% 80.41/53.58 | (111) ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39
% 80.41/53.58 |
% 80.41/53.58 | Applying alpha-rule on (111) yields:
% 80.41/53.58 | (112) ~ (all_35_0_39 = 0)
% 80.41/53.58 | (113) apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (22) with all_0_4_4, all_0_3_3, all_24_1_29, all_30_1_35 and discharging atoms line_connecting(all_0_4_4, all_0_3_3) = all_30_1_35, line_connecting(all_0_4_4, all_0_3_3) = all_24_1_29, yields:
% 80.41/53.58 | (114) all_30_1_35 = all_24_1_29
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (22) with all_0_5_5, all_0_3_3, all_22_1_27, all_26_1_31 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_26_1_31, line_connecting(all_0_5_5, all_0_3_3) = all_22_1_27, yields:
% 80.41/53.58 | (115) all_26_1_31 = all_22_1_27
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (22) with all_0_5_5, all_0_4_4, all_28_1_33, all_0_2_2 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_28_1_33, line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 80.41/53.58 | (116) all_28_1_33 = all_0_2_2
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (22) with all_0_5_5, all_0_4_4, all_20_1_25, all_28_1_33 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_28_1_33, line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25, yields:
% 80.41/53.58 | (117) all_28_1_33 = all_20_1_25
% 80.41/53.58 |
% 80.41/53.58 | Combining equations (116,117) yields a new equation:
% 80.41/53.58 | (118) all_20_1_25 = all_0_2_2
% 80.41/53.58 |
% 80.41/53.58 | Combining equations (118,117) yields a new equation:
% 80.41/53.58 | (116) all_28_1_33 = all_0_2_2
% 80.41/53.58 |
% 80.41/53.58 | From (114) and (94) follows:
% 80.41/53.58 | (120) apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34
% 80.41/53.58 |
% 80.41/53.58 | From (115) and (86) follows:
% 80.41/53.58 | (121) apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30
% 80.41/53.58 |
% 80.41/53.58 | From (116) and (90) follows:
% 80.41/53.58 | (122) apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32
% 80.41/53.58 |
% 80.41/53.58 | From (118) and (74) follows:
% 80.41/53.58 | (123) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (42) with all_0_4_4, all_0_2_2, all_28_0_32, all_35_0_39 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.58 | (124) all_35_0_39 = all_28_0_32
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (42) with all_0_5_5, all_0_2_2, all_20_0_24, all_32_0_36 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.58 | (125) all_32_0_36 = all_20_0_24
% 80.41/53.58 |
% 80.41/53.58 | Equations (124) can reduce 112 to:
% 80.41/53.58 | (88) ~ (all_28_0_32 = 0)
% 80.41/53.58 |
% 80.41/53.58 | Equations (125) can reduce 100 to:
% 80.41/53.58 | (72) ~ (all_20_0_24 = 0)
% 80.41/53.58 |
% 80.41/53.58 | From (124) and (113) follows:
% 80.41/53.58 | (122) apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32
% 80.41/53.58 |
% 80.41/53.58 | From (125) and (101) follows:
% 80.41/53.58 | (123) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (43) with all_30_0_34, all_0_1_1, all_24_1_29, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.58 | (130) all_30_0_34 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (43) with all_0_1_1, all_30_0_34, all_0_2_2, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.58 | (131) all_30_0_34 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0))
% 80.41/53.58 |
% 80.41/53.58 | Instantiating formula (43) with all_30_0_34, all_0_1_1, all_24_1_29, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.41/53.59 | (132) all_30_0_34 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (52) with all_0_1_1, all_30_0_34, all_0_2_2, all_24_1_29, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 80.41/53.59 | (133) all_30_0_34 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_30_0_34, all_30_0_34, all_24_1_29, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.59 | (134) all_30_0_34 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_30_0_34, all_30_0_34, all_24_1_29, all_24_1_29, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.41/53.59 | (135) all_30_0_34 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (52) with all_30_0_34, all_30_0_34, all_24_1_29, all_24_1_29, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, yields:
% 80.41/53.59 | (136) all_30_0_34 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_26_0_30, all_0_1_1, all_22_1_27, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.59 | (137) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_0_1_1, all_26_0_30, all_0_2_2, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.59 | (138) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_26_0_30, all_0_1_1, all_22_1_27, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.41/53.59 | (139) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_0_1_1, all_26_0_30, all_0_2_2, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.41/53.59 | (140) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (52) with all_26_0_30, all_0_1_1, all_22_1_27, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 80.41/53.59 | (141) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (52) with all_0_1_1, all_26_0_30, all_0_2_2, all_22_1_27, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 80.41/53.59 | (142) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_26_0_30, all_30_0_34, all_22_1_27, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.59 | (143) all_30_0_34 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_30_0_34, all_26_0_30, all_24_1_29, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.59 | (144) all_30_0_34 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0))
% 80.41/53.59 |
% 80.41/53.59 | Instantiating formula (43) with all_26_0_30, all_30_0_34, all_22_1_27, all_24_1_29, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.41/53.59 | (145) all_30_0_34 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_26_0_30, all_30_0_34, all_22_1_27, all_24_1_29, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, yields:
% 80.41/53.60 | (146) all_30_0_34 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_30_0_34, all_26_0_30, all_24_1_29, all_22_1_27, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, yields:
% 80.41/53.60 | (147) all_30_0_34 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (43) with all_26_0_30, all_26_0_30, all_22_1_27, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.60 | (148) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (43) with all_26_0_30, all_26_0_30, all_22_1_27, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.41/53.60 | (149) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_26_0_30, all_26_0_30, all_22_1_27, all_22_1_27, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, yields:
% 80.41/53.60 | (150) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_24_0_28, all_0_1_1, all_24_1_29, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.60 | (151) all_24_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_0_1_1, all_24_0_28, all_0_2_2, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.60 | (152) all_24_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (27) with all_24_0_28, all_0_1_1, all_0_2_2, all_24_1_29, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.60 | (153) all_24_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (27) with all_0_1_1, all_24_0_28, all_24_1_29, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.60 | (154) all_24_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_24_0_28, all_30_0_34, all_24_1_29, all_24_1_29, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.60 | (155) all_30_0_34 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_30_0_34, all_24_0_28, all_24_1_29, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.60 | (156) all_30_0_34 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_24_0_28, all_26_0_30, all_24_1_29, all_22_1_27, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.60 | (157) all_26_0_30 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.60 |
% 80.41/53.60 | Instantiating formula (52) with all_26_0_30, all_24_0_28, all_22_1_27, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.60 | (158) all_26_0_30 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.60 |
% 80.41/53.61 | Instantiating formula (27) with all_24_0_28, all_26_0_30, all_22_1_27, all_24_1_29, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.61 | (159) all_26_0_30 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (27) with all_26_0_30, all_24_0_28, all_24_1_29, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.61 | (160) all_26_0_30 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (35) with all_24_0_28, all_24_0_28, all_24_1_29, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.61 | (161) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (43) with all_24_0_28, all_24_0_28, all_24_1_29, all_24_1_29, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.41/53.61 | (162) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (52) with all_24_0_28, all_24_0_28, all_24_1_29, all_24_1_29, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, yields:
% 80.41/53.61 | (163) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (52) with all_28_0_32, all_0_1_1, all_0_2_2, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (164) all_28_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (52) with all_28_0_32, all_30_0_34, all_0_2_2, all_24_1_29, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (165) all_30_0_34 = 0 | all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (52) with all_30_0_34, all_28_0_32, all_24_1_29, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (166) all_30_0_34 = 0 | all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (27) with all_28_0_32, all_30_0_34, all_24_1_29, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (167) all_30_0_34 = 0 | all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (27) with all_30_0_34, all_28_0_32, all_0_2_2, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (168) all_30_0_34 = 0 | all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (52) with all_28_0_32, all_26_0_30, all_0_2_2, all_22_1_27, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (169) all_28_0_32 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (52) with all_26_0_30, all_28_0_32, all_22_1_27, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (170) all_28_0_32 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (27) with all_28_0_32, all_26_0_30, all_22_1_27, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (171) all_28_0_32 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.61 |
% 80.41/53.61 | Instantiating formula (27) with all_26_0_30, all_28_0_32, all_0_2_2, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.61 | (172) all_28_0_32 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (35) with all_28_0_32, all_24_0_28, all_0_2_2, all_24_1_29, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.62 | (173) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (35) with all_24_0_28, all_28_0_32, all_24_1_29, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 80.41/53.62 | (174) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (43) with all_28_0_32, all_24_0_28, all_0_2_2, all_24_1_29, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.41/53.62 | (175) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (43) with all_24_0_28, all_28_0_32, all_24_1_29, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.41/53.62 | (176) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (52) with all_28_0_32, all_24_0_28, all_0_2_2, all_24_1_29, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.62 | (177) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (52) with all_24_0_28, all_28_0_32, all_24_1_29, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.62 | (178) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (52) with all_28_0_32, all_28_0_32, all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, yields:
% 80.41/53.62 | (179) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (52) with all_22_0_26, all_0_1_1, all_22_1_27, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.62 | (180) all_22_0_26 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (52) with all_0_1_1, all_22_0_26, all_0_2_2, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.62 | (181) all_22_0_26 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (27) with all_22_0_26, all_0_1_1, all_0_2_2, all_22_1_27, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.62 | (182) all_22_0_26 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (27) with all_0_1_1, all_22_0_26, all_22_1_27, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.62 | (183) all_22_0_26 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (52) with all_22_0_26, all_30_0_34, all_22_1_27, all_24_1_29, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.62 | (184) all_30_0_34 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.62 |
% 80.41/53.62 | Instantiating formula (52) with all_30_0_34, all_22_0_26, all_24_1_29, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.62 | (185) all_30_0_34 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (27) with all_22_0_26, all_30_0_34, all_24_1_29, all_22_1_27, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (186) all_30_0_34 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (27) with all_30_0_34, all_22_0_26, all_22_1_27, all_24_1_29, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (187) all_30_0_34 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (52) with all_22_0_26, all_26_0_30, all_22_1_27, all_22_1_27, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (188) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (52) with all_22_0_26, all_24_0_28, all_22_1_27, all_24_1_29, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (189) all_24_0_28 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (52) with all_24_0_28, all_22_0_26, all_24_1_29, all_22_1_27, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (190) all_24_0_28 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (27) with all_22_0_26, all_24_0_28, all_24_1_29, all_22_1_27, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (191) all_24_0_28 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (27) with all_24_0_28, all_22_0_26, all_22_1_27, all_24_1_29, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (192) all_24_0_28 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (52) with all_22_0_26, all_28_0_32, all_22_1_27, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (193) all_28_0_32 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (52) with all_28_0_32, all_22_0_26, all_0_2_2, all_22_1_27, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (194) all_28_0_32 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (27) with all_22_0_26, all_28_0_32, all_0_2_2, all_22_1_27, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (195) all_28_0_32 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (27) with all_28_0_32, all_22_0_26, all_22_1_27, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (196) all_28_0_32 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (35) with all_22_0_26, all_22_0_26, all_22_1_27, all_22_1_27, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.41/53.63 | (197) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (52) with all_22_0_26, all_22_0_26, all_22_1_27, all_22_1_27, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, yields:
% 80.41/53.63 | (198) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.41/53.63 |
% 80.41/53.63 | Instantiating formula (52) with all_20_0_24, all_0_1_1, all_0_2_2, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.63 | (199) all_20_0_24 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_20_0_24, all_30_0_34, all_0_2_2, all_24_1_29, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (200) all_30_0_34 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_30_0_34, all_20_0_24, all_24_1_29, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (201) all_30_0_34 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (27) with all_20_0_24, all_30_0_34, all_24_1_29, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (202) all_30_0_34 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (27) with all_30_0_34, all_20_0_24, all_0_2_2, all_24_1_29, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_24_1_29) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (203) all_30_0_34 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_20_0_24, all_26_0_30, all_0_2_2, all_22_1_27, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (204) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (27) with all_20_0_24, all_26_0_30, all_22_1_27, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (205) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (27) with all_26_0_30, all_20_0_24, all_0_2_2, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (206) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_20_0_24, all_24_0_28, all_0_2_2, all_24_1_29, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (207) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_24_0_28, all_20_0_24, all_24_1_29, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (208) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (27) with all_20_0_24, all_24_0_28, all_24_1_29, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (209) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (27) with all_24_0_28, all_20_0_24, all_0_2_2, all_24_1_29, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_24_1_29) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (210) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_20_0_24, all_28_0_32, all_0_2_2, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (211) all_28_0_32 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (35) with all_20_0_24, all_22_0_26, all_0_2_2, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 80.41/53.64 | (212) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (35) with all_20_0_24, all_22_0_26, all_0_2_2, all_22_1_27, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.41/53.64 | (213) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (35) with all_22_0_26, all_20_0_24, all_22_1_27, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.41/53.64 | (214) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_20_0_24, all_22_0_26, all_0_2_2, all_22_1_27, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (215) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_22_0_26, all_20_0_24, all_22_1_27, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.64 | (216) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.41/53.64 |
% 80.41/53.64 | Instantiating formula (52) with all_20_0_24, all_20_0_24, all_0_2_2, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 80.41/53.65 | (217) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.41/53.65 |
% 80.41/53.65 | Instantiating formula (46) with all_28_0_32, all_0_1_1, all_0_2_2, all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 80.41/53.65 | (218) all_28_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.65 |
% 80.41/53.65 | Instantiating formula (46) with all_28_0_32, all_28_0_32, all_0_2_2, all_0_0_0, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 80.41/53.65 | (219) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.41/53.65 |
% 80.41/53.65 | Instantiating formula (46) with all_28_0_32, all_20_0_24, all_0_2_2, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 80.41/53.65 | (220) all_28_0_32 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.41/53.65 |
% 80.41/53.65 | Instantiating formula (46) with all_20_0_24, all_0_1_1, all_0_2_2, all_0_0_0, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 80.41/53.65 | (221) all_20_0_24 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.65 |
% 80.41/53.65 | Instantiating formula (46) with all_20_0_24, all_28_0_32, all_0_2_2, all_0_0_0, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 80.41/53.65 | (222) all_28_0_32 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.41/53.65 |
% 80.41/53.65 | Instantiating formula (46) with all_20_0_24, all_20_0_24, all_0_2_2, all_0_0_0, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 80.41/53.65 | (223) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.41/53.65 |
% 80.41/53.65 | Instantiating formula (8) with all_0_2_2, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms distinct_lines(all_0_0_0, all_0_2_2) = 0, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.41/53.65 | (224) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0))
% 80.41/53.65 |
% 80.41/53.65 | Instantiating (224) with all_81_0_44 yields:
% 80.41/53.65 | (225) (all_81_0_44 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (all_81_0_44 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_81_0_44 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | (all_81_0_44 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (96), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (226) ~ (all_33_0_37 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = all_33_0_37
% 80.41/53.65 |
% 80.41/53.65 | Applying alpha-rule on (226) yields:
% 80.41/53.65 | (227) ~ (all_33_0_37 = 0)
% 80.41/53.65 | (228) apart_point_and_line(all_0_4_4, all_0_0_0) = all_33_0_37
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (220), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (229) all_28_0_32 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (229) can reduce 88 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (88) ~ (all_28_0_32 = 0)
% 80.41/53.65 | (232) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (223), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (233) all_20_0_24 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (233) can reduce 72 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (72) ~ (all_20_0_24 = 0)
% 80.41/53.65 | (236) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (150), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (237) all_26_0_30 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (237) can reduce 84 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (84) ~ (all_26_0_30 = 0)
% 80.41/53.65 | (240) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (161), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (241) all_24_0_28 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (241) can reduce 80 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (80) ~ (all_24_0_28 = 0)
% 80.41/53.65 | (244) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (162), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (241) all_24_0_28 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (241) can reduce 80 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (80) ~ (all_24_0_28 = 0)
% 80.41/53.65 | (248) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (163), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (241) all_24_0_28 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (241) can reduce 80 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (80) ~ (all_24_0_28 = 0)
% 80.41/53.65 | (252) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (179), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (229) all_28_0_32 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (229) can reduce 88 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (88) ~ (all_28_0_32 = 0)
% 80.41/53.65 | (256) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (217), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (233) all_20_0_24 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (233) can reduce 72 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (72) ~ (all_20_0_24 = 0)
% 80.41/53.65 | (260) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (219), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (229) all_28_0_32 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (229) can reduce 88 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (88) ~ (all_28_0_32 = 0)
% 80.41/53.65 | (264) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.41/53.65 |
% 80.41/53.65 +-Applying beta-rule and splitting (164), into two cases.
% 80.41/53.65 |-Branch one:
% 80.41/53.65 | (229) all_28_0_32 = 0
% 80.41/53.65 |
% 80.41/53.65 | Equations (229) can reduce 88 to:
% 80.41/53.65 | (103) $false
% 80.41/53.65 |
% 80.41/53.65 |-The branch is then unsatisfiable
% 80.41/53.65 |-Branch two:
% 80.41/53.65 | (88) ~ (all_28_0_32 = 0)
% 80.41/53.65 | (268) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (167), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (269) all_30_0_34 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (269) can reduce 92 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (92) ~ (all_30_0_34 = 0)
% 80.41/53.66 | (272) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (165), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (269) all_30_0_34 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (269) can reduce 92 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (92) ~ (all_30_0_34 = 0)
% 80.41/53.66 | (276) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (166), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (269) all_30_0_34 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (269) can reduce 92 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (92) ~ (all_30_0_34 = 0)
% 80.41/53.66 | (280) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (158), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (237) all_26_0_30 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (237) can reduce 84 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (84) ~ (all_26_0_30 = 0)
% 80.41/53.66 | (284) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (221), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (233) all_20_0_24 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (233) can reduce 72 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (72) ~ (all_20_0_24 = 0)
% 80.41/53.66 | (288) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (168), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (269) all_30_0_34 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (269) can reduce 92 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (92) ~ (all_30_0_34 = 0)
% 80.41/53.66 | (292) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (181), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (293) all_22_0_26 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (293) can reduce 76 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (76) ~ (all_22_0_26 = 0)
% 80.41/53.66 | (296) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (152), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (241) all_24_0_28 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (241) can reduce 80 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (80) ~ (all_24_0_28 = 0)
% 80.41/53.66 | (300) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (216), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (293) all_22_0_26 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (293) can reduce 76 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (76) ~ (all_22_0_26 = 0)
% 80.41/53.66 | (304) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (151), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (241) all_24_0_28 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (241) can reduce 80 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (80) ~ (all_24_0_28 = 0)
% 80.41/53.66 | (308) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (213), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (293) all_22_0_26 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (293) can reduce 76 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (76) ~ (all_22_0_26 = 0)
% 80.41/53.66 | (312) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (214), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (293) all_22_0_26 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (293) can reduce 76 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (76) ~ (all_22_0_26 = 0)
% 80.41/53.66 | (316) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 80.41/53.66 |
% 80.41/53.66 +-Applying beta-rule and splitting (215), into two cases.
% 80.41/53.66 |-Branch one:
% 80.41/53.66 | (293) all_22_0_26 = 0
% 80.41/53.66 |
% 80.41/53.66 | Equations (293) can reduce 76 to:
% 80.41/53.66 | (103) $false
% 80.41/53.66 |
% 80.41/53.66 |-The branch is then unsatisfiable
% 80.41/53.66 |-Branch two:
% 80.41/53.66 | (76) ~ (all_22_0_26 = 0)
% 80.86/53.66 | (320) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.86/53.66 |
% 80.86/53.66 +-Applying beta-rule and splitting (218), into two cases.
% 80.86/53.66 |-Branch one:
% 80.86/53.66 | (229) all_28_0_32 = 0
% 80.86/53.66 |
% 80.86/53.66 | Equations (229) can reduce 88 to:
% 80.86/53.66 | (103) $false
% 80.86/53.66 |
% 80.86/53.66 |-The branch is then unsatisfiable
% 80.86/53.66 |-Branch two:
% 80.86/53.66 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.66 | (324) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.66 |
% 80.86/53.66 +-Applying beta-rule and splitting (169), into two cases.
% 80.86/53.66 |-Branch one:
% 80.86/53.66 | (229) all_28_0_32 = 0
% 80.86/53.66 |
% 80.86/53.66 | Equations (229) can reduce 88 to:
% 80.86/53.66 | (103) $false
% 80.86/53.66 |
% 80.86/53.66 |-The branch is then unsatisfiable
% 80.86/53.66 |-Branch two:
% 80.86/53.66 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.66 | (328) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.66 |
% 80.86/53.66 +-Applying beta-rule and splitting (170), into two cases.
% 80.86/53.66 |-Branch one:
% 80.86/53.66 | (229) all_28_0_32 = 0
% 80.86/53.66 |
% 80.86/53.66 | Equations (229) can reduce 88 to:
% 80.86/53.66 | (103) $false
% 80.86/53.66 |
% 80.86/53.66 |-The branch is then unsatisfiable
% 80.86/53.66 |-Branch two:
% 80.86/53.66 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.66 | (332) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.86/53.66 |
% 80.86/53.66 +-Applying beta-rule and splitting (171), into two cases.
% 80.86/53.66 |-Branch one:
% 80.86/53.66 | (229) all_28_0_32 = 0
% 80.86/53.66 |
% 80.86/53.66 | Equations (229) can reduce 88 to:
% 80.86/53.66 | (103) $false
% 80.86/53.66 |
% 80.86/53.66 |-The branch is then unsatisfiable
% 80.86/53.66 |-Branch two:
% 80.86/53.66 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.66 | (336) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.66 |
% 80.86/53.66 +-Applying beta-rule and splitting (172), into two cases.
% 80.86/53.66 |-Branch one:
% 80.86/53.66 | (229) all_28_0_32 = 0
% 80.86/53.66 |
% 80.86/53.66 | Equations (229) can reduce 88 to:
% 80.86/53.66 | (103) $false
% 80.86/53.66 |
% 80.86/53.66 |-The branch is then unsatisfiable
% 80.86/53.66 |-Branch two:
% 80.86/53.66 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.66 | (340) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.86/53.66 |
% 80.86/53.66 +-Applying beta-rule and splitting (182), into two cases.
% 80.86/53.66 |-Branch one:
% 80.86/53.66 | (293) all_22_0_26 = 0
% 80.86/53.66 |
% 80.86/53.66 | Equations (293) can reduce 76 to:
% 80.86/53.66 | (103) $false
% 80.86/53.66 |
% 80.86/53.66 |-The branch is then unsatisfiable
% 80.86/53.66 |-Branch two:
% 80.86/53.66 | (76) ~ (all_22_0_26 = 0)
% 80.86/53.66 | (344) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.86/53.66 |
% 80.86/53.66 +-Applying beta-rule and splitting (180), into two cases.
% 80.86/53.66 |-Branch one:
% 80.86/53.66 | (293) all_22_0_26 = 0
% 80.86/53.66 |
% 80.86/53.66 | Equations (293) can reduce 76 to:
% 80.86/53.66 | (103) $false
% 80.86/53.66 |
% 80.86/53.66 |-The branch is then unsatisfiable
% 80.86/53.66 |-Branch two:
% 80.86/53.66 | (76) ~ (all_22_0_26 = 0)
% 80.86/53.66 | (348) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (183), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (293) all_22_0_26 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (293) can reduce 76 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (76) ~ (all_22_0_26 = 0)
% 80.86/53.67 | (352) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (184), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (269) all_30_0_34 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (269) can reduce 92 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.67 | (356) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (175), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (229) all_28_0_32 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (229) can reduce 88 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.67 | (360) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (173), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (229) all_28_0_32 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (229) can reduce 88 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.67 | (364) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (174), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (229) all_28_0_32 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (229) can reduce 88 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.67 | (368) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (176), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (229) all_28_0_32 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (229) can reduce 88 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.67 | (372) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (177), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (229) all_28_0_32 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (229) can reduce 88 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.67 | (376) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (178), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (229) all_28_0_32 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (229) can reduce 88 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.67 | (380) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (153), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (241) all_24_0_28 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (241) can reduce 80 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (80) ~ (all_24_0_28 = 0)
% 80.86/53.67 | (384) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (154), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (241) all_24_0_28 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (241) can reduce 80 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (80) ~ (all_24_0_28 = 0)
% 80.86/53.67 | (388) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (155), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (269) all_30_0_34 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (269) can reduce 92 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.67 | (392) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (156), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (269) all_30_0_34 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (269) can reduce 92 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.67 | (396) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (159), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (237) all_26_0_30 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (237) can reduce 84 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.67 | (400) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (157), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (237) all_26_0_30 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (237) can reduce 84 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.67 | (404) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (160), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (237) all_26_0_30 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (237) can reduce 84 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.67 | (408) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (149), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (237) all_26_0_30 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (237) can reduce 84 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.67 | (412) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (396), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (241) all_24_0_28 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (241) can reduce 80 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (80) ~ (all_24_0_28 = 0)
% 80.86/53.67 | (416) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (400), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (241) all_24_0_28 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (241) can reduce 80 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (80) ~ (all_24_0_28 = 0)
% 80.86/53.67 | (420) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (404), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (241) all_24_0_28 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (241) can reduce 80 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (80) ~ (all_24_0_28 = 0)
% 80.86/53.67 | (424) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (232), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (233) all_20_0_24 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (233) can reduce 72 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (72) ~ (all_20_0_24 = 0)
% 80.86/53.67 | (428) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (148), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (237) all_26_0_30 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (237) can reduce 84 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.67 | (432) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 80.86/53.67 |
% 80.86/53.67 +-Applying beta-rule and splitting (146), into two cases.
% 80.86/53.67 |-Branch one:
% 80.86/53.67 | (269) all_30_0_34 = 0
% 80.86/53.67 |
% 80.86/53.67 | Equations (269) can reduce 92 to:
% 80.86/53.67 | (103) $false
% 80.86/53.67 |
% 80.86/53.67 |-The branch is then unsatisfiable
% 80.86/53.67 |-Branch two:
% 80.86/53.67 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.67 | (436) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (142), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (440) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (130), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (444) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (143), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (448) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (144), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (452) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (138), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (456) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (139), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (460) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (140), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (464) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (141), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (468) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (145), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (472) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (368), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (241) all_24_0_28 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (241) can reduce 80 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (80) ~ (all_24_0_28 = 0)
% 80.86/53.68 | (476) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (372), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (241) all_24_0_28 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (241) can reduce 80 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (80) ~ (all_24_0_28 = 0)
% 80.86/53.68 | (480) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (135), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (248) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (136), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (488) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (147), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (492) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (134), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (496) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_24_1_29) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (137), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (500) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (131), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (504) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (132), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (269) all_30_0_34 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (269) can reduce 92 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (92) ~ (all_30_0_34 = 0)
% 80.86/53.68 | (508) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (436), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (448), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (516) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (452), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (237) all_26_0_30 = 0
% 80.86/53.68 |
% 80.86/53.68 | Equations (237) can reduce 84 to:
% 80.86/53.68 | (103) $false
% 80.86/53.68 |
% 80.86/53.68 |-The branch is then unsatisfiable
% 80.86/53.68 |-Branch two:
% 80.86/53.68 | (84) ~ (all_26_0_30 = 0)
% 80.86/53.68 | (520) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0))
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (225), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (521) (all_81_0_44 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (all_81_0_44 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_81_0_44 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0)
% 80.86/53.68 |
% 80.86/53.68 +-Applying beta-rule and splitting (521), into two cases.
% 80.86/53.68 |-Branch one:
% 80.86/53.68 | (522) (all_81_0_44 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (all_81_0_44 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 80.86/53.69 |
% 80.86/53.69 +-Applying beta-rule and splitting (522), into two cases.
% 80.86/53.69 |-Branch one:
% 80.86/53.69 | (523) all_81_0_44 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0
% 80.86/53.69 |
% 80.86/53.69 | Applying alpha-rule on (523) yields:
% 80.86/53.69 | (524) all_81_0_44 = 0
% 80.86/53.69 | (525) apart_point_and_line(all_0_4_4, all_0_0_0) = 0
% 80.86/53.69 |
% 80.86/53.69 | Instantiating formula (42) with all_0_4_4, all_0_0_0, 0, all_33_0_37 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_33_0_37, apart_point_and_line(all_0_4_4, all_0_0_0) = 0, yields:
% 80.86/53.69 | (526) all_33_0_37 = 0
% 80.86/53.69 |
% 80.86/53.69 | Equations (526) can reduce 227 to:
% 80.86/53.69 | (103) $false
% 80.86/53.69 |
% 80.86/53.69 |-The branch is then unsatisfiable
% 80.86/53.69 |-Branch two:
% 80.86/53.69 | (528) all_81_0_44 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 80.86/53.69 |
% 80.86/53.69 | Applying alpha-rule on (528) yields:
% 80.86/53.69 | (524) all_81_0_44 = 0
% 80.86/53.69 | (530) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 80.86/53.69 |
% 80.86/53.69 +-Applying beta-rule and splitting (193), into two cases.
% 80.86/53.69 |-Branch one:
% 80.86/53.69 | (229) all_28_0_32 = 0
% 80.86/53.69 |
% 80.86/53.69 | Equations (229) can reduce 88 to:
% 80.86/53.69 | (103) $false
% 80.86/53.69 |
% 80.86/53.69 |-The branch is then unsatisfiable
% 80.86/53.69 |-Branch two:
% 80.86/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.69 | (534) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.86/53.69 |
% 80.86/53.69 +-Applying beta-rule and splitting (196), into two cases.
% 80.86/53.69 |-Branch one:
% 80.86/53.69 | (229) all_28_0_32 = 0
% 80.86/53.69 |
% 80.86/53.69 | Equations (229) can reduce 88 to:
% 80.86/53.69 | (103) $false
% 80.86/53.69 |
% 80.86/53.69 |-The branch is then unsatisfiable
% 80.86/53.69 |-Branch two:
% 80.86/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.86/53.69 | (538) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.86/53.69 |
% 80.86/53.69 +-Applying beta-rule and splitting (222), into two cases.
% 80.86/53.69 |-Branch one:
% 80.86/53.69 | (229) all_28_0_32 = 0
% 80.86/53.69 |
% 80.86/53.69 | Equations (229) can reduce 88 to:
% 80.86/53.69 | (103) $false
% 80.86/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.69 | (542) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.69 |
% 80.98/53.69 +-Applying beta-rule and splitting (194), into two cases.
% 80.98/53.69 |-Branch one:
% 80.98/53.69 | (229) all_28_0_32 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (229) can reduce 88 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.69 | (546) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.69 |
% 80.98/53.69 +-Applying beta-rule and splitting (195), into two cases.
% 80.98/53.69 |-Branch one:
% 80.98/53.69 | (229) all_28_0_32 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (229) can reduce 88 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.69 | (550) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.69 |
% 80.98/53.69 +-Applying beta-rule and splitting (276), into two cases.
% 80.98/53.69 |-Branch one:
% 80.98/53.69 | (229) all_28_0_32 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (229) can reduce 88 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.69 | (554) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.98/53.69 |
% 80.98/53.69 +-Applying beta-rule and splitting (211), into two cases.
% 80.98/53.69 |-Branch one:
% 80.98/53.69 | (229) all_28_0_32 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (229) can reduce 88 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.69 | (558) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.69 |
% 80.98/53.69 +-Applying beta-rule and splitting (272), into two cases.
% 80.98/53.69 |-Branch one:
% 80.98/53.69 | (229) all_28_0_32 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (229) can reduce 88 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.69 | (562) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.98/53.69 |
% 80.98/53.69 +-Applying beta-rule and splitting (292), into two cases.
% 80.98/53.69 |-Branch one:
% 80.98/53.69 | (229) all_28_0_32 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (229) can reduce 88 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.69 | (566) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.98/53.69 |
% 80.98/53.69 | Instantiating formula (42) with all_0_4_4, all_0_2_2, 0, all_28_0_32 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_28_0_32, apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields:
% 80.98/53.69 | (229) all_28_0_32 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (229) can reduce 88 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (569) all_81_0_44 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0
% 80.98/53.69 |
% 80.98/53.69 | Applying alpha-rule on (569) yields:
% 80.98/53.69 | (524) all_81_0_44 = 0
% 80.98/53.69 | (571) apart_point_and_line(all_0_5_5, all_0_0_0) = 0
% 80.98/53.69 |
% 80.98/53.69 +-Applying beta-rule and splitting (97), into two cases.
% 80.98/53.69 |-Branch one:
% 80.98/53.69 | (572) ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_5_5, all_0_0_0) = all_34_0_38
% 80.98/53.69 |
% 80.98/53.69 | Applying alpha-rule on (572) yields:
% 80.98/53.69 | (573) ~ (all_34_0_38 = 0)
% 80.98/53.69 | (574) apart_point_and_line(all_0_5_5, all_0_0_0) = all_34_0_38
% 80.98/53.69 |
% 80.98/53.69 | Instantiating formula (42) with all_0_5_5, all_0_0_0, 0, all_34_0_38 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_34_0_38, apart_point_and_line(all_0_5_5, all_0_0_0) = 0, yields:
% 80.98/53.69 | (575) all_34_0_38 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (575) can reduce 573 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (577) ~ (all_34_0_38 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_34_0_38
% 80.98/53.69 |
% 80.98/53.69 | Applying alpha-rule on (577) yields:
% 80.98/53.69 | (573) ~ (all_34_0_38 = 0)
% 80.98/53.69 | (579) distinct_points(all_0_4_4, all_0_5_5) = all_34_0_38
% 80.98/53.69 |
% 80.98/53.69 | Instantiating formula (38) with all_34_0_38, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_4_4, all_0_5_5) = all_34_0_38, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 80.98/53.69 | (580) all_34_0_38 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 80.98/53.69 |
% 80.98/53.69 +-Applying beta-rule and splitting (580), into two cases.
% 80.98/53.69 |-Branch one:
% 80.98/53.69 | (581) distinct_points(all_0_5_5, all_0_5_5) = 0
% 80.98/53.69 |
% 80.98/53.69 | Instantiating formula (3) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 80.98/53.69 | (582) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (583) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 80.98/53.69 | (575) all_34_0_38 = 0
% 80.98/53.69 |
% 80.98/53.69 | Equations (575) can reduce 573 to:
% 80.98/53.69 | (103) $false
% 80.98/53.69 |
% 80.98/53.69 |-The branch is then unsatisfiable
% 80.98/53.69 |-Branch two:
% 80.98/53.69 | (586) all_81_0_44 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 80.98/53.69 |
% 80.98/53.70 | Applying alpha-rule on (586) yields:
% 80.98/53.70 | (524) all_81_0_44 = 0
% 80.98/53.70 | (588) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (197), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (293) all_22_0_26 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (293) can reduce 76 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (76) ~ (all_22_0_26 = 0)
% 80.98/53.70 | (432) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (198), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (293) all_22_0_26 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (293) can reduce 76 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (76) ~ (all_22_0_26 = 0)
% 80.98/53.70 | (596) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (133), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (269) all_30_0_34 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (269) can reduce 92 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (92) ~ (all_30_0_34 = 0)
% 80.98/53.70 | (600) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (192), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (241) all_24_0_28 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (241) can reduce 80 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.70 | (604) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (193), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (229) all_28_0_32 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (229) can reduce 88 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.70 | (534) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (196), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (229) all_28_0_32 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (229) can reduce 88 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.70 | (538) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (222), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (229) all_28_0_32 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (229) can reduce 88 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.70 | (542) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (194), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (229) all_28_0_32 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (229) can reduce 88 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.70 | (546) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (195), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (229) all_28_0_32 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (229) can reduce 88 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.70 | (550) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (189), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (241) all_24_0_28 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (241) can reduce 80 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.70 | (628) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (185), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (269) all_30_0_34 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (269) can reduce 92 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (92) ~ (all_30_0_34 = 0)
% 80.98/53.70 | (632) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (186), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (269) all_30_0_34 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (269) can reduce 92 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (92) ~ (all_30_0_34 = 0)
% 80.98/53.70 | (636) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (187), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (269) all_30_0_34 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (269) can reduce 92 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (92) ~ (all_30_0_34 = 0)
% 80.98/53.70 | (640) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (188), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (237) all_26_0_30 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (237) can reduce 84 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.70 | (644) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (190), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (241) all_24_0_28 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (241) can reduce 80 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.70 | (648) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (191), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (241) all_24_0_28 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (241) can reduce 80 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.70 | (652) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (276), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (229) all_28_0_32 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (229) can reduce 88 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.70 | (554) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (304), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (233) all_20_0_24 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (233) can reduce 72 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.70 | (660) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.98/53.70 |
% 80.98/53.70 +-Applying beta-rule and splitting (312), into two cases.
% 80.98/53.70 |-Branch one:
% 80.98/53.70 | (233) all_20_0_24 = 0
% 80.98/53.70 |
% 80.98/53.70 | Equations (233) can reduce 72 to:
% 80.98/53.70 | (103) $false
% 80.98/53.70 |
% 80.98/53.70 |-The branch is then unsatisfiable
% 80.98/53.70 |-Branch two:
% 80.98/53.70 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.70 | (664) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (316), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (233) all_20_0_24 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (233) can reduce 72 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.71 | (668) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (320), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (233) all_20_0_24 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (233) can reduce 72 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.71 | (672) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (328), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (237) all_26_0_30 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (237) can reduce 84 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.71 | (676) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (332), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (237) all_26_0_30 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (237) can reduce 84 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.71 | (680) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (336), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (237) all_26_0_30 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (237) can reduce 84 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.71 | (684) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (340), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (237) all_26_0_30 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (237) can reduce 84 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.71 | (688) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (356), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (293) all_22_0_26 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (293) can reduce 76 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (76) ~ (all_22_0_26 = 0)
% 80.98/53.71 | (692) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (408), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (241) all_24_0_28 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (241) can reduce 80 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.71 | (696) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (492), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (237) all_26_0_30 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (237) can reduce 84 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.71 | (700) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_24_1_29) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (206), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (237) all_26_0_30 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (237) can reduce 84 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.71 | (704) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (207), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (241) all_24_0_28 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (241) can reduce 80 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.71 | (708) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (208), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (241) all_24_0_28 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (241) can reduce 80 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.71 | (712) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (209), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (241) all_24_0_28 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (241) can reduce 80 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.71 | (716) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (212), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (293) all_22_0_26 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (293) can reduce 76 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (76) ~ (all_22_0_26 = 0)
% 80.98/53.71 | (720) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (210), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (241) all_24_0_28 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (241) can reduce 80 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (80) ~ (all_24_0_28 = 0)
% 80.98/53.71 | (724) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (199), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (233) all_20_0_24 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (233) can reduce 72 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.71 | (728) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (200), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (269) all_30_0_34 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (269) can reduce 92 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (92) ~ (all_30_0_34 = 0)
% 80.98/53.71 | (732) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (201), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (269) all_30_0_34 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (269) can reduce 92 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (92) ~ (all_30_0_34 = 0)
% 80.98/53.71 | (736) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.98/53.71 |
% 80.98/53.71 +-Applying beta-rule and splitting (202), into two cases.
% 80.98/53.71 |-Branch one:
% 80.98/53.71 | (269) all_30_0_34 = 0
% 80.98/53.71 |
% 80.98/53.71 | Equations (269) can reduce 92 to:
% 80.98/53.71 | (103) $false
% 80.98/53.71 |
% 80.98/53.71 |-The branch is then unsatisfiable
% 80.98/53.71 |-Branch two:
% 80.98/53.71 | (92) ~ (all_30_0_34 = 0)
% 80.98/53.71 | (740) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (203), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (269) all_30_0_34 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (269) can reduce 92 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (92) ~ (all_30_0_34 = 0)
% 80.98/53.72 | (744) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (204), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (237) all_26_0_30 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (237) can reduce 84 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.72 | (748) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (205), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (237) all_26_0_30 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (237) can reduce 84 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (84) ~ (all_26_0_30 = 0)
% 80.98/53.72 | (752) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (211), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (229) all_28_0_32 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (229) can reduce 88 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (88) ~ (all_28_0_32 = 0)
% 80.98/53.72 | (558) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (542), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (760) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (716), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (764) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (720), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (768) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (752), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (772) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (724), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (776) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (732), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (780) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (704), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (784) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (708), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (788) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (712), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 80.98/53.72 | (792) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 80.98/53.72 |
% 80.98/53.72 +-Applying beta-rule and splitting (736), into two cases.
% 80.98/53.72 |-Branch one:
% 80.98/53.72 | (233) all_20_0_24 = 0
% 80.98/53.72 |
% 80.98/53.72 | Equations (233) can reduce 72 to:
% 80.98/53.72 | (103) $false
% 80.98/53.72 |
% 80.98/53.72 |-The branch is then unsatisfiable
% 80.98/53.72 |-Branch two:
% 80.98/53.72 | (72) ~ (all_20_0_24 = 0)
% 81.14/53.72 | (796) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 81.14/53.72 |
% 81.14/53.72 +-Applying beta-rule and splitting (740), into two cases.
% 81.14/53.72 |-Branch one:
% 81.14/53.72 | (233) all_20_0_24 = 0
% 81.14/53.72 |
% 81.14/53.72 | Equations (233) can reduce 72 to:
% 81.14/53.72 | (103) $false
% 81.14/53.72 |
% 81.14/53.72 |-The branch is then unsatisfiable
% 81.14/53.72 |-Branch two:
% 81.14/53.72 | (72) ~ (all_20_0_24 = 0)
% 81.14/53.72 | (800) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_24_1_29) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 81.14/53.72 |
% 81.14/53.72 +-Applying beta-rule and splitting (744), into two cases.
% 81.14/53.72 |-Branch one:
% 81.14/53.72 | (233) all_20_0_24 = 0
% 81.14/53.72 |
% 81.14/53.72 | Equations (233) can reduce 72 to:
% 81.14/53.72 | (103) $false
% 81.14/53.72 |
% 81.14/53.72 |-The branch is then unsatisfiable
% 81.14/53.72 |-Branch two:
% 81.14/53.72 | (72) ~ (all_20_0_24 = 0)
% 81.14/53.72 | (804) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_24_1_29) = 0) | ( ~ (v0 = 0) & distinct_lines(all_24_1_29, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 81.14/53.72 |
% 81.14/53.72 +-Applying beta-rule and splitting (748), into two cases.
% 81.14/53.72 |-Branch one:
% 81.14/53.72 | (233) all_20_0_24 = 0
% 81.14/53.72 |
% 81.14/53.72 | Equations (233) can reduce 72 to:
% 81.14/53.72 | (103) $false
% 81.14/53.72 |
% 81.14/53.72 |-The branch is then unsatisfiable
% 81.14/53.72 |-Branch two:
% 81.14/53.72 | (72) ~ (all_20_0_24 = 0)
% 81.14/53.72 | (808) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 81.14/53.73 |
% 81.14/53.73 +-Applying beta-rule and splitting (558), into two cases.
% 81.14/53.73 |-Branch one:
% 81.14/53.73 | (233) all_20_0_24 = 0
% 81.14/53.73 |
% 81.14/53.73 | Equations (233) can reduce 72 to:
% 81.14/53.73 | (103) $false
% 81.14/53.73 |
% 81.14/53.73 |-The branch is then unsatisfiable
% 81.14/53.73 |-Branch two:
% 81.14/53.73 | (72) ~ (all_20_0_24 = 0)
% 81.14/53.73 | (812) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 81.14/53.73 |
% 81.14/53.73 | Instantiating formula (42) with all_0_5_5, all_0_2_2, 0, all_20_0_24 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields:
% 81.14/53.73 | (233) all_20_0_24 = 0
% 81.14/53.73 |
% 81.14/53.73 | Equations (233) can reduce 72 to:
% 81.14/53.73 | (103) $false
% 81.14/53.73 |
% 81.14/53.73 |-The branch is then unsatisfiable
% 81.17/53.73 |-Branch two:
% 81.17/53.73 | (815) ~ (all_33_0_37 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_33_0_37
% 81.17/53.73 |
% 81.17/53.73 | Applying alpha-rule on (815) yields:
% 81.17/53.73 | (227) ~ (all_33_0_37 = 0)
% 81.17/53.73 | (817) distinct_points(all_0_4_4, all_0_5_5) = all_33_0_37
% 81.17/53.73 |
% 81.17/53.73 | Instantiating formula (38) with all_33_0_37, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_4_4, all_0_5_5) = all_33_0_37, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 81.17/53.73 | (818) all_33_0_37 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 81.17/53.73 |
% 81.17/53.73 +-Applying beta-rule and splitting (818), into two cases.
% 81.17/53.73 |-Branch one:
% 81.17/53.73 | (581) distinct_points(all_0_5_5, all_0_5_5) = 0
% 81.17/53.73 |
% 81.17/53.73 | Instantiating formula (3) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 81.17/53.73 | (582) $false
% 81.17/53.73 |
% 81.17/53.73 |-The branch is then unsatisfiable
% 81.17/53.73 |-Branch two:
% 81.17/53.73 | (583) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 81.17/53.73 | (526) all_33_0_37 = 0
% 81.17/53.73 |
% 81.17/53.73 | Equations (526) can reduce 227 to:
% 81.17/53.73 | (103) $false
% 81.17/53.73 |
% 81.17/53.73 |-The branch is then unsatisfiable
% 81.17/53.73 |-Branch two:
% 81.17/53.73 | (824) ~ (all_35_0_39 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39
% 81.17/53.73 |
% 81.17/53.73 | Applying alpha-rule on (824) yields:
% 81.17/53.73 | (112) ~ (all_35_0_39 = 0)
% 81.17/53.73 | (826) distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39
% 81.17/53.73 |
% 81.17/53.73 | Instantiating formula (24) with all_0_5_5, all_0_4_4, all_35_0_39, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 81.17/53.73 | (827) all_35_0_39 = 0
% 81.17/53.73 |
% 81.17/53.73 | Equations (827) can reduce 112 to:
% 81.17/53.73 | (103) $false
% 81.17/53.73 |
% 81.17/53.73 |-The branch is then unsatisfiable
% 81.17/53.73 |-Branch two:
% 81.17/53.73 | (829) ~ (distinct_lines(all_0_0_0, all_0_2_2) = 0)
% 81.17/53.73 | (102) all_0_1_1 = 0
% 81.17/53.73 |
% 81.17/53.73 | Equations (102) can reduce 33 to:
% 81.17/53.73 | (103) $false
% 81.17/53.73 |
% 81.17/53.73 |-The branch is then unsatisfiable
% 81.17/53.73 |-Branch two:
% 81.17/53.73 | (832) ~ (all_32_0_36 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36
% 81.17/53.73 |
% 81.17/53.73 | Applying alpha-rule on (832) yields:
% 81.17/53.73 | (100) ~ (all_32_0_36 = 0)
% 81.17/53.73 | (834) distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36
% 81.17/53.73 |
% 81.17/53.73 | Instantiating formula (24) with all_0_5_5, all_0_4_4, all_32_0_36, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 81.17/53.73 | (835) all_32_0_36 = 0
% 81.17/53.73 |
% 81.17/53.73 | Equations (835) can reduce 100 to:
% 81.17/53.73 | (103) $false
% 81.17/53.73 |
% 81.17/53.73 |-The branch is then unsatisfiable
% 81.17/53.73 % SZS output end Proof for theBenchmark
% 81.17/53.73
% 81.17/53.73 53107ms
%------------------------------------------------------------------------------