TSTP Solution File: GEO205+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO205+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 03:48:40 EDT 2022
% Result : Theorem 5.21s 1.83s
% Output : Proof 23.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO205+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jun 18 16:29:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.58 ____ _
% 0.56/0.58 ___ / __ \_____(_)___ ________ __________
% 0.56/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.58
% 0.56/0.58 A Theorem Prover for First-Order Logic
% 0.61/0.58 (ePrincess v.1.0)
% 0.61/0.58
% 0.61/0.58 (c) Philipp Rümmer, 2009-2015
% 0.61/0.58 (c) Peter Backeman, 2014-2015
% 0.61/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.58 Bug reports to peter@backeman.se
% 0.61/0.58
% 0.61/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.58
% 0.61/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.52/0.89 Prover 0: Preprocessing ...
% 1.86/1.01 Prover 0: Warning: ignoring some quantifiers
% 1.86/1.03 Prover 0: Constructing countermodel ...
% 2.38/1.19 Prover 0: gave up
% 2.38/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.49/1.21 Prover 1: Preprocessing ...
% 2.91/1.31 Prover 1: Constructing countermodel ...
% 3.11/1.37 Prover 1: gave up
% 3.11/1.37 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.11/1.39 Prover 2: Preprocessing ...
% 3.70/1.52 Prover 2: Warning: ignoring some quantifiers
% 3.70/1.53 Prover 2: Constructing countermodel ...
% 5.21/1.83 Prover 2: proved (454ms)
% 5.21/1.83
% 5.21/1.83 No countermodel exists, formula is valid
% 5.21/1.83 % SZS status Theorem for theBenchmark
% 5.21/1.83
% 5.21/1.83 Generating proof ... Warning: ignoring some quantifiers
% 22.33/6.85 found it (size 461)
% 22.33/6.85
% 22.33/6.85 % SZS output start Proof for theBenchmark
% 22.33/6.85 Assumed formulas after preprocessing and simplification:
% 22.33/6.85 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = 0 & distinct_lines(v1, v2) = v3 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v11) = v13) | ~ (apart_point_and_line(v9, v10) = v12) | ~ (distinct_points(v8, v9) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v8, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v11) = v13) | ~ (apart_point_and_line(v8, v11) = v12) | ~ (distinct_lines(v10, v11) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v10) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v11) = v13) | ~ (apart_point_and_line(v8, v10) = v12) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v10) = 0) | (v14 = 0 & apart_point_and_line(v8, v11) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v10) = v13) | ~ (apart_point_and_line(v8, v11) = v12) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v10) = v13) | ~ (apart_point_and_line(v8, v10) = v12) | ~ (distinct_lines(v10, v11) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v11) = 0) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v8, v11) = v13) | ~ (apart_point_and_line(v8, v10) = v12) | ~ (distinct_points(v8, v9) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v9, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v10, v9) = v12) | ~ (distinct_points(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & apart_point_and_line(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v10) = v12) | ~ (distinct_lines(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & apart_point_and_line(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (convergent_lines(v9, v10) = v12) | ~ (convergent_lines(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (convergent_lines(v8, v10) = v12) | ~ (distinct_lines(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (distinct_lines(v9, v10) = v12) | ~ (distinct_lines(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (distinct_points(v9, v10) = v12) | ~ (distinct_points(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & distinct_points(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v10, v9) = v11) | ~ (apart_point_and_line(v8, v9) = 0) | distinct_points(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v10) = v11) | ~ (apart_point_and_line(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | apart_point_and_line(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_points(v8, v10) = v11) | apart_point_and_line(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v9, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | convergent_lines(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_lines(v9, v10) = v11) | ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_lines(v8, v10) = v11) | ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_points(v9, v10) = v11) | ~ (distinct_points(v8, v9) = 0) | distinct_points(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_points(v8, v10) = v11) | ~ (distinct_points(v8, v9) = 0) | distinct_points(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection_point(v11, v10) = v9) | ~ (intersection_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (line_connecting(v11, v10) = v9) | ~ (line_connecting(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (apart_point_and_line(v11, v10) = v9) | ~ (apart_point_and_line(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (convergent_lines(v11, v10) = v9) | ~ (convergent_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_lines(v11, v10) = v9) | ~ (distinct_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_points(v11, v10) = v9) | ~ (distinct_points(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) | ~ (distinct_points(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v9, v11) = 0) | (v12 = 0 & apart_point_and_line(v9, v10) = 0) | (v12 = 0 & apart_point_and_line(v8, v11) = 0) | (v12 = 0 & apart_point_and_line(v8, v10) = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & apart_point_and_line(v10, v9) = v11) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & apart_point_and_line(v10, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & apart_point_and_line(v9, v10) = v11) | ( ~ (v11 = 0) & distinct_points(v8, v9) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & apart_point_and_line(v8, v10) = v11) | ( ~ (v11 = 0) & distinct_points(v8, v9) = v11))) & ! [v8] : ! [v9] : ( ~ (convergent_lines(v8, v9) = 0) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & intersection_point(v8, v9) = v10 & apart_point_and_line(v10, v9) = v11)) & ! [v8] : ! [v9] : ( ~ (convergent_lines(v8, v9) = 0) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & intersection_point(v8, v9) = v10 & apart_point_and_line(v10, v8) = v11)) & ! [v8] : ! [v9] : ( ~ (distinct_points(v8, v9) = 0) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & line_connecting(v8, v9) = v10 & apart_point_and_line(v9, v10) = v11)) & ! [v8] : ! [v9] : ( ~ (distinct_points(v8, v9) = 0) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & line_connecting(v8, v9) = v10 & apart_point_and_line(v8, v10) = v11)) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0) & ? [v8] : ? [v9] : ? [v10] : intersection_point(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : line_connecting(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : apart_point_and_line(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : convergent_lines(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : distinct_lines(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : distinct_points(v9, v8) = v10 & ((v7 = 0 & intersection_point(v0, v2) = v6 & intersection_point(v0, v1) = v5 & distinct_points(v5, v6) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v2) = v4)))
% 22.55/6.91 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 22.55/6.91 | (1) ~ (all_0_4_4 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = 0 & distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ((all_0_0_0 = 0 & intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1 & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_points(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_0_3_3 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3))
% 22.55/6.92 |
% 22.55/6.92 | Applying alpha-rule on (1) yields:
% 22.55/6.92 | (2) ! [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)))
% 22.55/6.92 | (3) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 22.55/6.92 | (4) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 22.55/6.92 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 22.55/6.92 | (6) distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4
% 22.55/6.92 | (7) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 22.55/6.92 | (8) ! [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)))
% 22.55/6.92 | (9) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 22.55/6.93 | (10) ! [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)))
% 22.55/6.93 | (11) ! [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))
% 22.55/6.93 | (12) convergent_lines(all_0_7_7, all_0_6_6) = 0
% 22.55/6.93 | (13) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 22.55/6.93 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 22.55/6.93 | (15) ! [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)))
% 22.55/6.93 | (16) ! [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))
% 22.55/6.93 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 22.55/6.93 | (18) ! [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)
% 22.55/6.93 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 22.55/6.93 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 22.55/6.93 | (21) ! [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)
% 22.55/6.93 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 22.55/6.93 | (23) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 22.55/6.93 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 22.55/6.93 | (25) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 22.55/6.93 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 22.55/6.93 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 22.55/6.93 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.55/6.93 | (29) ! [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)))
% 22.55/6.93 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 22.55/6.93 | (31) ! [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)
% 22.55/6.93 | (32) ! [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)))
% 22.55/6.93 | (33) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 22.55/6.93 | (34) ! [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)))
% 22.55/6.93 | (35) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 22.55/6.93 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 22.55/6.94 | (37) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 22.55/6.94 | (38) ! [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))
% 22.55/6.94 | (39) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 22.55/6.94 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 22.55/6.94 | (41) ! [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)))
% 22.55/6.94 | (42) ! [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))
% 22.55/6.94 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 22.55/6.94 | (44) ! [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)))
% 22.55/6.94 | (45) ~ (all_0_4_4 = 0)
% 22.55/6.94 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 22.55/6.94 | (47) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 22.55/6.94 | (48) ! [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)))
% 22.55/6.94 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.55/6.94 | (50) (all_0_0_0 = 0 & intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1 & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_points(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_0_3_3 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3)
% 22.55/6.94 | (51) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 22.55/6.94 | (52) ! [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)))
% 22.55/6.94 | (53) ! [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))
% 22.55/6.94 |
% 22.55/6.94 | Instantiating formula (9) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 22.55/6.94 | (54) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(v0, all_0_6_6) = v1)
% 22.55/6.94 |
% 22.55/6.94 | Instantiating formula (51) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 22.55/6.94 | (55) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(v0, all_0_7_7) = v1)
% 22.86/6.94 |
% 22.86/6.94 | Instantiating formula (5) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 22.86/6.94 | (56) all_0_4_4 = 0 | convergent_lines(all_0_7_7, all_0_5_5) = 0
% 22.86/6.94 |
% 22.86/6.94 | Instantiating formula (16) with all_0_4_4, all_0_4_4, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 22.86/6.94 | (57) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0)
% 22.86/6.94 |
% 22.86/6.94 | Instantiating (55) with all_20_0_26, all_20_1_27 yields:
% 22.86/6.94 | (58) ~ (all_20_0_26 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_20_1_27 & apart_point_and_line(all_20_1_27, all_0_7_7) = all_20_0_26
% 22.86/6.94 |
% 22.86/6.94 | Applying alpha-rule on (58) yields:
% 22.86/6.94 | (59) ~ (all_20_0_26 = 0)
% 22.86/6.94 | (60) intersection_point(all_0_7_7, all_0_6_6) = all_20_1_27
% 22.86/6.94 | (61) apart_point_and_line(all_20_1_27, all_0_7_7) = all_20_0_26
% 22.86/6.94 |
% 22.86/6.94 | Instantiating (54) with all_22_0_28, all_22_1_29 yields:
% 22.86/6.94 | (62) ~ (all_22_0_28 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_22_1_29 & apart_point_and_line(all_22_1_29, all_0_6_6) = all_22_0_28
% 22.86/6.95 |
% 22.86/6.95 | Applying alpha-rule on (62) yields:
% 22.86/6.95 | (63) ~ (all_22_0_28 = 0)
% 22.86/6.95 | (64) intersection_point(all_0_7_7, all_0_6_6) = all_22_1_29
% 22.86/6.95 | (65) apart_point_and_line(all_22_1_29, all_0_6_6) = all_22_0_28
% 22.86/6.95 |
% 22.86/6.95 +-Applying beta-rule and splitting (56), into two cases.
% 22.86/6.95 |-Branch one:
% 22.86/6.95 | (66) convergent_lines(all_0_7_7, all_0_5_5) = 0
% 22.86/6.95 |
% 22.86/6.95 +-Applying beta-rule and splitting (50), into two cases.
% 22.86/6.95 |-Branch one:
% 22.86/6.95 | (67) all_0_0_0 = 0 & intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1 & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_points(all_0_2_2, all_0_1_1) = 0
% 22.86/6.95 |
% 22.86/6.95 | Applying alpha-rule on (67) yields:
% 22.86/6.95 | (68) all_0_0_0 = 0
% 22.86/6.95 | (69) intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1
% 22.86/6.95 | (70) intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2
% 22.86/6.95 | (71) distinct_points(all_0_2_2, all_0_1_1) = 0
% 22.86/6.95 |
% 22.86/6.95 +-Applying beta-rule and splitting (57), into two cases.
% 22.86/6.95 |-Branch one:
% 22.86/6.95 | (72) all_0_4_4 = 0
% 22.86/6.95 |
% 22.86/6.95 | Equations (72) can reduce 45 to:
% 22.86/6.95 | (73) $false
% 22.86/6.95 |
% 22.86/6.95 |-The branch is then unsatisfiable
% 22.86/6.95 |-Branch two:
% 22.86/6.95 | (45) ~ (all_0_4_4 = 0)
% 22.86/6.95 | (75) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0)
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (40) with all_0_7_7, all_0_6_6, all_20_1_27, all_22_1_29 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_22_1_29, intersection_point(all_0_7_7, all_0_6_6) = all_20_1_27, yields:
% 22.86/6.95 | (76) all_22_1_29 = all_20_1_27
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (40) with all_0_7_7, all_0_6_6, all_0_2_2, all_22_1_29 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_22_1_29, intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 22.86/6.95 | (77) all_22_1_29 = all_0_2_2
% 22.86/6.95 |
% 22.86/6.95 | Combining equations (77,76) yields a new equation:
% 22.86/6.95 | (78) all_20_1_27 = all_0_2_2
% 22.86/6.95 |
% 22.86/6.95 | Combining equations (78,76) yields a new equation:
% 22.86/6.95 | (77) all_22_1_29 = all_0_2_2
% 22.86/6.95 |
% 22.86/6.95 | From (77) and (65) follows:
% 22.86/6.95 | (80) apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28
% 22.86/6.95 |
% 22.86/6.95 | From (78) and (61) follows:
% 22.86/6.95 | (81) apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (34) with all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1, yields:
% 22.86/6.95 | (82) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = v0))
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (44) with all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1, yields:
% 22.86/6.95 | (83) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_7_7) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = v0))
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (41) with all_22_0_28, all_22_0_28, all_0_6_6, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.86/6.95 | (84) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (41) with all_20_0_26, all_22_0_28, all_0_7_7, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.86/6.95 | (85) all_22_0_28 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (41) with all_22_0_28, all_20_0_26, all_0_6_6, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.86/6.95 | (86) all_22_0_28 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (41) with all_20_0_26, all_20_0_26, all_0_7_7, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.86/6.95 | (87) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (9) with all_0_5_5, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 22.86/6.95 | (88) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_5_5) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (51) with all_0_5_5, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 22.86/6.95 | (89) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_5_5) = v0 & apart_point_and_line(v0, all_0_7_7) = v1)
% 22.86/6.95 |
% 22.86/6.95 | Instantiating formula (8) with all_22_0_28, all_22_0_28, all_0_6_6, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.95 | (90) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 22.86/6.96 |
% 22.86/6.96 | Instantiating formula (8) with all_22_0_28, all_20_0_26, all_0_6_6, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96 | (91) all_22_0_28 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0))
% 22.86/6.96 |
% 22.86/6.96 | Instantiating formula (8) with all_20_0_26, all_22_0_28, all_0_7_7, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96 | (92) all_22_0_28 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0))
% 22.86/6.96 |
% 22.86/6.96 | Instantiating formula (8) with all_20_0_26, all_20_0_26, all_0_7_7, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96 | (93) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0))
% 22.86/6.96 |
% 22.86/6.96 | Instantiating formula (13) with all_0_1_1, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96 | (94) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_2_2, all_0_1_1) = v0 & apart_point_and_line(all_0_1_1, v0) = v1)
% 22.86/6.96 |
% 22.86/6.96 | Instantiating formula (25) with all_0_1_1, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96 | (95) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_2_2, all_0_1_1) = v0 & apart_point_and_line(all_0_2_2, v0) = v1)
% 22.86/6.96 |
% 22.86/6.96 | Instantiating (95) with all_47_0_31, all_47_1_32 yields:
% 22.86/6.96 | (96) ~ (all_47_0_31 = 0) & line_connecting(all_0_2_2, all_0_1_1) = all_47_1_32 & apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31
% 22.86/6.96 |
% 22.86/6.96 | Applying alpha-rule on (96) yields:
% 22.86/6.96 | (97) ~ (all_47_0_31 = 0)
% 22.86/6.96 | (98) line_connecting(all_0_2_2, all_0_1_1) = all_47_1_32
% 22.86/6.96 | (99) apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31
% 22.86/6.96 |
% 22.86/6.96 | Instantiating (94) with all_49_0_33, all_49_1_34 yields:
% 22.86/6.96 | (100) ~ (all_49_0_33 = 0) & line_connecting(all_0_2_2, all_0_1_1) = all_49_1_34 & apart_point_and_line(all_0_1_1, all_49_1_34) = all_49_0_33
% 22.86/6.96 |
% 22.86/6.96 | Applying alpha-rule on (100) yields:
% 22.86/6.96 | (101) ~ (all_49_0_33 = 0)
% 22.86/6.96 | (102) line_connecting(all_0_2_2, all_0_1_1) = all_49_1_34
% 22.86/6.96 | (103) apart_point_and_line(all_0_1_1, all_49_1_34) = all_49_0_33
% 22.86/6.96 |
% 22.86/6.96 | Instantiating (89) with all_51_0_35, all_51_1_36 yields:
% 22.86/6.96 | (104) ~ (all_51_0_35 = 0) & intersection_point(all_0_7_7, all_0_5_5) = all_51_1_36 & apart_point_and_line(all_51_1_36, all_0_7_7) = all_51_0_35
% 22.86/6.96 |
% 22.86/6.96 | Applying alpha-rule on (104) yields:
% 22.86/6.96 | (105) ~ (all_51_0_35 = 0)
% 22.86/6.96 | (106) intersection_point(all_0_7_7, all_0_5_5) = all_51_1_36
% 22.86/6.96 | (107) apart_point_and_line(all_51_1_36, all_0_7_7) = all_51_0_35
% 22.86/6.96 |
% 22.86/6.96 | Instantiating (88) with all_53_0_37, all_53_1_38 yields:
% 22.86/6.96 | (108) ~ (all_53_0_37 = 0) & intersection_point(all_0_7_7, all_0_5_5) = all_53_1_38 & apart_point_and_line(all_53_1_38, all_0_5_5) = all_53_0_37
% 22.86/6.96 |
% 22.86/6.96 | Applying alpha-rule on (108) yields:
% 22.86/6.96 | (109) ~ (all_53_0_37 = 0)
% 22.86/6.96 | (110) intersection_point(all_0_7_7, all_0_5_5) = all_53_1_38
% 22.86/6.96 | (111) apart_point_and_line(all_53_1_38, all_0_5_5) = all_53_0_37
% 22.86/6.96 |
% 22.86/6.96 | Instantiating (83) with all_55_0_39 yields:
% 22.86/6.96 | (112) ( ~ (all_55_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_7_7) = all_55_0_39) | ( ~ (all_55_0_39 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_55_0_39)
% 22.86/6.96 |
% 22.86/6.96 | Instantiating (82) with all_56_0_40 yields:
% 22.86/6.96 | (113) ( ~ (all_56_0_40 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_40) | ( ~ (all_56_0_40 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_56_0_40)
% 22.86/6.96 |
% 22.86/6.96 +-Applying beta-rule and splitting (112), into two cases.
% 22.86/6.96 |-Branch one:
% 22.86/6.96 | (114) ~ (all_55_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_7_7) = all_55_0_39
% 22.86/6.96 |
% 22.86/6.96 | Applying alpha-rule on (114) yields:
% 22.86/6.96 | (115) ~ (all_55_0_39 = 0)
% 22.86/6.96 | (116) apart_point_and_line(all_0_1_1, all_0_7_7) = all_55_0_39
% 22.86/6.96 |
% 22.86/6.96 +-Applying beta-rule and splitting (113), into two cases.
% 22.86/6.96 |-Branch one:
% 22.86/6.96 | (117) ~ (all_56_0_40 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_40
% 22.86/6.96 |
% 22.86/6.96 | Applying alpha-rule on (117) yields:
% 22.86/6.96 | (118) ~ (all_56_0_40 = 0)
% 22.86/6.96 | (119) apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_40
% 22.86/6.96 |
% 22.86/6.96 +-Applying beta-rule and splitting (90), into two cases.
% 22.86/6.96 |-Branch one:
% 22.86/6.96 | (120) all_22_0_28 = 0
% 22.86/6.96 |
% 22.86/6.96 | Equations (120) can reduce 63 to:
% 22.86/6.96 | (73) $false
% 22.86/6.96 |
% 22.86/6.96 |-The branch is then unsatisfiable
% 22.86/6.96 |-Branch two:
% 22.86/6.96 | (63) ~ (all_22_0_28 = 0)
% 22.86/6.96 | (123) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 22.86/6.96 |
% 22.86/6.96 +-Applying beta-rule and splitting (93), into two cases.
% 22.86/6.96 |-Branch one:
% 22.86/6.96 | (124) all_20_0_26 = 0
% 22.86/6.96 |
% 22.86/6.96 | Equations (124) can reduce 59 to:
% 22.86/6.96 | (73) $false
% 22.86/6.96 |
% 22.86/6.96 |-The branch is then unsatisfiable
% 22.86/6.96 |-Branch two:
% 22.86/6.96 | (59) ~ (all_20_0_26 = 0)
% 22.86/6.96 | (127) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0))
% 22.86/6.96 |
% 22.86/6.96 +-Applying beta-rule and splitting (84), into two cases.
% 22.86/6.96 |-Branch one:
% 22.86/6.96 | (120) all_22_0_28 = 0
% 22.86/6.96 |
% 22.86/6.96 | Equations (120) can reduce 63 to:
% 22.86/6.96 | (73) $false
% 22.86/6.96 |
% 22.86/6.96 |-The branch is then unsatisfiable
% 22.86/6.96 |-Branch two:
% 22.86/6.96 | (63) ~ (all_22_0_28 = 0)
% 22.86/6.96 | (131) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.86/6.97 |
% 22.86/6.97 +-Applying beta-rule and splitting (87), into two cases.
% 22.86/6.97 |-Branch one:
% 22.86/6.97 | (124) all_20_0_26 = 0
% 22.86/6.97 |
% 22.86/6.97 | Equations (124) can reduce 59 to:
% 22.86/6.97 | (73) $false
% 22.86/6.97 |
% 22.86/6.97 |-The branch is then unsatisfiable
% 22.86/6.97 |-Branch two:
% 22.86/6.97 | (59) ~ (all_20_0_26 = 0)
% 22.86/6.97 | (135) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.86/6.97 |
% 22.86/6.97 +-Applying beta-rule and splitting (86), into two cases.
% 22.86/6.97 |-Branch one:
% 22.86/6.97 | (120) all_22_0_28 = 0
% 22.86/6.97 |
% 22.86/6.97 | Equations (120) can reduce 63 to:
% 22.86/6.97 | (73) $false
% 22.86/6.97 |
% 22.86/6.97 |-The branch is then unsatisfiable
% 22.86/6.97 |-Branch two:
% 22.86/6.97 | (63) ~ (all_22_0_28 = 0)
% 22.86/6.97 | (139) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.86/6.97 |
% 22.86/6.97 +-Applying beta-rule and splitting (92), into two cases.
% 22.86/6.97 |-Branch one:
% 22.86/6.97 | (120) all_22_0_28 = 0
% 22.86/6.97 |
% 22.86/6.97 | Equations (120) can reduce 63 to:
% 22.86/6.97 | (73) $false
% 22.86/6.97 |
% 22.86/6.97 |-The branch is then unsatisfiable
% 22.86/6.97 |-Branch two:
% 22.86/6.97 | (63) ~ (all_22_0_28 = 0)
% 22.86/6.97 | (143) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0))
% 22.86/6.97 |
% 22.86/6.97 +-Applying beta-rule and splitting (91), into two cases.
% 22.86/6.97 |-Branch one:
% 22.86/6.97 | (120) all_22_0_28 = 0
% 22.86/6.97 |
% 22.86/6.97 | Equations (120) can reduce 63 to:
% 22.86/6.97 | (73) $false
% 22.86/6.97 |
% 22.86/6.97 |-The branch is then unsatisfiable
% 22.86/6.97 |-Branch two:
% 22.86/6.97 | (63) ~ (all_22_0_28 = 0)
% 22.86/6.97 | (147) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0))
% 22.98/6.97 |
% 22.98/6.97 +-Applying beta-rule and splitting (85), into two cases.
% 22.98/6.97 |-Branch one:
% 22.98/6.97 | (120) all_22_0_28 = 0
% 22.98/6.97 |
% 22.98/6.97 | Equations (120) can reduce 63 to:
% 22.98/6.97 | (73) $false
% 22.98/6.97 |
% 22.98/6.97 |-The branch is then unsatisfiable
% 22.98/6.97 |-Branch two:
% 22.98/6.97 | (63) ~ (all_22_0_28 = 0)
% 22.98/6.97 | (151) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/6.97 |
% 22.98/6.97 +-Applying beta-rule and splitting (139), into two cases.
% 22.98/6.97 |-Branch one:
% 22.98/6.97 | (124) all_20_0_26 = 0
% 22.98/6.97 |
% 22.98/6.97 | Equations (124) can reduce 59 to:
% 22.98/6.97 | (73) $false
% 22.98/6.97 |
% 22.98/6.97 |-The branch is then unsatisfiable
% 22.98/6.97 |-Branch two:
% 22.98/6.97 | (59) ~ (all_20_0_26 = 0)
% 22.98/6.97 | (155) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/6.97 |
% 22.98/6.97 +-Applying beta-rule and splitting (147), into two cases.
% 22.98/6.97 |-Branch one:
% 22.98/6.97 | (124) all_20_0_26 = 0
% 22.98/6.97 |
% 22.98/6.97 | Equations (124) can reduce 59 to:
% 22.98/6.97 | (73) $false
% 22.98/6.97 |
% 22.98/6.97 |-The branch is then unsatisfiable
% 22.98/6.97 |-Branch two:
% 22.98/6.97 | (59) ~ (all_20_0_26 = 0)
% 22.98/6.97 | (159) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0))
% 22.98/6.97 |
% 22.98/6.97 +-Applying beta-rule and splitting (143), into two cases.
% 22.98/6.97 |-Branch one:
% 22.98/6.97 | (124) all_20_0_26 = 0
% 22.98/6.97 |
% 22.98/6.97 | Equations (124) can reduce 59 to:
% 22.98/6.97 | (73) $false
% 22.98/6.97 |
% 22.98/6.97 |-The branch is then unsatisfiable
% 22.98/6.97 |-Branch two:
% 22.98/6.97 | (59) ~ (all_20_0_26 = 0)
% 22.98/6.97 | (163) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0))
% 22.98/6.97 |
% 22.98/6.97 | Instantiating (163) with all_110_0_51 yields:
% 22.98/6.97 | (164) (all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (all_110_0_51 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51)
% 22.98/6.97 |
% 22.98/6.97 +-Applying beta-rule and splitting (151), into two cases.
% 22.98/6.97 |-Branch one:
% 22.98/6.97 | (124) all_20_0_26 = 0
% 22.98/6.97 |
% 22.98/6.97 | Equations (124) can reduce 59 to:
% 22.98/6.97 | (73) $false
% 22.98/6.97 |
% 22.98/6.97 |-The branch is then unsatisfiable
% 22.98/6.97 |-Branch two:
% 22.98/6.97 | (59) ~ (all_20_0_26 = 0)
% 22.98/6.97 | (168) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/6.97 |
% 22.98/6.97 | Instantiating formula (40) with all_0_7_7, all_0_5_5, all_53_1_38, all_0_1_1 and discharging atoms intersection_point(all_0_7_7, all_0_5_5) = all_53_1_38, intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1, yields:
% 22.98/6.97 | (169) all_53_1_38 = all_0_1_1
% 22.98/6.97 |
% 22.98/6.97 | Instantiating formula (40) with all_0_7_7, all_0_5_5, all_51_1_36, all_53_1_38 and discharging atoms intersection_point(all_0_7_7, all_0_5_5) = all_53_1_38, intersection_point(all_0_7_7, all_0_5_5) = all_51_1_36, yields:
% 22.98/6.97 | (170) all_53_1_38 = all_51_1_36
% 22.98/6.97 |
% 22.98/6.97 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_47_1_32, all_49_1_34 and discharging atoms line_connecting(all_0_2_2, all_0_1_1) = all_49_1_34, line_connecting(all_0_2_2, all_0_1_1) = all_47_1_32, yields:
% 22.98/6.97 | (171) all_49_1_34 = all_47_1_32
% 22.98/6.97 |
% 22.98/6.97 | Combining equations (169,170) yields a new equation:
% 22.98/6.97 | (172) all_51_1_36 = all_0_1_1
% 22.98/6.97 |
% 22.98/6.97 | Combining equations (172,170) yields a new equation:
% 22.98/6.97 | (169) all_53_1_38 = all_0_1_1
% 22.98/6.97 |
% 22.98/6.97 | From (169) and (111) follows:
% 22.98/6.98 | (174) apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37
% 22.98/6.98 |
% 22.98/6.98 | From (172) and (107) follows:
% 22.98/6.98 | (175) apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35
% 22.98/6.98 |
% 22.98/6.98 | From (171) and (103) follows:
% 22.98/6.98 | (176) apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (43) with all_0_1_1, all_0_5_5, all_53_0_37, all_56_0_40 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_40, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, yields:
% 22.98/6.98 | (177) all_56_0_40 = all_53_0_37
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (43) with all_0_1_1, all_0_7_7, all_51_0_35, all_55_0_39 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_55_0_39, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/6.98 | (178) all_55_0_39 = all_51_0_35
% 22.98/6.98 |
% 22.98/6.98 | Equations (177) can reduce 118 to:
% 22.98/6.98 | (109) ~ (all_53_0_37 = 0)
% 22.98/6.98 |
% 22.98/6.98 | Equations (178) can reduce 115 to:
% 22.98/6.98 | (105) ~ (all_51_0_35 = 0)
% 22.98/6.98 |
% 22.98/6.98 | From (177) and (119) follows:
% 22.98/6.98 | (174) apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37
% 22.98/6.98 |
% 22.98/6.98 | From (178) and (116) follows:
% 22.98/6.98 | (175) apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (41) with all_49_0_33, all_22_0_28, all_47_1_32, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.98 | (183) all_49_0_33 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (41) with all_22_0_28, all_49_0_33, all_0_6_6, all_47_1_32, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.98 | (184) all_49_0_33 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (52) with all_49_0_33, all_22_0_28, all_0_6_6, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.98 | (185) all_49_0_33 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (52) with all_22_0_28, all_49_0_33, all_47_1_32, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.98 | (186) all_49_0_33 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (41) with all_49_0_33, all_20_0_26, all_47_1_32, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.98 | (187) all_49_0_33 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (41) with all_20_0_26, all_49_0_33, all_0_7_7, all_47_1_32, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.98 | (188) all_49_0_33 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (52) with all_49_0_33, all_20_0_26, all_0_7_7, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.98 | (189) all_49_0_33 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.98 |
% 22.98/6.98 | Instantiating formula (52) with all_20_0_26, all_49_0_33, all_47_1_32, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.98 | (190) all_49_0_33 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (15) with all_49_0_33, all_49_0_33, all_47_1_32, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/6.99 | (191) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (41) with all_49_0_33, all_49_0_33, all_47_1_32, all_47_1_32, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, yields:
% 22.98/6.99 | (192) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (41) with all_53_0_37, all_22_0_28, all_0_5_5, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.99 | (193) all_53_0_37 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (41) with all_22_0_28, all_53_0_37, all_0_6_6, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.99 | (194) all_53_0_37 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (52) with all_53_0_37, all_22_0_28, all_0_6_6, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.99 | (195) all_53_0_37 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (52) with all_22_0_28, all_53_0_37, all_0_5_5, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.99 | (196) all_53_0_37 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (41) with all_53_0_37, all_20_0_26, all_0_5_5, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.99 | (197) all_53_0_37 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (41) with all_20_0_26, all_53_0_37, all_0_7_7, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.99 | (198) all_53_0_37 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (52) with all_53_0_37, all_20_0_26, all_0_7_7, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.99 | (199) all_53_0_37 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (52) with all_20_0_26, all_53_0_37, all_0_5_5, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.99 | (200) all_53_0_37 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (15) with all_53_0_37, all_49_0_33, all_0_5_5, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/6.99 | (201) all_53_0_37 = 0 | all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (15) with all_49_0_33, all_53_0_37, all_47_1_32, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/6.99 | (202) all_53_0_37 = 0 | all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0))
% 22.98/6.99 |
% 22.98/6.99 | Instantiating formula (41) with all_53_0_37, all_49_0_33, all_0_5_5, all_47_1_32, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, yields:
% 22.98/7.00 | (203) all_53_0_37 = 0 | all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (41) with all_49_0_33, all_53_0_37, all_47_1_32, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, yields:
% 22.98/7.00 | (204) all_53_0_37 = 0 | all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (15) with all_53_0_37, all_53_0_37, all_0_5_5, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.00 | (205) all_53_0_37 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (41) with all_53_0_37, all_53_0_37, all_0_5_5, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, yields:
% 22.98/7.00 | (206) all_53_0_37 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (11) with all_53_0_37, all_0_4_4, all_0_5_5, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 22.98/7.00 | (207) all_53_0_37 = 0 | all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = v0)
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (41) with all_51_0_35, all_22_0_28, all_0_7_7, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.00 | (208) all_51_0_35 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (41) with all_22_0_28, all_51_0_35, all_0_6_6, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.00 | (209) all_51_0_35 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (52) with all_51_0_35, all_22_0_28, all_0_6_6, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.00 | (210) all_51_0_35 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (52) with all_22_0_28, all_51_0_35, all_0_7_7, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.00 | (211) all_51_0_35 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (41) with all_20_0_26, all_51_0_35, all_0_7_7, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/7.00 | (212) all_51_0_35 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (15) with all_51_0_35, all_49_0_33, all_0_7_7, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.00 | (213) all_51_0_35 = 0 | all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 22.98/7.00 |
% 22.98/7.00 | Instantiating formula (15) with all_49_0_33, all_51_0_35, all_47_1_32, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.01 | (214) all_51_0_35 = 0 | all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0))
% 22.98/7.01 |
% 22.98/7.01 | Instantiating formula (41) with all_51_0_35, all_49_0_33, all_0_7_7, all_47_1_32, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.01 | (215) all_51_0_35 = 0 | all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.01 |
% 22.98/7.01 | Instantiating formula (41) with all_49_0_33, all_51_0_35, all_47_1_32, all_0_7_7, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.01 | (216) all_51_0_35 = 0 | all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.01 |
% 22.98/7.01 | Instantiating formula (15) with all_51_0_35, all_53_0_37, all_0_7_7, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.01 | (217) all_53_0_37 = 0 | all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0))
% 22.98/7.01 |
% 22.98/7.01 | Instantiating formula (15) with all_53_0_37, all_51_0_35, all_0_5_5, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.01 | (218) all_53_0_37 = 0 | all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0))
% 22.98/7.01 |
% 22.98/7.01 | Instantiating formula (41) with all_51_0_35, all_53_0_37, all_0_7_7, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.01 | (219) all_53_0_37 = 0 | all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (41) with all_53_0_37, all_51_0_35, all_0_5_5, all_0_7_7, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.02 | (220) all_53_0_37 = 0 | all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (41) with all_51_0_35, all_51_0_35, all_0_7_7, all_0_7_7, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.02 | (221) all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (8) with all_47_0_31, all_22_0_28, all_47_1_32, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.02 | (222) all_47_0_31 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (8) with all_22_0_28, all_47_0_31, all_0_6_6, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.02 | (223) all_47_0_31 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (41) with all_47_0_31, all_22_0_28, all_47_1_32, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.02 | (224) all_47_0_31 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (41) with all_22_0_28, all_47_0_31, all_0_6_6, all_47_1_32, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.02 | (225) all_47_0_31 = 0 | all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (8) with all_47_0_31, all_20_0_26, all_47_1_32, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.02 | (226) all_47_0_31 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (8) with all_20_0_26, all_47_0_31, all_0_7_7, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.02 | (227) all_47_0_31 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (41) with all_47_0_31, all_20_0_26, all_47_1_32, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/7.02 | (228) all_47_0_31 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (41) with all_20_0_26, all_47_0_31, all_0_7_7, all_47_1_32, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/7.02 | (229) all_47_0_31 = 0 | all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/7.02 |
% 22.98/7.02 | Instantiating formula (41) with all_49_0_33, all_47_0_31, all_47_1_32, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 22.98/7.02 | (230) all_49_0_33 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.02 |
% 23.24/7.02 | Instantiating formula (41) with all_47_0_31, all_53_0_37, all_47_1_32, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.02 | (231) all_53_0_37 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.02 |
% 23.24/7.02 | Instantiating formula (41) with all_53_0_37, all_47_0_31, all_0_5_5, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.02 | (232) all_53_0_37 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.02 |
% 23.24/7.02 | Instantiating formula (52) with all_47_0_31, all_53_0_37, all_0_5_5, all_47_1_32, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.02 | (233) all_53_0_37 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.02 |
% 23.24/7.02 | Instantiating formula (52) with all_53_0_37, all_47_0_31, all_47_1_32, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.02 | (234) all_53_0_37 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.02 |
% 23.24/7.02 | Instantiating formula (41) with all_47_0_31, all_51_0_35, all_47_1_32, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03 | (235) all_51_0_35 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.03 |
% 23.24/7.03 | Instantiating formula (41) with all_51_0_35, all_47_0_31, all_0_7_7, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03 | (236) all_51_0_35 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.03 |
% 23.24/7.03 | Instantiating formula (52) with all_47_0_31, all_51_0_35, all_0_7_7, all_47_1_32, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03 | (237) all_51_0_35 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.03 |
% 23.24/7.03 | Instantiating formula (52) with all_51_0_35, all_47_0_31, all_47_1_32, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03 | (238) all_51_0_35 = 0 | all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.03 |
% 23.24/7.03 | Instantiating formula (8) with all_47_0_31, all_47_0_31, all_47_1_32, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 23.24/7.03 | (239) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0))
% 23.24/7.03 |
% 23.24/7.03 | Instantiating formula (41) with all_47_0_31, all_47_0_31, all_47_1_32, all_47_1_32, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03 | (240) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (191), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (241) all_49_0_33 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (241) can reduce 101 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.03 | (244) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (192), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (241) all_49_0_33 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (241) can reduce 101 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.03 | (248) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (205), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (249) all_53_0_37 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (249) can reduce 109 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.03 | (252) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (206), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (249) all_53_0_37 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (249) can reduce 109 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.03 | (256) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (221), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (257) all_51_0_35 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (257) can reduce 105 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (105) ~ (all_51_0_35 = 0)
% 23.24/7.03 | (260) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (239), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (261) all_47_0_31 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (261) can reduce 97 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (97) ~ (all_47_0_31 = 0)
% 23.24/7.03 | (264) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (240), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (261) all_47_0_31 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (261) can reduce 97 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (97) ~ (all_47_0_31 = 0)
% 23.24/7.03 | (268) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (183), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (241) all_49_0_33 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (241) can reduce 101 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.03 | (272) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (184), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (241) all_49_0_33 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (241) can reduce 101 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.03 | (276) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.03 |
% 23.24/7.03 +-Applying beta-rule and splitting (185), into two cases.
% 23.24/7.03 |-Branch one:
% 23.24/7.03 | (241) all_49_0_33 = 0
% 23.24/7.03 |
% 23.24/7.03 | Equations (241) can reduce 101 to:
% 23.24/7.03 | (73) $false
% 23.24/7.03 |
% 23.24/7.03 |-The branch is then unsatisfiable
% 23.24/7.03 |-Branch two:
% 23.24/7.03 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.03 | (280) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (230), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (241) all_49_0_33 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (241) can reduce 101 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.04 | (284) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (231), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (288) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (201), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (292) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (197), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (296) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (193), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (300) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (194), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (304) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (203), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (308) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (232), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (312) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (233), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (316) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (186), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (241) all_49_0_33 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (241) can reduce 101 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.04 | (320) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (189), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (241) all_49_0_33 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (241) can reduce 101 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.04 | (324) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (215), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (257) all_51_0_35 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (257) can reduce 105 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (105) ~ (all_51_0_35 = 0)
% 23.24/7.04 | (328) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (204), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (332) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (195), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (336) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (196), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (249) all_53_0_37 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (249) can reduce 109 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.04 | (340) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04 |
% 23.24/7.04 +-Applying beta-rule and splitting (216), into two cases.
% 23.24/7.04 |-Branch one:
% 23.24/7.04 | (257) all_51_0_35 = 0
% 23.24/7.04 |
% 23.24/7.04 | Equations (257) can reduce 105 to:
% 23.24/7.04 | (73) $false
% 23.24/7.04 |
% 23.24/7.04 |-The branch is then unsatisfiable
% 23.24/7.04 |-Branch two:
% 23.24/7.04 | (105) ~ (all_51_0_35 = 0)
% 23.24/7.04 | (344) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (217), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (249) all_53_0_37 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (249) can reduce 109 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.05 | (348) all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (218), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (249) all_53_0_37 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (249) can reduce 109 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.05 | (352) all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (198), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (249) all_53_0_37 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (249) can reduce 109 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.05 | (356) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (199), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (249) all_53_0_37 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (249) can reduce 109 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.05 | (360) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (200), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (249) all_53_0_37 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (249) can reduce 109 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.05 | (364) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (222), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (261) all_47_0_31 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (261) can reduce 97 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (97) ~ (all_47_0_31 = 0)
% 23.24/7.05 | (368) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (202), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (249) all_53_0_37 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (249) can reduce 109 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (109) ~ (all_53_0_37 = 0)
% 23.24/7.05 | (372) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (236), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (257) all_51_0_35 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (257) can reduce 105 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (105) ~ (all_51_0_35 = 0)
% 23.24/7.05 | (376) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (187), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (241) all_49_0_33 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (241) can reduce 101 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (101) ~ (all_49_0_33 = 0)
% 23.24/7.05 | (380) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.05 |
% 23.24/7.05 +-Applying beta-rule and splitting (223), into two cases.
% 23.24/7.05 |-Branch one:
% 23.24/7.05 | (261) all_47_0_31 = 0
% 23.24/7.05 |
% 23.24/7.05 | Equations (261) can reduce 97 to:
% 23.24/7.05 | (73) $false
% 23.24/7.05 |
% 23.24/7.05 |-The branch is then unsatisfiable
% 23.24/7.05 |-Branch two:
% 23.24/7.05 | (97) ~ (all_47_0_31 = 0)
% 23.24/7.05 | (384) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0))
% 23.38/7.05 |
% 23.38/7.05 +-Applying beta-rule and splitting (188), into two cases.
% 23.38/7.05 |-Branch one:
% 23.38/7.05 | (241) all_49_0_33 = 0
% 23.38/7.05 |
% 23.38/7.05 | Equations (241) can reduce 101 to:
% 23.38/7.05 | (73) $false
% 23.38/7.05 |
% 23.38/7.05 |-The branch is then unsatisfiable
% 23.38/7.05 |-Branch two:
% 23.38/7.05 | (101) ~ (all_49_0_33 = 0)
% 23.38/7.05 | (388) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.05 |
% 23.38/7.05 +-Applying beta-rule and splitting (224), into two cases.
% 23.38/7.05 |-Branch one:
% 23.38/7.05 | (261) all_47_0_31 = 0
% 23.38/7.05 |
% 23.38/7.05 | Equations (261) can reduce 97 to:
% 23.38/7.05 | (73) $false
% 23.38/7.05 |
% 23.38/7.05 |-The branch is then unsatisfiable
% 23.38/7.05 |-Branch two:
% 23.38/7.05 | (97) ~ (all_47_0_31 = 0)
% 23.38/7.05 | (392) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.05 |
% 23.38/7.05 +-Applying beta-rule and splitting (190), into two cases.
% 23.38/7.05 |-Branch one:
% 23.38/7.05 | (241) all_49_0_33 = 0
% 23.38/7.05 |
% 23.38/7.05 | Equations (241) can reduce 101 to:
% 23.38/7.05 | (73) $false
% 23.38/7.05 |
% 23.38/7.05 |-The branch is then unsatisfiable
% 23.38/7.05 |-Branch two:
% 23.38/7.05 | (101) ~ (all_49_0_33 = 0)
% 23.38/7.05 | (396) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.05 |
% 23.38/7.05 +-Applying beta-rule and splitting (238), into two cases.
% 23.38/7.05 |-Branch one:
% 23.38/7.05 | (257) all_51_0_35 = 0
% 23.38/7.05 |
% 23.38/7.05 | Equations (257) can reduce 105 to:
% 23.38/7.05 | (73) $false
% 23.38/7.05 |
% 23.38/7.05 |-The branch is then unsatisfiable
% 23.38/7.05 |-Branch two:
% 23.38/7.05 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.05 | (400) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.05 |
% 23.38/7.05 +-Applying beta-rule and splitting (225), into two cases.
% 23.38/7.05 |-Branch one:
% 23.38/7.05 | (261) all_47_0_31 = 0
% 23.38/7.05 |
% 23.38/7.05 | Equations (261) can reduce 97 to:
% 23.38/7.05 | (73) $false
% 23.38/7.05 |
% 23.38/7.05 |-The branch is then unsatisfiable
% 23.38/7.05 |-Branch two:
% 23.38/7.05 | (97) ~ (all_47_0_31 = 0)
% 23.38/7.05 | (404) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.05 |
% 23.38/7.05 +-Applying beta-rule and splitting (226), into two cases.
% 23.38/7.05 |-Branch one:
% 23.38/7.05 | (261) all_47_0_31 = 0
% 23.38/7.05 |
% 23.38/7.05 | Equations (261) can reduce 97 to:
% 23.38/7.05 | (73) $false
% 23.38/7.05 |
% 23.38/7.05 |-The branch is then unsatisfiable
% 23.38/7.05 |-Branch two:
% 23.38/7.05 | (97) ~ (all_47_0_31 = 0)
% 23.38/7.05 | (408) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0))
% 23.38/7.05 |
% 23.38/7.05 +-Applying beta-rule and splitting (229), into two cases.
% 23.38/7.05 |-Branch one:
% 23.38/7.05 | (261) all_47_0_31 = 0
% 23.38/7.05 |
% 23.38/7.05 | Equations (261) can reduce 97 to:
% 23.38/7.05 | (73) $false
% 23.38/7.05 |
% 23.38/7.05 |-The branch is then unsatisfiable
% 23.38/7.05 |-Branch two:
% 23.38/7.05 | (97) ~ (all_47_0_31 = 0)
% 23.38/7.05 | (412) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.05 |
% 23.38/7.05 +-Applying beta-rule and splitting (227), into two cases.
% 23.38/7.05 |-Branch one:
% 23.38/7.05 | (261) all_47_0_31 = 0
% 23.38/7.05 |
% 23.38/7.05 | Equations (261) can reduce 97 to:
% 23.38/7.05 | (73) $false
% 23.38/7.05 |
% 23.38/7.05 |-The branch is then unsatisfiable
% 23.38/7.05 |-Branch two:
% 23.38/7.05 | (97) ~ (all_47_0_31 = 0)
% 23.38/7.05 | (416) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (228), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (261) all_47_0_31 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (261) can reduce 97 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (97) ~ (all_47_0_31 = 0)
% 23.38/7.06 | (420) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (234), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (249) all_53_0_37 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (249) can reduce 109 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (109) ~ (all_53_0_37 = 0)
% 23.38/7.06 | (424) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (235), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (428) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (237), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (432) all_47_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (207), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (249) all_53_0_37 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (249) can reduce 109 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (109) ~ (all_53_0_37 = 0)
% 23.38/7.06 | (436) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = v0)
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (208), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (440) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (209), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (444) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (210), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (448) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (213), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (452) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (211), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (456) all_22_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (212), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (460) all_20_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (214), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (257) all_51_0_35 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (257) can reduce 105 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.06 | (464) all_49_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (219), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (249) all_53_0_37 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (249) can reduce 109 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (109) ~ (all_53_0_37 = 0)
% 23.38/7.06 | (468) all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (220), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (249) all_53_0_37 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (249) can reduce 109 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (109) ~ (all_53_0_37 = 0)
% 23.38/7.06 | (472) all_51_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (272), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (120) all_22_0_28 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (120) can reduce 63 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (63) ~ (all_22_0_28 = 0)
% 23.38/7.06 | (476) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (276), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (120) all_22_0_28 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (120) can reduce 63 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (63) ~ (all_22_0_28 = 0)
% 23.38/7.06 | (480) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06 |
% 23.38/7.06 +-Applying beta-rule and splitting (300), into two cases.
% 23.38/7.06 |-Branch one:
% 23.38/7.06 | (120) all_22_0_28 = 0
% 23.38/7.06 |
% 23.38/7.06 | Equations (120) can reduce 63 to:
% 23.38/7.06 | (73) $false
% 23.38/7.06 |
% 23.38/7.06 |-The branch is then unsatisfiable
% 23.38/7.06 |-Branch two:
% 23.38/7.06 | (63) ~ (all_22_0_28 = 0)
% 23.38/7.06 | (484) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (304), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (120) all_22_0_28 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (120) can reduce 63 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (63) ~ (all_22_0_28 = 0)
% 23.38/7.07 | (488) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (324), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (124) all_20_0_26 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (124) can reduce 59 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.07 | (492) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (348), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (257) all_51_0_35 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (257) can reduce 105 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.07 | (496) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (360), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (124) all_20_0_26 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (124) can reduce 59 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.07 | (500) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (364), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (124) all_20_0_26 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (124) can reduce 59 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.07 | (504) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (368), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (120) all_22_0_28 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (120) can reduce 63 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (63) ~ (all_22_0_28 = 0)
% 23.38/7.07 | (508) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (380), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (124) all_20_0_26 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (124) can reduce 59 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.07 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (388), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (124) all_20_0_26 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (124) can reduce 59 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.07 | (516) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (404), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (120) all_22_0_28 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (120) can reduce 63 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (63) ~ (all_22_0_28 = 0)
% 23.38/7.07 | (520) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (408), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (124) all_20_0_26 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (124) can reduce 59 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.07 | (524) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (416), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (124) all_20_0_26 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (124) can reduce 59 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.07 | (528) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (436), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (72) all_0_4_4 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (72) can reduce 45 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (45) ~ (all_0_4_4 = 0)
% 23.38/7.07 | (532) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = v0)
% 23.38/7.07 |
% 23.38/7.07 | Instantiating (532) with all_418_0_790 yields:
% 23.38/7.07 | (533) ~ (all_418_0_790 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = all_418_0_790
% 23.38/7.07 |
% 23.38/7.07 | Applying alpha-rule on (533) yields:
% 23.38/7.07 | (534) ~ (all_418_0_790 = 0)
% 23.38/7.07 | (535) apart_point_and_line(all_0_1_1, all_0_6_6) = all_418_0_790
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (440), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (120) all_22_0_28 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (120) can reduce 63 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (63) ~ (all_22_0_28 = 0)
% 23.38/7.07 | (539) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07 |
% 23.38/7.07 | Instantiating (539) with all_423_0_791 yields:
% 23.38/7.07 | (540) (all_423_0_791 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_423_0_791 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (all_423_0_791 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791) | ( ~ (all_423_0_791 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_423_0_791)
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (460), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (124) all_20_0_26 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (124) can reduce 59 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.07 | (544) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (468), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (257) all_51_0_35 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (257) can reduce 105 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.07 | (548) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.38/7.07 |
% 23.38/7.07 +-Applying beta-rule and splitting (472), into two cases.
% 23.38/7.07 |-Branch one:
% 23.38/7.07 | (257) all_51_0_35 = 0
% 23.38/7.07 |
% 23.38/7.07 | Equations (257) can reduce 105 to:
% 23.38/7.07 | (73) $false
% 23.38/7.07 |
% 23.38/7.07 |-The branch is then unsatisfiable
% 23.38/7.07 |-Branch two:
% 23.38/7.07 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.08 | (552) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (164), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (553) (all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0)
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (553), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (554) all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0
% 23.38/7.08 |
% 23.38/7.08 | Applying alpha-rule on (554) yields:
% 23.38/7.08 | (555) all_110_0_51 = 0
% 23.38/7.08 | (556) apart_point_and_line(all_0_1_1, all_0_6_6) = 0
% 23.38/7.08 |
% 23.38/7.08 | Instantiating formula (43) with all_0_1_1, all_0_6_6, 0, all_418_0_790 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_418_0_790, apart_point_and_line(all_0_1_1, all_0_6_6) = 0, yields:
% 23.38/7.08 | (557) all_418_0_790 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (557) can reduce 534 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (559) all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0
% 23.38/7.08 |
% 23.38/7.08 | Applying alpha-rule on (559) yields:
% 23.38/7.08 | (555) all_110_0_51 = 0
% 23.38/7.08 | (561) apart_point_and_line(all_0_1_1, all_0_7_7) = 0
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (352), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (257) all_51_0_35 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (257) can reduce 105 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (105) ~ (all_51_0_35 = 0)
% 23.38/7.08 | (565) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0))
% 23.38/7.08 |
% 23.38/7.08 | Instantiating formula (43) with all_0_1_1, all_0_7_7, 0, all_51_0_35 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_1_1, all_0_7_7) = 0, yields:
% 23.38/7.08 | (257) all_51_0_35 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (257) can reduce 105 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (568) ~ (all_110_0_51 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51
% 23.38/7.08 |
% 23.38/7.08 | Applying alpha-rule on (568) yields:
% 23.38/7.08 | (569) ~ (all_110_0_51 = 0)
% 23.38/7.08 | (570) distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (296), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (124) all_20_0_26 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (124) can reduce 59 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.08 | (574) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (356), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (124) all_20_0_26 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (124) can reduce 59 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.08 | (578) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (396), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (124) all_20_0_26 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (124) can reduce 59 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.08 | (582) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (412), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (124) all_20_0_26 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (124) can reduce 59 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.08 | (586) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (420), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (124) all_20_0_26 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (124) can reduce 59 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (59) ~ (all_20_0_26 = 0)
% 23.38/7.08 | (590) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (540), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (591) (all_423_0_791 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_423_0_791 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (all_423_0_791 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791)
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (591), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (592) (all_423_0_791 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_423_0_791 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0)
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (592), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (593) all_423_0_791 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0
% 23.38/7.08 |
% 23.38/7.08 | Applying alpha-rule on (593) yields:
% 23.38/7.08 | (594) all_423_0_791 = 0
% 23.38/7.08 | (556) apart_point_and_line(all_0_1_1, all_0_6_6) = 0
% 23.38/7.08 |
% 23.38/7.08 | Instantiating formula (43) with all_0_1_1, all_0_6_6, 0, all_418_0_790 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_418_0_790, apart_point_and_line(all_0_1_1, all_0_6_6) = 0, yields:
% 23.38/7.08 | (557) all_418_0_790 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (557) can reduce 534 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (598) all_423_0_791 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 23.38/7.08 |
% 23.38/7.08 | Applying alpha-rule on (598) yields:
% 23.38/7.08 | (594) all_423_0_791 = 0
% 23.38/7.08 | (600) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 23.38/7.08 |
% 23.38/7.08 | Instantiating formula (43) with all_0_2_2, all_0_7_7, 0, all_20_0_26 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 23.38/7.08 | (124) all_20_0_26 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (124) can reduce 59 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (603) ~ (all_423_0_791 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791
% 23.38/7.08 |
% 23.38/7.08 | Applying alpha-rule on (603) yields:
% 23.38/7.08 | (604) ~ (all_423_0_791 = 0)
% 23.38/7.08 | (605) distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791
% 23.38/7.08 |
% 23.38/7.08 | Instantiating formula (17) with all_0_6_6, all_0_7_7, all_110_0_51, all_423_0_791 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791, distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51, yields:
% 23.38/7.08 | (606) all_423_0_791 = all_110_0_51
% 23.38/7.08 |
% 23.38/7.08 | Equations (606) can reduce 604 to:
% 23.38/7.08 | (569) ~ (all_110_0_51 = 0)
% 23.38/7.08 |
% 23.38/7.08 | From (606) and (605) follows:
% 23.38/7.08 | (570) distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51
% 23.38/7.08 |
% 23.38/7.08 | Instantiating formula (5) with all_110_0_51, all_0_7_7, all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51, yields:
% 23.38/7.08 | (609) all_110_0_51 = 0 | convergent_lines(all_0_7_7, all_0_7_7) = 0
% 23.38/7.08 |
% 23.38/7.08 +-Applying beta-rule and splitting (609), into two cases.
% 23.38/7.08 |-Branch one:
% 23.38/7.08 | (610) convergent_lines(all_0_7_7, all_0_7_7) = 0
% 23.38/7.08 |
% 23.38/7.08 | Instantiating formula (3) with all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_7_7) = 0, yields:
% 23.38/7.08 | (611) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (612) ~ (convergent_lines(all_0_7_7, all_0_7_7) = 0)
% 23.38/7.08 | (555) all_110_0_51 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (555) can reduce 569 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.08 |-Branch two:
% 23.38/7.08 | (615) ~ (all_423_0_791 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_423_0_791
% 23.38/7.08 |
% 23.38/7.08 | Applying alpha-rule on (615) yields:
% 23.38/7.08 | (604) ~ (all_423_0_791 = 0)
% 23.38/7.08 | (617) distinct_points(all_0_2_2, all_0_1_1) = all_423_0_791
% 23.38/7.08 |
% 23.38/7.08 | Instantiating formula (14) with all_0_2_2, all_0_1_1, all_423_0_791, 0 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_423_0_791, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 23.38/7.08 | (594) all_423_0_791 = 0
% 23.38/7.08 |
% 23.38/7.08 | Equations (594) can reduce 604 to:
% 23.38/7.08 | (73) $false
% 23.38/7.08 |
% 23.38/7.08 |-The branch is then unsatisfiable
% 23.38/7.09 |-Branch two:
% 23.38/7.09 | (620) ~ (all_56_0_40 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_56_0_40
% 23.38/7.09 |
% 23.38/7.09 | Applying alpha-rule on (620) yields:
% 23.38/7.09 | (118) ~ (all_56_0_40 = 0)
% 23.38/7.09 | (622) convergent_lines(all_0_7_7, all_0_5_5) = all_56_0_40
% 23.38/7.09 |
% 23.38/7.09 | Instantiating formula (19) with all_0_7_7, all_0_5_5, all_56_0_40, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = all_56_0_40, convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 23.38/7.09 | (623) all_56_0_40 = 0
% 23.38/7.09 |
% 23.38/7.09 | Equations (623) can reduce 118 to:
% 23.38/7.09 | (73) $false
% 23.38/7.09 |
% 23.38/7.09 |-The branch is then unsatisfiable
% 23.38/7.09 |-Branch two:
% 23.38/7.09 | (625) ~ (all_55_0_39 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_55_0_39
% 23.38/7.09 |
% 23.38/7.09 | Applying alpha-rule on (625) yields:
% 23.38/7.09 | (115) ~ (all_55_0_39 = 0)
% 23.38/7.09 | (627) convergent_lines(all_0_7_7, all_0_5_5) = all_55_0_39
% 23.38/7.09 |
% 23.38/7.09 | Instantiating formula (19) with all_0_7_7, all_0_5_5, all_55_0_39, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = all_55_0_39, convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 23.38/7.09 | (628) all_55_0_39 = 0
% 23.38/7.09 |
% 23.38/7.09 | Equations (628) can reduce 115 to:
% 23.38/7.09 | (73) $false
% 23.38/7.09 |
% 23.38/7.09 |-The branch is then unsatisfiable
% 23.38/7.09 |-Branch two:
% 23.38/7.09 | (630) ~ (all_0_3_3 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3
% 23.38/7.09 |
% 23.38/7.09 | Applying alpha-rule on (630) yields:
% 23.38/7.09 | (631) ~ (all_0_3_3 = 0)
% 23.38/7.09 | (632) convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3
% 23.38/7.09 |
% 23.38/7.09 | Instantiating formula (19) with all_0_7_7, all_0_5_5, 0, all_0_3_3 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3, convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 23.38/7.09 | (633) all_0_3_3 = 0
% 23.38/7.09 |
% 23.38/7.09 | Equations (633) can reduce 631 to:
% 23.38/7.09 | (73) $false
% 23.38/7.09 |
% 23.38/7.09 |-The branch is then unsatisfiable
% 23.38/7.09 |-Branch two:
% 23.38/7.09 | (635) ~ (convergent_lines(all_0_7_7, all_0_5_5) = 0)
% 23.38/7.09 | (72) all_0_4_4 = 0
% 23.38/7.09 |
% 23.38/7.09 | Equations (72) can reduce 45 to:
% 23.38/7.09 | (73) $false
% 23.38/7.09 |
% 23.38/7.09 |-The branch is then unsatisfiable
% 23.38/7.09 % SZS output end Proof for theBenchmark
% 23.38/7.09
% 23.38/7.09 6497ms
%------------------------------------------------------------------------------