TSTP Solution File: GEO180+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO180+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:17 EDT 2022
% Result : Theorem 4.90s 1.89s
% Output : Proof 9.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO180+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 04:06:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.51/0.62 ____ _
% 0.51/0.62 ___ / __ \_____(_)___ ________ __________
% 0.51/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.62
% 0.51/0.62 A Theorem Prover for First-Order Logic
% 0.51/0.63 (ePrincess v.1.0)
% 0.51/0.63
% 0.51/0.63 (c) Philipp Rümmer, 2009-2015
% 0.51/0.63 (c) Peter Backeman, 2014-2015
% 0.51/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.63 Bug reports to peter@backeman.se
% 0.51/0.63
% 0.51/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.63
% 0.51/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.96 Prover 0: Preprocessing ...
% 1.96/1.11 Prover 0: Warning: ignoring some quantifiers
% 2.09/1.14 Prover 0: Constructing countermodel ...
% 2.69/1.36 Prover 0: gave up
% 2.69/1.36 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.84/1.39 Prover 1: Preprocessing ...
% 3.30/1.49 Prover 1: Constructing countermodel ...
% 3.52/1.55 Prover 1: gave up
% 3.52/1.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.64/1.57 Prover 2: Preprocessing ...
% 4.27/1.69 Prover 2: Warning: ignoring some quantifiers
% 4.27/1.70 Prover 2: Constructing countermodel ...
% 4.90/1.89 Prover 2: proved (341ms)
% 4.90/1.89
% 4.90/1.89 No countermodel exists, formula is valid
% 4.90/1.89 % SZS status Theorem for theBenchmark
% 4.90/1.89
% 4.90/1.89 Generating proof ... Warning: ignoring some quantifiers
% 8.48/2.67 found it (size 232)
% 8.48/2.67
% 8.48/2.67 % SZS output start Proof for theBenchmark
% 8.48/2.67 Assumed formulas after preprocessing and simplification:
% 8.48/2.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v1) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v0, v4) = v5 & distinct_points(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8)
% 8.48/2.71 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 8.48/2.71 | (1) ~ (all_0_0_0 = 0) & line_connecting(all_0_3_3, all_0_4_4) = all_0_1_1 & line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 8.48/2.73 |
% 8.48/2.73 | Applying alpha-rule on (1) yields:
% 8.48/2.73 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 8.48/2.73 | (3) ! [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))
% 8.48/2.73 | (4) ! [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))
% 8.48/2.73 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 8.48/2.73 | (6) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 8.48/2.73 | (7) ! [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)))
% 8.48/2.73 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 8.48/2.73 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 8.48/2.73 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 8.48/2.73 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 8.48/2.73 | (12) ! [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)))
% 8.48/2.74 | (13) ! [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)
% 8.48/2.74 | (14) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 8.48/2.74 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 8.48/2.74 | (16) ! [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)))
% 8.48/2.74 | (17) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 8.48/2.74 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 8.48/2.74 | (19) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 8.48/2.74 | (20) ! [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)
% 8.48/2.74 | (21) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 8.48/2.74 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 8.48/2.74 | (23) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 8.48/2.74 | (24) ~ (all_0_0_0 = 0)
% 8.48/2.74 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 8.48/2.74 | (26) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 8.48/2.74 | (27) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 8.48/2.74 | (28) ! [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))
% 8.48/2.74 | (29) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 8.48/2.74 | (30) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 8.48/2.74 | (31) ! [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)))
% 8.48/2.74 | (32) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 8.48/2.74 | (33) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 8.48/2.74 | (34) distinct_points(all_0_5_5, all_0_4_4) = 0
% 8.48/2.74 | (35) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 8.48/2.74 | (36) ! [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)))
% 8.48/2.74 | (37) ! [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)
% 8.48/2.74 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 8.48/2.74 | (39) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 8.48/2.75 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 8.48/2.75 | (41) ! [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)))
% 8.48/2.75 | (42) ! [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)))
% 8.48/2.75 | (43) ! [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))
% 8.48/2.75 | (44) ! [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)))
% 8.48/2.75 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 8.48/2.75 | (46) ! [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))
% 8.48/2.75 | (47) line_connecting(all_0_3_3, all_0_4_4) = all_0_1_1
% 8.48/2.75 | (48) ! [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))
% 8.48/2.75 | (49) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 8.48/2.75 | (50) apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0
% 8.48/2.75 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 8.48/2.75 | (52) ! [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)))
% 8.48/2.75 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 8.48/2.75 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 8.48/2.75 | (55) ! [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)
% 8.48/2.75 |
% 8.48/2.75 | Instantiating formula (44) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_4_4) = all_0_1_1, yields:
% 8.48/2.75 | (56) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 8.48/2.75 |
% 8.48/2.75 | Instantiating formula (52) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_4_4) = all_0_1_1, yields:
% 8.48/2.75 | (57) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 8.48/2.75 |
% 8.48/2.75 | Instantiating formula (44) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 8.48/2.75 | (58) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.48/2.75 |
% 8.48/2.75 | Instantiating formula (52) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 8.48/2.75 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.48/2.76 |
% 8.48/2.76 | Instantiating formula (31) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_1_1, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields:
% 8.48/2.76 | (60) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.48/2.76 |
% 8.48/2.76 | Instantiating formula (7) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.48/2.76 | (61) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 8.48/2.76 |
% 8.48/2.76 | Instantiating formula (21) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.48/2.76 | (62) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 8.48/2.76 |
% 8.48/2.76 | Instantiating formula (17) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.48/2.76 | (63) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 8.48/2.76 |
% 8.48/2.76 | Instantiating (63) with all_20_0_24, all_20_1_25 yields:
% 8.48/2.76 | (64) ~ (all_20_0_24 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25 & apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 8.48/2.76 |
% 8.48/2.76 | Applying alpha-rule on (64) yields:
% 8.48/2.76 | (65) ~ (all_20_0_24 = 0)
% 8.48/2.76 | (66) line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25
% 8.48/2.76 | (67) apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 8.48/2.76 |
% 8.48/2.76 | Instantiating (62) with all_22_0_26, all_22_1_27 yields:
% 8.48/2.76 | (68) ~ (all_22_0_26 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27 & apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26
% 8.48/2.76 |
% 8.48/2.76 | Applying alpha-rule on (68) yields:
% 8.48/2.76 | (69) ~ (all_22_0_26 = 0)
% 8.48/2.76 | (70) line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27
% 8.48/2.76 | (71) apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26
% 8.48/2.76 |
% 8.48/2.76 | Instantiating (59) with all_24_0_28 yields:
% 8.48/2.76 | (72) ( ~ (all_24_0_28 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28) | ( ~ (all_24_0_28 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28)
% 8.48/2.76 |
% 8.48/2.76 | Instantiating (58) with all_25_0_29 yields:
% 8.48/2.76 | (73) ( ~ (all_25_0_29 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29) | ( ~ (all_25_0_29 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29)
% 8.98/2.76 |
% 8.98/2.76 | Instantiating (57) with all_26_0_30 yields:
% 8.98/2.76 | (74) ( ~ (all_26_0_30 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30) | ( ~ (all_26_0_30 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_26_0_30)
% 8.98/2.76 |
% 8.98/2.76 | Instantiating (56) with all_27_0_31 yields:
% 8.98/2.76 | (75) ( ~ (all_27_0_31 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = all_27_0_31) | ( ~ (all_27_0_31 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_27_0_31)
% 8.98/2.76 |
% 8.98/2.76 +-Applying beta-rule and splitting (72), into two cases.
% 8.98/2.76 |-Branch one:
% 8.98/2.76 | (76) ~ (all_24_0_28 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28
% 8.98/2.76 |
% 8.98/2.76 | Applying alpha-rule on (76) yields:
% 8.98/2.76 | (77) ~ (all_24_0_28 = 0)
% 8.98/2.76 | (78) apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28
% 8.98/2.76 |
% 8.98/2.76 +-Applying beta-rule and splitting (73), into two cases.
% 8.98/2.76 |-Branch one:
% 8.98/2.76 | (79) ~ (all_25_0_29 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29
% 8.98/2.76 |
% 8.98/2.76 | Applying alpha-rule on (79) yields:
% 8.98/2.76 | (80) ~ (all_25_0_29 = 0)
% 8.98/2.76 | (81) apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29
% 8.98/2.76 |
% 8.98/2.76 +-Applying beta-rule and splitting (60), into two cases.
% 8.98/2.76 |-Branch one:
% 8.98/2.76 | (82) all_0_0_0 = 0
% 8.98/2.76 |
% 8.98/2.76 | Equations (82) can reduce 24 to:
% 8.98/2.76 | (83) $false
% 8.98/2.76 |
% 8.98/2.76 |-The branch is then unsatisfiable
% 8.98/2.76 |-Branch two:
% 8.98/2.76 | (24) ~ (all_0_0_0 = 0)
% 8.98/2.76 | (85) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.98/2.76 |
% 8.98/2.76 +-Applying beta-rule and splitting (61), into two cases.
% 8.98/2.76 |-Branch one:
% 8.98/2.76 | (82) all_0_0_0 = 0
% 8.98/2.76 |
% 8.98/2.76 | Equations (82) can reduce 24 to:
% 8.98/2.76 | (83) $false
% 8.98/2.76 |
% 8.98/2.76 |-The branch is then unsatisfiable
% 8.98/2.76 |-Branch two:
% 8.98/2.76 | (24) ~ (all_0_0_0 = 0)
% 8.98/2.76 | (89) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 8.98/2.76 |
% 8.98/2.76 | Instantiating formula (40) with all_0_5_5, all_0_4_4, all_22_1_27, all_0_2_2 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27, line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 8.98/2.76 | (90) all_22_1_27 = all_0_2_2
% 8.98/2.76 |
% 8.98/2.76 | Instantiating formula (40) with all_0_5_5, all_0_4_4, all_20_1_25, all_22_1_27 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27, line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25, yields:
% 8.98/2.77 | (91) all_22_1_27 = all_20_1_25
% 8.98/2.77 |
% 8.98/2.77 | Combining equations (90,91) yields a new equation:
% 8.98/2.77 | (92) all_20_1_25 = all_0_2_2
% 8.98/2.77 |
% 8.98/2.77 | Combining equations (92,91) yields a new equation:
% 8.98/2.77 | (90) all_22_1_27 = all_0_2_2
% 8.98/2.77 |
% 8.98/2.77 | From (90) and (71) follows:
% 8.98/2.77 | (94) apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26
% 8.98/2.77 |
% 8.98/2.77 | From (92) and (67) follows:
% 8.98/2.77 | (95) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (8) with all_0_4_4, all_0_2_2, all_22_0_26, all_25_0_29 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 8.98/2.77 | (96) all_25_0_29 = all_22_0_26
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (8) with all_0_5_5, all_0_2_2, all_20_0_24, all_24_0_28 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.77 | (97) all_24_0_28 = all_20_0_24
% 8.98/2.77 |
% 8.98/2.77 | Equations (96) can reduce 80 to:
% 8.98/2.77 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.77 |
% 8.98/2.77 | Equations (97) can reduce 77 to:
% 8.98/2.77 | (65) ~ (all_20_0_24 = 0)
% 8.98/2.77 |
% 8.98/2.77 | From (96) and (81) follows:
% 8.98/2.77 | (94) apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26
% 8.98/2.77 |
% 8.98/2.77 | From (97) and (78) follows:
% 8.98/2.77 | (95) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (37) with all_22_0_26, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = 0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 8.98/2.77 | (102) all_22_0_26 = 0 | distinct_points(all_0_3_3, all_0_4_4) = 0
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (31) with all_22_0_26, all_0_0_0, all_0_2_2, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields:
% 8.98/2.77 | (103) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (31) with all_0_0_0, all_22_0_26, all_0_1_1, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields:
% 8.98/2.77 | (104) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (41) with all_22_0_26, all_0_0_0, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields:
% 8.98/2.77 | (105) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (41) with all_0_0_0, all_22_0_26, all_0_2_2, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields:
% 8.98/2.77 | (106) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (42) with all_22_0_26, all_22_0_26, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.98/2.77 | (107) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 8.98/2.77 |
% 8.98/2.77 | Instantiating formula (31) with all_22_0_26, all_22_0_26, all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 8.98/2.77 | (108) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 8.98/2.78 |
% 8.98/2.78 | Instantiating formula (7) with all_20_0_24, all_0_0_0, all_0_2_2, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.98/2.78 | (109) all_20_0_24 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 8.98/2.78 |
% 8.98/2.78 | Instantiating formula (7) with all_0_0_0, all_20_0_24, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.98/2.78 | (110) all_20_0_24 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 8.98/2.78 |
% 8.98/2.78 | Instantiating formula (31) with all_20_0_24, all_0_0_0, all_0_2_2, all_0_1_1, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.78 | (111) all_20_0_24 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.98/2.78 |
% 8.98/2.78 | Instantiating formula (31) with all_0_0_0, all_20_0_24, all_0_1_1, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.78 | (112) all_20_0_24 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.98/2.78 |
% 8.98/2.78 | Instantiating formula (31) with all_20_0_24, all_22_0_26, all_0_2_2, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.78 | (113) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.98/2.78 |
% 8.98/2.78 | Instantiating formula (31) with all_22_0_26, all_20_0_24, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.78 | (114) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.98/2.78 |
% 8.98/2.78 | Instantiating formula (7) with all_20_0_24, all_20_0_24, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.98/2.78 | (115) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 8.98/2.78 |
% 8.98/2.78 | Instantiating formula (31) with all_20_0_24, all_20_0_24, all_0_2_2, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.78 | (116) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.98/2.78 |
% 8.98/2.78 +-Applying beta-rule and splitting (74), into two cases.
% 8.98/2.78 |-Branch one:
% 8.98/2.78 | (117) ~ (all_26_0_30 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30
% 8.98/2.78 |
% 8.98/2.78 | Applying alpha-rule on (117) yields:
% 8.98/2.78 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.78 | (119) apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30
% 8.98/2.78 |
% 8.98/2.78 +-Applying beta-rule and splitting (107), into two cases.
% 8.98/2.78 |-Branch one:
% 8.98/2.78 | (120) all_22_0_26 = 0
% 8.98/2.78 |
% 8.98/2.78 | Equations (120) can reduce 69 to:
% 8.98/2.78 | (83) $false
% 8.98/2.78 |
% 8.98/2.78 |-The branch is then unsatisfiable
% 8.98/2.78 |-Branch two:
% 8.98/2.78 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.78 | (123) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 8.98/2.78 |
% 8.98/2.78 +-Applying beta-rule and splitting (108), into two cases.
% 8.98/2.78 |-Branch one:
% 8.98/2.78 | (120) all_22_0_26 = 0
% 8.98/2.78 |
% 8.98/2.78 | Equations (120) can reduce 69 to:
% 8.98/2.78 | (83) $false
% 8.98/2.78 |
% 8.98/2.78 |-The branch is then unsatisfiable
% 8.98/2.78 |-Branch two:
% 8.98/2.78 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.78 | (127) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 8.98/2.78 |
% 8.98/2.78 +-Applying beta-rule and splitting (106), into two cases.
% 8.98/2.78 |-Branch one:
% 8.98/2.78 | (120) all_22_0_26 = 0
% 8.98/2.78 |
% 8.98/2.78 | Equations (120) can reduce 69 to:
% 8.98/2.78 | (83) $false
% 8.98/2.78 |
% 8.98/2.78 |-The branch is then unsatisfiable
% 8.98/2.78 |-Branch two:
% 8.98/2.78 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.78 | (131) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.98/2.78 |
% 8.98/2.78 +-Applying beta-rule and splitting (115), into two cases.
% 8.98/2.78 |-Branch one:
% 8.98/2.78 | (132) all_20_0_24 = 0
% 8.98/2.78 |
% 8.98/2.78 | Equations (132) can reduce 65 to:
% 8.98/2.78 | (83) $false
% 8.98/2.78 |
% 8.98/2.78 |-The branch is then unsatisfiable
% 8.98/2.78 |-Branch two:
% 8.98/2.78 | (65) ~ (all_20_0_24 = 0)
% 8.98/2.78 | (135) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (116), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (132) all_20_0_24 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (132) can reduce 65 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (65) ~ (all_20_0_24 = 0)
% 8.98/2.79 | (139) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (111), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (132) all_20_0_24 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (132) can reduce 65 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (65) ~ (all_20_0_24 = 0)
% 8.98/2.79 | (143) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (114), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (120) all_22_0_26 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (120) can reduce 69 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.79 | (147) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (113), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (120) all_22_0_26 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (120) can reduce 69 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.79 | (151) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (109), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (132) all_20_0_24 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (132) can reduce 65 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (65) ~ (all_20_0_24 = 0)
% 8.98/2.79 | (155) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (110), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (132) all_20_0_24 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (132) can reduce 65 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (65) ~ (all_20_0_24 = 0)
% 8.98/2.79 | (159) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (112), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (132) all_20_0_24 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (132) can reduce 65 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (65) ~ (all_20_0_24 = 0)
% 8.98/2.79 | (163) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (131), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (82) all_0_0_0 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (82) can reduce 24 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (24) ~ (all_0_0_0 = 0)
% 8.98/2.79 | (167) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (102), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (168) distinct_points(all_0_3_3, all_0_4_4) = 0
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (163), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (82) all_0_0_0 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (82) can reduce 24 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (24) ~ (all_0_0_0 = 0)
% 8.98/2.79 | (172) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (75), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (173) ~ (all_27_0_31 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = all_27_0_31
% 8.98/2.79 |
% 8.98/2.79 | Applying alpha-rule on (173) yields:
% 8.98/2.79 | (174) ~ (all_27_0_31 = 0)
% 8.98/2.79 | (175) apart_point_and_line(all_0_4_4, all_0_1_1) = all_27_0_31
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (159), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (82) all_0_0_0 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (82) can reduce 24 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (24) ~ (all_0_0_0 = 0)
% 8.98/2.79 | (179) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 8.98/2.79 |
% 8.98/2.79 | Instantiating (179) with all_131_0_61 yields:
% 8.98/2.79 | (180) (all_131_0_61 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_131_0_61 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_131_0_61 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_131_0_61)
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (180), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (181) (all_131_0_61 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_131_0_61 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (181), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (182) all_131_0_61 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 8.98/2.79 |
% 8.98/2.79 | Applying alpha-rule on (182) yields:
% 8.98/2.79 | (183) all_131_0_61 = 0
% 8.98/2.79 | (184) apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 8.98/2.79 |
% 8.98/2.79 | Instantiating formula (8) with all_0_4_4, all_0_1_1, 0, all_27_0_31 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_27_0_31, apart_point_and_line(all_0_4_4, all_0_1_1) = 0, yields:
% 8.98/2.79 | (185) all_27_0_31 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (185) can reduce 174 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (187) all_131_0_61 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 8.98/2.79 |
% 8.98/2.79 | Applying alpha-rule on (187) yields:
% 8.98/2.79 | (183) all_131_0_61 = 0
% 8.98/2.79 | (189) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 8.98/2.79 |
% 8.98/2.79 +-Applying beta-rule and splitting (103), into two cases.
% 8.98/2.79 |-Branch one:
% 8.98/2.79 | (120) all_22_0_26 = 0
% 8.98/2.79 |
% 8.98/2.79 | Equations (120) can reduce 69 to:
% 8.98/2.79 | (83) $false
% 8.98/2.79 |
% 8.98/2.79 |-The branch is then unsatisfiable
% 8.98/2.79 |-Branch two:
% 8.98/2.79 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.79 | (193) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.98/2.80 |
% 8.98/2.80 +-Applying beta-rule and splitting (104), into two cases.
% 8.98/2.80 |-Branch one:
% 8.98/2.80 | (120) all_22_0_26 = 0
% 8.98/2.80 |
% 8.98/2.80 | Equations (120) can reduce 69 to:
% 8.98/2.80 | (83) $false
% 8.98/2.80 |
% 8.98/2.80 |-The branch is then unsatisfiable
% 8.98/2.80 |-Branch two:
% 8.98/2.80 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.80 | (197) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.98/2.80 |
% 8.98/2.80 +-Applying beta-rule and splitting (105), into two cases.
% 8.98/2.80 |-Branch one:
% 8.98/2.80 | (120) all_22_0_26 = 0
% 8.98/2.80 |
% 8.98/2.80 | Equations (120) can reduce 69 to:
% 8.98/2.80 | (83) $false
% 8.98/2.80 |
% 8.98/2.80 |-The branch is then unsatisfiable
% 8.98/2.80 |-Branch two:
% 8.98/2.80 | (69) ~ (all_22_0_26 = 0)
% 8.98/2.80 | (201) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (8) with all_0_4_4, all_0_2_2, 0, all_22_0_26 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields:
% 8.98/2.80 | (120) all_22_0_26 = 0
% 8.98/2.80 |
% 8.98/2.80 | Equations (120) can reduce 69 to:
% 8.98/2.80 | (83) $false
% 8.98/2.80 |
% 8.98/2.80 |-The branch is then unsatisfiable
% 8.98/2.80 |-Branch two:
% 8.98/2.80 | (204) ~ (all_131_0_61 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_131_0_61
% 8.98/2.80 |
% 8.98/2.80 | Applying alpha-rule on (204) yields:
% 8.98/2.80 | (205) ~ (all_131_0_61 = 0)
% 8.98/2.80 | (206) distinct_lines(all_0_2_2, all_0_1_1) = all_131_0_61
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (31) with all_26_0_30, all_22_0_26, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 8.98/2.80 | (207) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (31) with all_22_0_26, all_26_0_30, all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 8.98/2.80 | (208) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (41) with all_26_0_30, all_22_0_26, all_0_2_2, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 8.98/2.80 | (209) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (41) with all_22_0_26, all_26_0_30, all_0_1_1, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 8.98/2.80 | (210) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (31) with all_26_0_30, all_0_0_0, all_0_1_1, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_1_1) = all_0_0_0, yields:
% 8.98/2.80 | (211) all_26_0_30 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (31) with all_26_0_30, all_20_0_24, all_0_1_1, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.80 | (212) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (31) with all_20_0_24, all_26_0_30, all_0_2_2, all_0_1_1, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.80 | (213) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (41) with all_26_0_30, all_20_0_24, all_0_2_2, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.80 | (214) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (41) with all_20_0_24, all_26_0_30, all_0_1_1, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 8.98/2.80 | (215) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (31) with all_26_0_30, all_26_0_30, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, yields:
% 8.98/2.80 | (216) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (31) with all_26_0_30, all_27_0_31, all_0_1_1, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_1_1) = all_27_0_31, yields:
% 8.98/2.80 | (217) all_27_0_31 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 8.98/2.80 |
% 8.98/2.80 | Instantiating formula (31) with all_27_0_31, all_27_0_31, all_0_1_1, all_0_1_1, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_27_0_31, yields:
% 8.98/2.80 | (218) all_27_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 8.98/2.81 |
% 8.98/2.81 | Instantiating formula (20) with all_131_0_61, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = 0, distinct_lines(all_0_2_2, all_0_1_1) = all_131_0_61, yields:
% 8.98/2.81 | (219) all_131_0_61 = 0 | apart_point_and_line(all_0_3_3, all_0_1_1) = 0
% 8.98/2.81 |
% 8.98/2.81 | Instantiating formula (48) with all_26_0_30, all_131_0_61, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, distinct_lines(all_0_2_2, all_0_1_1) = all_131_0_61, yields:
% 8.98/2.81 | (220) all_131_0_61 = 0 | all_26_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = v0)
% 8.98/2.81 |
% 8.98/2.81 | Instantiating formula (42) with all_22_0_26, all_27_0_31, all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_27_0_31, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, distinct_points(all_0_3_3, all_0_4_4) = 0, yields:
% 8.98/2.81 | (221) all_27_0_31 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 8.98/2.81 |
% 8.98/2.81 | Instantiating formula (42) with all_27_0_31, all_22_0_26, all_0_1_1, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_27_0_31, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, distinct_points(all_0_3_3, all_0_4_4) = 0, yields:
% 8.98/2.81 | (222) all_27_0_31 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (219), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (223) apart_point_and_line(all_0_3_3, all_0_1_1) = 0
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (220), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (183) all_131_0_61 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (183) can reduce 205 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (205) ~ (all_131_0_61 = 0)
% 8.98/2.81 | (227) all_26_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = v0)
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (221), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (185) all_27_0_31 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (185) can reduce 174 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (174) ~ (all_27_0_31 = 0)
% 8.98/2.81 | (231) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (227), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (232) all_26_0_30 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (232) can reduce 118 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.81 | (235) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = v0)
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (216), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (232) all_26_0_30 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (232) can reduce 118 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.81 | (239) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (218), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (185) all_27_0_31 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (185) can reduce 174 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (174) ~ (all_27_0_31 = 0)
% 8.98/2.81 | (243) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (222), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (185) all_27_0_31 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (185) can reduce 174 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (174) ~ (all_27_0_31 = 0)
% 8.98/2.81 | (247) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (208), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (232) all_26_0_30 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (232) can reduce 118 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.81 | (251) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (207), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (232) all_26_0_30 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (232) can reduce 118 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.81 | (255) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (217), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (185) all_27_0_31 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (185) can reduce 174 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (174) ~ (all_27_0_31 = 0)
% 8.98/2.81 | (259) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (212), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (232) all_26_0_30 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (232) can reduce 118 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.81 | (263) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (210), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (232) all_26_0_30 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (232) can reduce 118 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.81 | (267) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (211), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (232) all_26_0_30 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (232) can reduce 118 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.81 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.81 | (271) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 8.98/2.81 |
% 8.98/2.81 +-Applying beta-rule and splitting (213), into two cases.
% 8.98/2.81 |-Branch one:
% 8.98/2.81 | (232) all_26_0_30 = 0
% 8.98/2.81 |
% 8.98/2.81 | Equations (232) can reduce 118 to:
% 8.98/2.81 | (83) $false
% 8.98/2.81 |
% 8.98/2.81 |-The branch is then unsatisfiable
% 8.98/2.81 |-Branch two:
% 8.98/2.82 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.82 | (275) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 8.98/2.82 |
% 8.98/2.82 +-Applying beta-rule and splitting (209), into two cases.
% 8.98/2.82 |-Branch one:
% 8.98/2.82 | (232) all_26_0_30 = 0
% 8.98/2.82 |
% 8.98/2.82 | Equations (232) can reduce 118 to:
% 8.98/2.82 | (83) $false
% 8.98/2.82 |
% 8.98/2.82 |-The branch is then unsatisfiable
% 8.98/2.82 |-Branch two:
% 8.98/2.82 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.82 | (279) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 8.98/2.82 |
% 8.98/2.82 +-Applying beta-rule and splitting (214), into two cases.
% 8.98/2.82 |-Branch one:
% 8.98/2.82 | (232) all_26_0_30 = 0
% 8.98/2.82 |
% 8.98/2.82 | Equations (232) can reduce 118 to:
% 8.98/2.82 | (83) $false
% 8.98/2.82 |
% 8.98/2.82 |-The branch is then unsatisfiable
% 8.98/2.82 |-Branch two:
% 8.98/2.82 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.82 | (283) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 8.98/2.82 |
% 8.98/2.82 +-Applying beta-rule and splitting (215), into two cases.
% 8.98/2.82 |-Branch one:
% 8.98/2.82 | (232) all_26_0_30 = 0
% 8.98/2.82 |
% 8.98/2.82 | Equations (232) can reduce 118 to:
% 8.98/2.82 | (83) $false
% 8.98/2.82 |
% 8.98/2.82 |-The branch is then unsatisfiable
% 8.98/2.82 |-Branch two:
% 8.98/2.82 | (118) ~ (all_26_0_30 = 0)
% 8.98/2.82 | (287) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 9.21/2.82 |
% 9.21/2.82 +-Applying beta-rule and splitting (259), into two cases.
% 9.21/2.82 |-Branch one:
% 9.21/2.82 | (232) all_26_0_30 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (232) can reduce 118 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (118) ~ (all_26_0_30 = 0)
% 9.21/2.82 | (291) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 9.21/2.82 |
% 9.21/2.82 | Instantiating formula (8) with all_0_3_3, all_0_1_1, 0, all_26_0_30 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_3_3, all_0_1_1) = 0, yields:
% 9.21/2.82 | (232) all_26_0_30 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (232) can reduce 118 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (294) ~ (apart_point_and_line(all_0_3_3, all_0_1_1) = 0)
% 9.21/2.82 | (183) all_131_0_61 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (183) can reduce 205 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (297) ~ (all_27_0_31 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_27_0_31
% 9.21/2.82 |
% 9.21/2.82 | Applying alpha-rule on (297) yields:
% 9.21/2.82 | (174) ~ (all_27_0_31 = 0)
% 9.21/2.82 | (299) distinct_points(all_0_3_3, all_0_4_4) = all_27_0_31
% 9.21/2.82 |
% 9.21/2.82 | Instantiating formula (25) with all_0_3_3, all_0_4_4, 0, all_27_0_31 and discharging atoms distinct_points(all_0_3_3, all_0_4_4) = all_27_0_31, distinct_points(all_0_3_3, all_0_4_4) = 0, yields:
% 9.21/2.82 | (185) all_27_0_31 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (185) can reduce 174 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (302) ~ (distinct_points(all_0_3_3, all_0_4_4) = 0)
% 9.21/2.82 | (120) all_22_0_26 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (120) can reduce 69 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (305) ~ (all_26_0_30 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_26_0_30
% 9.21/2.82 |
% 9.21/2.82 | Applying alpha-rule on (305) yields:
% 9.21/2.82 | (118) ~ (all_26_0_30 = 0)
% 9.21/2.82 | (307) distinct_points(all_0_3_3, all_0_4_4) = all_26_0_30
% 9.21/2.82 |
% 9.21/2.82 +-Applying beta-rule and splitting (107), into two cases.
% 9.21/2.82 |-Branch one:
% 9.21/2.82 | (120) all_22_0_26 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (120) can reduce 69 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (69) ~ (all_22_0_26 = 0)
% 9.21/2.82 | (123) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.21/2.82 |
% 9.21/2.82 +-Applying beta-rule and splitting (108), into two cases.
% 9.21/2.82 |-Branch one:
% 9.21/2.82 | (120) all_22_0_26 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (120) can reduce 69 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (69) ~ (all_22_0_26 = 0)
% 9.21/2.82 | (127) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.21/2.82 |
% 9.21/2.82 +-Applying beta-rule and splitting (106), into two cases.
% 9.21/2.82 |-Branch one:
% 9.21/2.82 | (120) all_22_0_26 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (120) can reduce 69 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (69) ~ (all_22_0_26 = 0)
% 9.21/2.82 | (131) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.21/2.82 |
% 9.21/2.82 +-Applying beta-rule and splitting (114), into two cases.
% 9.21/2.82 |-Branch one:
% 9.21/2.82 | (120) all_22_0_26 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (120) can reduce 69 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (69) ~ (all_22_0_26 = 0)
% 9.21/2.82 | (147) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.21/2.82 |
% 9.21/2.82 +-Applying beta-rule and splitting (113), into two cases.
% 9.21/2.82 |-Branch one:
% 9.21/2.82 | (120) all_22_0_26 = 0
% 9.21/2.82 |
% 9.21/2.82 | Equations (120) can reduce 69 to:
% 9.21/2.82 | (83) $false
% 9.21/2.82 |
% 9.21/2.82 |-The branch is then unsatisfiable
% 9.21/2.82 |-Branch two:
% 9.21/2.82 | (69) ~ (all_22_0_26 = 0)
% 9.21/2.82 | (151) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.21/2.82 |
% 9.21/2.82 +-Applying beta-rule and splitting (102), into two cases.
% 9.21/2.82 |-Branch one:
% 9.21/2.82 | (168) distinct_points(all_0_3_3, all_0_4_4) = 0
% 9.21/2.82 |
% 9.21/2.82 | Instantiating formula (25) with all_0_3_3, all_0_4_4, 0, all_26_0_30 and discharging atoms distinct_points(all_0_3_3, all_0_4_4) = all_26_0_30, distinct_points(all_0_3_3, all_0_4_4) = 0, yields:
% 9.21/2.83 | (232) all_26_0_30 = 0
% 9.21/2.83 |
% 9.21/2.83 | Equations (232) can reduce 118 to:
% 9.21/2.83 | (83) $false
% 9.21/2.83 |
% 9.21/2.83 |-The branch is then unsatisfiable
% 9.21/2.83 |-Branch two:
% 9.21/2.83 | (302) ~ (distinct_points(all_0_3_3, all_0_4_4) = 0)
% 9.21/2.83 | (120) all_22_0_26 = 0
% 9.21/2.83 |
% 9.21/2.83 | Equations (120) can reduce 69 to:
% 9.21/2.83 | (83) $false
% 9.21/2.83 |
% 9.21/2.83 |-The branch is then unsatisfiable
% 9.21/2.83 |-Branch two:
% 9.21/2.83 | (334) ~ (all_25_0_29 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29
% 9.21/2.83 |
% 9.21/2.83 | Applying alpha-rule on (334) yields:
% 9.21/2.83 | (80) ~ (all_25_0_29 = 0)
% 9.21/2.83 | (336) distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29
% 9.21/2.83 |
% 9.21/2.83 | Instantiating formula (25) with all_0_5_5, all_0_4_4, all_25_0_29, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 9.21/2.83 | (337) all_25_0_29 = 0
% 9.21/2.83 |
% 9.21/2.83 | Equations (337) can reduce 80 to:
% 9.21/2.83 | (83) $false
% 9.21/2.83 |
% 9.21/2.83 |-The branch is then unsatisfiable
% 9.21/2.83 |-Branch two:
% 9.21/2.83 | (339) ~ (all_24_0_28 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28
% 9.21/2.83 |
% 9.21/2.83 | Applying alpha-rule on (339) yields:
% 9.21/2.83 | (77) ~ (all_24_0_28 = 0)
% 9.21/2.83 | (341) distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28
% 9.21/2.83 |
% 9.21/2.83 | Instantiating formula (25) with all_0_5_5, all_0_4_4, all_24_0_28, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 9.21/2.83 | (342) all_24_0_28 = 0
% 9.21/2.83 |
% 9.21/2.83 | Equations (342) can reduce 77 to:
% 9.21/2.83 | (83) $false
% 9.21/2.83 |
% 9.21/2.83 |-The branch is then unsatisfiable
% 9.21/2.83 % SZS output end Proof for theBenchmark
% 9.21/2.83
% 9.21/2.83 2185ms
%------------------------------------------------------------------------------