%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO177+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 03:48:12 EDT 2022 % Result : Theorem 4.94s 1.85s % Output : Proof 16.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO177+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n026.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Fri Jun 17 23:40:24 EDT 2022 % 0.12/0.34 % CPUTime : % 0.56/0.59 ____ _ % 0.56/0.59 ___ / __ \_____(_)___ ________ __________ % 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.59 % 0.56/0.59 A Theorem Prover for First-Order Logic % 0.56/0.59 (ePrincess v.1.0) % 0.56/0.59 % 0.56/0.59 (c) Philipp Rümmer, 2009-2015 % 0.56/0.59 (c) Peter Backeman, 2014-2015 % 0.56/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.59 Bug reports to peter@backeman.se % 0.56/0.59 % 0.56/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.59 % 0.56/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.66/0.93 Prover 0: Preprocessing ... % 1.84/1.07 Prover 0: Warning: ignoring some quantifiers % 2.03/1.09 Prover 0: Constructing countermodel ... % 2.58/1.32 Prover 0: gave up % 2.58/1.32 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.82/1.34 Prover 1: Preprocessing ... % 3.10/1.43 Prover 1: Constructing countermodel ... % 3.38/1.50 Prover 1: gave up % 3.38/1.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.51/1.52 Prover 2: Preprocessing ... % 4.04/1.64 Prover 2: Warning: ignoring some quantifiers % 4.04/1.65 Prover 2: Constructing countermodel ... % 4.94/1.85 Prover 2: proved (349ms) % 4.94/1.85 % 4.94/1.85 No countermodel exists, formula is valid % 4.94/1.85 % SZS status Theorem for theBenchmark % 4.94/1.85 % 4.94/1.85 Generating proof ... Warning: ignoring some quantifiers % 15.36/4.27 found it (size 636) % 15.36/4.27 % 15.36/4.27 % SZS output start Proof for theBenchmark % 15.36/4.27 Assumed formulas after preprocessing and simplification: % 15.36/4.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) = v7 & apart_point_and_line(v3, v7) = v9 & apart_point_and_line(v2, v7) = v8 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v11, v12) = v14) | ~ (distinct_points(v10, v11) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v10, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v10, v13) = v14) | ~ (distinct_lines(v12, v13) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v12) = v15) | ~ (apart_point_and_line(v10, v13) = v14) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v12) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v12, v13) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v10, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_points(v10, v11) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v11, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v12, v11) = v14) | ~ (distinct_points(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (convergent_lines(v11, v12) = v14) | ~ (convergent_lines(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (convergent_lines(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (distinct_lines(v11, v12) = v14) | ~ (distinct_lines(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & distinct_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (distinct_points(v11, v12) = v14) | ~ (distinct_points(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & distinct_points(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v12, v11) = v13) | ~ (apart_point_and_line(v10, v11) = 0) | distinct_points(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v12) = v13) | ~ (apart_point_and_line(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = 0) | ~ (distinct_lines(v11, v12) = v13) | apart_point_and_line(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = 0) | ~ (distinct_points(v10, v12) = v13) | apart_point_and_line(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v11, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v11) = 0) | ~ (distinct_lines(v11, v12) = v13) | convergent_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_lines(v11, v12) = v13) | ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_lines(v10, v12) = v13) | ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_points(v11, v12) = v13) | ~ (distinct_points(v10, v11) = 0) | distinct_points(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_points(v10, v12) = v13) | ~ (distinct_points(v10, v11) = 0) | distinct_points(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (intersection_point(v13, v12) = v11) | ~ (intersection_point(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (line_connecting(v13, v12) = v11) | ~ (line_connecting(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (apart_point_and_line(v13, v12) = v11) | ~ (apart_point_and_line(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (convergent_lines(v13, v12) = v11) | ~ (convergent_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (distinct_lines(v13, v12) = v11) | ~ (distinct_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (distinct_points(v13, v12) = v11) | ~ (distinct_points(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (distinct_lines(v12, v13) = 0) | ~ (distinct_points(v10, v11) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v11, v13) = 0) | (v14 = 0 & apart_point_and_line(v11, v12) = 0) | (v14 = 0 & apart_point_and_line(v10, v13) = 0) | (v14 = 0 & apart_point_and_line(v10, v12) = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v11) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v11, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v10, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v11) = v13)) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v10) = v13)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v11, v12) = v13)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v10, v12) = v13)) & ! [v10] : ~ (convergent_lines(v10, v10) = 0) & ! [v10] : ~ (distinct_lines(v10, v10) = 0) & ! [v10] : ~ (distinct_points(v10, v10) = 0) & ? [v10] : ? [v11] : ? [v12] : intersection_point(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : line_connecting(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : apart_point_and_line(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : convergent_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : distinct_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : distinct_points(v11, v10) = v12 & ((v6 = 0 & apart_point_and_line(v1, v4) = 0) | (v5 = 0 & apart_point_and_line(v0, v4) = 0))) % 15.51/4.32 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields: % 15.51/4.32 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5 & line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2 & apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0 & apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1 & distinct_points(all_0_7_7, all_0_6_6) = 0 & distinct_points(all_0_9_9, all_0_8_8) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ((all_0_3_3 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_0_4_4 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0)) % 15.70/4.34 | % 15.70/4.34 | Applying alpha-rule on (1) yields: % 15.70/4.34 | (2) distinct_points(all_0_9_9, all_0_8_8) = 0 % 15.70/4.34 | (3) ! [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) % 15.70/4.34 | (4) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 15.70/4.34 | (5) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 15.70/4.34 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 15.70/4.34 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 15.70/4.34 | (8) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 15.70/4.34 | (9) distinct_points(all_0_7_7, all_0_6_6) = 0 % 15.70/4.34 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 15.70/4.34 | (11) ! [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))) % 15.70/4.34 | (12) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 15.70/4.34 | (13) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 15.70/4.34 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 15.70/4.34 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 15.70/4.34 | (16) ! [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))) % 15.70/4.34 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 15.70/4.34 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 15.70/4.34 | (19) ! [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))) % 15.70/4.34 | (20) ~ (all_0_1_1 = 0) % 15.70/4.34 | (21) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 15.70/4.34 | (22) ! [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) % 15.70/4.34 | (23) ! [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) % 15.70/4.34 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 15.70/4.35 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 15.70/4.35 | (26) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 15.70/4.35 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 15.70/4.35 | (28) ! [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)) % 15.70/4.35 | (29) apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0 % 15.70/4.35 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 15.70/4.35 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 15.70/4.35 | (32) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 15.70/4.35 | (33) ! [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)) % 15.70/4.35 | (34) apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1 % 15.70/4.35 | (35) ~ (all_0_0_0 = 0) % 15.70/4.35 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 15.70/4.35 | (37) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 15.70/4.35 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 15.70/4.35 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 15.70/4.35 | (40) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 15.70/4.35 | (41) line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5 % 15.70/4.35 | (42) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 15.70/4.35 | (43) ! [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)) % 15.70/4.35 | (44) ! [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))) % 15.70/4.35 | (45) ! [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)) % 15.70/4.35 | (46) (all_0_3_3 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_0_4_4 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) % 15.70/4.35 | (47) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 15.70/4.35 | (48) ! [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)) % 15.70/4.35 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 15.70/4.35 | (50) ! [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))) % 15.70/4.35 | (51) ! [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) % 15.70/4.35 | (52) ! [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))) % 15.70/4.35 | (53) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 15.70/4.35 | (54) line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2 % 15.70/4.36 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 15.70/4.36 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 15.70/4.36 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 15.70/4.36 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (19) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields: % 15.70/4.36 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields: % 15.70/4.36 | (60) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (19) with all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields: % 15.70/4.36 | (61) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (16) with all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields: % 15.70/4.36 | (62) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (10) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, yields: % 15.70/4.36 | (63) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (10) with all_0_1_1, all_0_0_0, all_0_2_2, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields: % 15.70/4.36 | (64) all_0_0_0 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (10) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields: % 15.70/4.36 | (65) all_0_0_0 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (10) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields: % 15.70/4.36 | (66) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (50) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.36 | (67) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (49) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.36 | (68) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (42) with all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.36 | (69) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(all_0_6_6, v0) = v1) % 15.70/4.36 | % 15.70/4.36 | Instantiating formula (4) with all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.36 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(all_0_7_7, v0) = v1) % 15.70/4.37 | % 15.70/4.37 | Instantiating formula (42) with all_0_8_8, all_0_9_9 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = 0, yields: % 15.70/4.37 | (71) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(all_0_8_8, v0) = v1) % 15.70/4.37 | % 15.70/4.37 | Instantiating formula (4) with all_0_8_8, all_0_9_9 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = 0, yields: % 15.70/4.37 | (72) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(all_0_9_9, v0) = v1) % 15.70/4.37 | % 15.70/4.37 | Instantiating (72) with all_20_0_28, all_20_1_29 yields: % 15.70/4.37 | (73) ~ (all_20_0_28 = 0) & line_connecting(all_0_9_9, all_0_8_8) = all_20_1_29 & apart_point_and_line(all_0_9_9, all_20_1_29) = all_20_0_28 % 15.70/4.37 | % 15.70/4.37 | Applying alpha-rule on (73) yields: % 15.70/4.37 | (74) ~ (all_20_0_28 = 0) % 15.70/4.37 | (75) line_connecting(all_0_9_9, all_0_8_8) = all_20_1_29 % 15.70/4.37 | (76) apart_point_and_line(all_0_9_9, all_20_1_29) = all_20_0_28 % 15.70/4.37 | % 15.70/4.37 | Instantiating (71) with all_22_0_30, all_22_1_31 yields: % 15.70/4.37 | (77) ~ (all_22_0_30 = 0) & line_connecting(all_0_9_9, all_0_8_8) = all_22_1_31 & apart_point_and_line(all_0_8_8, all_22_1_31) = all_22_0_30 % 15.70/4.37 | % 15.70/4.37 | Applying alpha-rule on (77) yields: % 15.70/4.37 | (78) ~ (all_22_0_30 = 0) % 15.70/4.37 | (79) line_connecting(all_0_9_9, all_0_8_8) = all_22_1_31 % 15.70/4.37 | (80) apart_point_and_line(all_0_8_8, all_22_1_31) = all_22_0_30 % 15.70/4.37 | % 15.70/4.37 | Instantiating (70) with all_24_0_32, all_24_1_33 yields: % 15.70/4.37 | (81) ~ (all_24_0_32 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_24_1_33 & apart_point_and_line(all_0_7_7, all_24_1_33) = all_24_0_32 % 15.70/4.37 | % 15.70/4.37 | Applying alpha-rule on (81) yields: % 15.70/4.37 | (82) ~ (all_24_0_32 = 0) % 15.70/4.37 | (83) line_connecting(all_0_7_7, all_0_6_6) = all_24_1_33 % 15.70/4.37 | (84) apart_point_and_line(all_0_7_7, all_24_1_33) = all_24_0_32 % 15.70/4.37 | % 15.70/4.37 | Instantiating (62) with all_26_0_34 yields: % 15.70/4.37 | (85) ( ~ (all_26_0_34 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = all_26_0_34) | ( ~ (all_26_0_34 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_26_0_34) % 15.70/4.37 | % 15.70/4.37 | Instantiating (69) with all_27_0_35, all_27_1_36 yields: % 15.70/4.37 | (86) ~ (all_27_0_35 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_27_1_36 & apart_point_and_line(all_0_6_6, all_27_1_36) = all_27_0_35 % 15.70/4.37 | % 15.70/4.37 | Applying alpha-rule on (86) yields: % 15.70/4.37 | (87) ~ (all_27_0_35 = 0) % 15.70/4.37 | (88) line_connecting(all_0_7_7, all_0_6_6) = all_27_1_36 % 15.70/4.37 | (89) apart_point_and_line(all_0_6_6, all_27_1_36) = all_27_0_35 % 15.70/4.37 | % 15.70/4.37 | Instantiating (61) with all_29_0_37 yields: % 15.70/4.37 | (90) ( ~ (all_29_0_37 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = all_29_0_37) | ( ~ (all_29_0_37 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_29_0_37) % 15.70/4.37 | % 15.70/4.37 | Instantiating (60) with all_30_0_38 yields: % 15.70/4.37 | (91) ( ~ (all_30_0_38 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = all_30_0_38) | ( ~ (all_30_0_38 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_30_0_38) % 15.70/4.37 | % 15.70/4.37 | Instantiating (59) with all_31_0_39 yields: % 15.70/4.37 | (92) ( ~ (all_31_0_39 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = all_31_0_39) | ( ~ (all_31_0_39 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_31_0_39) % 15.70/4.37 | % 15.70/4.37 +-Applying beta-rule and splitting (91), into two cases. % 15.70/4.37 |-Branch one: % 15.70/4.37 | (93) ~ (all_30_0_38 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = all_30_0_38 % 15.70/4.37 | % 15.70/4.37 | Applying alpha-rule on (93) yields: % 15.70/4.37 | (94) ~ (all_30_0_38 = 0) % 15.70/4.37 | (95) apart_point_and_line(all_0_7_7, all_0_5_5) = all_30_0_38 % 15.70/4.37 | % 15.70/4.37 +-Applying beta-rule and splitting (85), into two cases. % 15.70/4.37 |-Branch one: % 15.70/4.37 | (96) ~ (all_26_0_34 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = all_26_0_34 % 15.70/4.37 | % 15.70/4.37 | Applying alpha-rule on (96) yields: % 15.70/4.37 | (97) ~ (all_26_0_34 = 0) % 15.70/4.37 | (98) apart_point_and_line(all_0_9_9, all_0_2_2) = all_26_0_34 % 15.70/4.37 | % 15.70/4.37 +-Applying beta-rule and splitting (63), into two cases. % 15.70/4.37 |-Branch one: % 15.70/4.37 | (99) all_0_0_0 = 0 % 15.70/4.37 | % 15.70/4.37 | Equations (99) can reduce 35 to: % 15.70/4.37 | (100) $false % 15.70/4.37 | % 15.70/4.37 |-The branch is then unsatisfiable % 15.70/4.37 |-Branch two: % 15.70/4.37 | (35) ~ (all_0_0_0 = 0) % 15.70/4.37 | (102) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 15.70/4.37 | % 15.70/4.37 +-Applying beta-rule and splitting (65), into two cases. % 15.70/4.37 |-Branch one: % 15.70/4.37 | (99) all_0_0_0 = 0 % 15.70/4.37 | % 15.70/4.37 | Equations (99) can reduce 35 to: % 15.70/4.37 | (100) $false % 15.70/4.37 | % 15.70/4.37 |-The branch is then unsatisfiable % 15.70/4.37 |-Branch two: % 15.70/4.37 | (35) ~ (all_0_0_0 = 0) % 15.70/4.37 | (106) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 15.70/4.37 | % 15.70/4.37 +-Applying beta-rule and splitting (64), into two cases. % 15.70/4.37 |-Branch one: % 15.70/4.37 | (99) all_0_0_0 = 0 % 15.70/4.37 | % 15.70/4.37 | Equations (99) can reduce 35 to: % 15.70/4.37 | (100) $false % 15.70/4.37 | % 15.70/4.37 |-The branch is then unsatisfiable % 15.70/4.37 |-Branch two: % 15.70/4.37 | (35) ~ (all_0_0_0 = 0) % 15.70/4.37 | (110) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 15.70/4.37 | % 15.70/4.37 +-Applying beta-rule and splitting (90), into two cases. % 15.70/4.37 |-Branch one: % 15.70/4.37 | (111) ~ (all_29_0_37 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = all_29_0_37 % 15.70/4.38 | % 15.70/4.38 | Applying alpha-rule on (111) yields: % 15.70/4.38 | (112) ~ (all_29_0_37 = 0) % 15.70/4.38 | (113) apart_point_and_line(all_0_8_8, all_0_2_2) = all_29_0_37 % 15.70/4.38 | % 15.70/4.38 +-Applying beta-rule and splitting (66), into two cases. % 15.70/4.38 |-Branch one: % 15.70/4.38 | (114) all_0_1_1 = 0 % 15.70/4.38 | % 15.70/4.38 | Equations (114) can reduce 20 to: % 15.70/4.38 | (100) $false % 15.70/4.38 | % 15.70/4.38 |-The branch is then unsatisfiable % 15.70/4.38 |-Branch two: % 15.70/4.38 | (20) ~ (all_0_1_1 = 0) % 15.70/4.38 | (117) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 15.70/4.38 | % 15.70/4.38 +-Applying beta-rule and splitting (67), into two cases. % 15.70/4.38 |-Branch one: % 15.70/4.38 | (99) all_0_0_0 = 0 % 15.70/4.38 | % 15.70/4.38 | Equations (99) can reduce 35 to: % 15.70/4.38 | (100) $false % 15.70/4.38 | % 15.70/4.38 |-The branch is then unsatisfiable % 15.70/4.38 |-Branch two: % 15.70/4.38 | (35) ~ (all_0_0_0 = 0) % 15.70/4.38 | (121) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 15.70/4.38 | % 15.70/4.38 +-Applying beta-rule and splitting (68), into two cases. % 15.70/4.38 |-Branch one: % 15.70/4.38 | (114) all_0_1_1 = 0 % 15.70/4.38 | % 15.70/4.38 | Equations (114) can reduce 20 to: % 15.70/4.38 | (100) $false % 15.70/4.38 | % 15.70/4.38 |-The branch is then unsatisfiable % 15.70/4.38 |-Branch two: % 15.70/4.38 | (20) ~ (all_0_1_1 = 0) % 15.70/4.38 | (125) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)) % 15.70/4.38 | % 15.70/4.38 +-Applying beta-rule and splitting (92), into two cases. % 15.70/4.38 |-Branch one: % 15.70/4.38 | (126) ~ (all_31_0_39 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = all_31_0_39 % 15.70/4.38 | % 15.70/4.38 | Applying alpha-rule on (126) yields: % 15.70/4.38 | (127) ~ (all_31_0_39 = 0) % 15.70/4.38 | (128) apart_point_and_line(all_0_6_6, all_0_5_5) = all_31_0_39 % 15.70/4.38 | % 15.70/4.38 +-Applying beta-rule and splitting (110), into two cases. % 15.70/4.38 |-Branch one: % 15.70/4.38 | (114) all_0_1_1 = 0 % 15.70/4.38 | % 15.70/4.38 | Equations (114) can reduce 20 to: % 15.70/4.38 | (100) $false % 15.70/4.38 | % 15.70/4.38 |-The branch is then unsatisfiable % 15.70/4.38 |-Branch two: % 15.70/4.38 | (20) ~ (all_0_1_1 = 0) % 15.70/4.38 | (132) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 15.70/4.38 | % 15.70/4.38 | Instantiating formula (14) with all_0_7_7, all_0_6_6, all_27_1_36, all_0_5_5 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_27_1_36, line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields: % 15.70/4.38 | (133) all_27_1_36 = all_0_5_5 % 15.70/4.38 | % 15.70/4.38 | Instantiating formula (14) with all_0_7_7, all_0_6_6, all_24_1_33, all_27_1_36 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_27_1_36, line_connecting(all_0_7_7, all_0_6_6) = all_24_1_33, yields: % 15.70/4.38 | (134) all_27_1_36 = all_24_1_33 % 15.70/4.38 | % 15.70/4.38 | Instantiating formula (14) with all_0_9_9, all_0_8_8, all_22_1_31, all_0_2_2 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_22_1_31, line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields: % 15.70/4.38 | (135) all_22_1_31 = all_0_2_2 % 15.70/4.38 | % 15.70/4.38 | Instantiating formula (14) with all_0_9_9, all_0_8_8, all_20_1_29, all_22_1_31 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_22_1_31, line_connecting(all_0_9_9, all_0_8_8) = all_20_1_29, yields: % 15.70/4.38 | (136) all_22_1_31 = all_20_1_29 % 15.70/4.38 | % 15.70/4.38 | Combining equations (133,134) yields a new equation: % 15.70/4.38 | (137) all_24_1_33 = all_0_5_5 % 15.70/4.38 | % 15.70/4.38 | Combining equations (136,135) yields a new equation: % 15.70/4.38 | (138) all_20_1_29 = all_0_2_2 % 15.70/4.38 | % 15.70/4.38 | Simplifying 138 yields: % 15.70/4.38 | (139) all_20_1_29 = all_0_2_2 % 15.70/4.38 | % 15.70/4.38 | Combining equations (137,134) yields a new equation: % 15.70/4.38 | (133) all_27_1_36 = all_0_5_5 % 15.70/4.38 | % 15.70/4.38 | From (133) and (89) follows: % 15.70/4.38 | (141) apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35 % 15.70/4.38 | % 15.70/4.38 | From (137) and (84) follows: % 15.70/4.38 | (142) apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32 % 15.70/4.38 | % 15.70/4.38 | From (135) and (80) follows: % 15.70/4.38 | (143) apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30 % 15.70/4.38 | % 15.70/4.38 | From (139) and (76) follows: % 15.70/4.38 | (144) apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28 % 15.70/4.38 | % 15.70/4.38 | Instantiating formula (25) with all_0_6_6, all_0_5_5, all_27_0_35, all_31_0_39 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_31_0_39, apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, yields: % 15.70/4.38 | (145) all_31_0_39 = all_27_0_35 % 15.70/4.38 | % 15.70/4.38 | Instantiating formula (25) with all_0_7_7, all_0_5_5, all_24_0_32, all_30_0_38 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_30_0_38, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 15.70/4.38 | (146) all_30_0_38 = all_24_0_32 % 15.70/4.38 | % 15.70/4.38 | Instantiating formula (25) with all_0_8_8, all_0_2_2, all_22_0_30, all_29_0_37 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_29_0_37, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 15.70/4.38 | (147) all_29_0_37 = all_22_0_30 % 15.70/4.38 | % 15.70/4.38 | Instantiating formula (25) with all_0_9_9, all_0_2_2, all_20_0_28, all_26_0_34 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_26_0_34, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 15.70/4.38 | (148) all_26_0_34 = all_20_0_28 % 15.70/4.38 | % 15.70/4.38 | Equations (145) can reduce 127 to: % 15.70/4.38 | (87) ~ (all_27_0_35 = 0) % 15.70/4.38 | % 15.70/4.38 | Equations (146) can reduce 94 to: % 15.70/4.38 | (82) ~ (all_24_0_32 = 0) % 15.70/4.38 | % 15.70/4.38 | Equations (147) can reduce 112 to: % 15.70/4.38 | (78) ~ (all_22_0_30 = 0) % 15.70/4.38 | % 15.70/4.38 | Equations (148) can reduce 97 to: % 15.70/4.38 | (74) ~ (all_20_0_28 = 0) % 15.70/4.38 | % 15.70/4.38 | From (145) and (128) follows: % 15.70/4.38 | (141) apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35 % 15.70/4.38 | % 15.70/4.38 | From (146) and (95) follows: % 15.70/4.38 | (142) apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32 % 15.70/4.39 | % 15.70/4.39 | From (147) and (113) follows: % 15.70/4.39 | (143) apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30 % 15.70/4.39 | % 15.70/4.39 | From (148) and (98) follows: % 15.70/4.39 | (144) apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28 % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (50) with all_27_0_35, all_0_0_0, all_0_5_5, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.39 | (157) all_27_0_35 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (50) with all_0_0_0, all_27_0_35, all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.39 | (158) all_27_0_35 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (10) with all_27_0_35, all_0_0_0, all_0_5_5, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, yields: % 15.70/4.39 | (159) all_27_0_35 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (10) with all_0_0_0, all_27_0_35, all_0_2_2, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, yields: % 15.70/4.39 | (160) all_27_0_35 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (10) with all_27_0_35, all_0_1_1, all_0_5_5, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields: % 15.70/4.39 | (161) all_27_0_35 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (10) with all_0_1_1, all_27_0_35, all_0_2_2, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields: % 15.70/4.39 | (162) all_27_0_35 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (58) with all_27_0_35, all_0_1_1, all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields: % 15.70/4.39 | (163) all_27_0_35 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (58) with all_0_1_1, all_27_0_35, all_0_5_5, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields: % 15.70/4.39 | (164) all_27_0_35 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (50) with all_27_0_35, all_27_0_35, all_0_5_5, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.39 | (165) all_27_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (10) with all_27_0_35, all_27_0_35, all_0_5_5, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, yields: % 15.70/4.39 | (166) all_27_0_35 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (10) with all_24_0_32, all_0_0_0, all_0_5_5, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 15.70/4.39 | (167) all_24_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 15.70/4.39 | % 15.70/4.39 | Instantiating formula (10) with all_0_0_0, all_24_0_32, all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 15.70/4.39 | (168) all_24_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 15.70/4.40 | % 15.70/4.40 | Instantiating formula (58) with all_24_0_32, all_0_0_0, all_0_2_2, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 15.70/4.40 | (169) all_24_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 15.70/4.40 | % 15.70/4.40 | Instantiating formula (58) with all_0_0_0, all_24_0_32, all_0_5_5, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 15.70/4.40 | (170) all_24_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 15.70/4.40 | % 15.70/4.40 | Instantiating formula (49) with all_24_0_32, all_0_1_1, all_0_5_5, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.40 | (171) all_24_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 15.70/4.40 | % 15.70/4.40 | Instantiating formula (49) with all_0_1_1, all_24_0_32, all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 15.70/4.40 | (172) all_24_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 15.70/4.40 | % 15.70/4.40 | Instantiating formula (10) with all_24_0_32, all_0_1_1, all_0_5_5, all_0_2_2, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 15.70/4.40 | (173) all_24_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 15.70/4.40 | % 15.70/4.40 | Instantiating formula (10) with all_0_1_1, all_24_0_32, all_0_2_2, all_0_5_5, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 15.70/4.40 | (174) all_24_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 15.70/4.40 | % 15.70/4.40 | Instantiating formula (10) with all_24_0_32, all_27_0_35, all_0_5_5, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 15.70/4.40 | (175) all_27_0_35 = 0 | all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.40 | % 16.04/4.40 | Instantiating formula (10) with all_27_0_35, all_24_0_32, all_0_5_5, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 16.04/4.40 | (176) all_27_0_35 = 0 | all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.40 | % 16.04/4.40 | Instantiating formula (49) with all_24_0_32, all_24_0_32, all_0_5_5, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 16.04/4.40 | (177) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 16.04/4.40 | % 16.04/4.40 | Instantiating formula (10) with all_24_0_32, all_24_0_32, all_0_5_5, all_0_5_5, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, yields: % 16.04/4.40 | (178) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.04/4.40 | % 16.04/4.40 | Instantiating formula (10) with all_22_0_30, all_0_0_0, all_0_2_2, all_0_2_2, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.40 | (179) all_22_0_30 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.04/4.40 | % 16.04/4.40 | Instantiating formula (10) with all_0_0_0, all_22_0_30, all_0_2_2, all_0_2_2, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.40 | (180) all_22_0_30 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.04/4.40 | % 16.04/4.41 | Instantiating formula (10) with all_22_0_30, all_0_1_1, all_0_2_2, all_0_2_2, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (181) all_22_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (10) with all_0_1_1, all_22_0_30, all_0_2_2, all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (182) all_22_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (10) with all_22_0_30, all_27_0_35, all_0_2_2, all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (183) all_27_0_35 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (10) with all_27_0_35, all_22_0_30, all_0_5_5, all_0_2_2, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (184) all_27_0_35 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (58) with all_22_0_30, all_27_0_35, all_0_5_5, all_0_2_2, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (185) all_27_0_35 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (58) with all_27_0_35, all_22_0_30, all_0_2_2, all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (186) all_27_0_35 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (10) with all_22_0_30, all_24_0_32, all_0_2_2, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (187) all_24_0_32 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (10) with all_24_0_32, all_22_0_30, all_0_5_5, all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (188) all_24_0_32 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (58) with all_22_0_30, all_24_0_32, all_0_5_5, all_0_2_2, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (189) all_24_0_32 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (58) with all_24_0_32, all_22_0_30, all_0_2_2, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.41 | (190) all_24_0_32 = 0 | all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.41 | % 16.04/4.41 | Instantiating formula (10) with all_22_0_30, all_22_0_30, all_0_2_2, all_0_2_2, all_0_8_8, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, yields: % 16.04/4.42 | (191) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_20_0_28, all_0_0_0, all_0_2_2, all_0_2_2, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (192) all_20_0_28 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_0_0_0, all_20_0_28, all_0_2_2, all_0_2_2, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (193) all_20_0_28 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_20_0_28, all_0_1_1, all_0_2_2, all_0_2_2, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (194) all_20_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_0_1_1, all_20_0_28, all_0_2_2, all_0_2_2, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (195) all_20_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_20_0_28, all_27_0_35, all_0_2_2, all_0_5_5, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (196) all_27_0_35 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_27_0_35, all_20_0_28, all_0_5_5, all_0_2_2, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (197) all_27_0_35 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (58) with all_20_0_28, all_27_0_35, all_0_5_5, all_0_2_2, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (198) all_27_0_35 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (58) with all_27_0_35, all_20_0_28, all_0_2_2, all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_27_0_35, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (199) all_27_0_35 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_20_0_28, all_24_0_32, all_0_2_2, all_0_5_5, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (200) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_24_0_32, all_20_0_28, all_0_5_5, all_0_2_2, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (201) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (58) with all_20_0_28, all_24_0_32, all_0_5_5, all_0_2_2, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (202) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (58) with all_24_0_32, all_20_0_28, all_0_2_2, all_0_5_5, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.42 | (203) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.04/4.42 | % 16.04/4.42 | Instantiating formula (10) with all_20_0_28, all_22_0_30, all_0_2_2, all_0_2_2, all_0_9_9, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.43 | (204) all_22_0_30 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0)) % 16.04/4.43 | % 16.04/4.43 | Instantiating formula (10) with all_20_0_28, all_20_0_28, all_0_2_2, all_0_2_2, all_0_9_9, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, yields: % 16.04/4.43 | (205) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (46), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (206) all_0_3_3 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0 % 16.04/4.43 | % 16.04/4.43 | Applying alpha-rule on (206) yields: % 16.04/4.43 | (207) all_0_3_3 = 0 % 16.04/4.43 | (208) apart_point_and_line(all_0_8_8, all_0_5_5) = 0 % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (191), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (209) all_22_0_30 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (209) can reduce 78 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (78) ~ (all_22_0_30 = 0) % 16.04/4.43 | (212) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (205), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (213) all_20_0_28 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (213) can reduce 74 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (74) ~ (all_20_0_28 = 0) % 16.04/4.43 | (216) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (177), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (217) all_24_0_32 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (217) can reduce 82 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (82) ~ (all_24_0_32 = 0) % 16.04/4.43 | (220) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (178), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (217) all_24_0_32 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (217) can reduce 82 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (82) ~ (all_24_0_32 = 0) % 16.04/4.43 | (224) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (165), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (225) all_27_0_35 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (225) can reduce 87 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (87) ~ (all_27_0_35 = 0) % 16.04/4.43 | (228) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (166), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (225) all_27_0_35 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (225) can reduce 87 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (87) ~ (all_27_0_35 = 0) % 16.04/4.43 | (232) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (160), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (225) all_27_0_35 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (225) can reduce 87 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (87) ~ (all_27_0_35 = 0) % 16.04/4.43 | (236) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (183), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (225) all_27_0_35 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (225) can reduce 87 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (87) ~ (all_27_0_35 = 0) % 16.04/4.43 | (240) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (157), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (225) all_27_0_35 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (225) can reduce 87 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (87) ~ (all_27_0_35 = 0) % 16.04/4.43 | (244) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (201), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (217) all_24_0_32 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (217) can reduce 82 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (82) ~ (all_24_0_32 = 0) % 16.04/4.43 | (248) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.04/4.43 | % 16.04/4.43 +-Applying beta-rule and splitting (189), into two cases. % 16.04/4.43 |-Branch one: % 16.04/4.43 | (217) all_24_0_32 = 0 % 16.04/4.43 | % 16.04/4.43 | Equations (217) can reduce 82 to: % 16.04/4.43 | (100) $false % 16.04/4.43 | % 16.04/4.43 |-The branch is then unsatisfiable % 16.04/4.43 |-Branch two: % 16.04/4.43 | (82) ~ (all_24_0_32 = 0) % 16.04/4.43 | (252) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (161), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (225) all_27_0_35 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (225) can reduce 87 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (87) ~ (all_27_0_35 = 0) % 16.04/4.44 | (256) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (162), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (225) all_27_0_35 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (225) can reduce 87 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (87) ~ (all_27_0_35 = 0) % 16.04/4.44 | (260) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (163), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (225) all_27_0_35 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (225) can reduce 87 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (87) ~ (all_27_0_35 = 0) % 16.04/4.44 | (264) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (167), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (217) all_24_0_32 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (217) can reduce 82 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (82) ~ (all_24_0_32 = 0) % 16.04/4.44 | (268) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (190), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (217) all_24_0_32 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (217) can reduce 82 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (82) ~ (all_24_0_32 = 0) % 16.04/4.44 | (272) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (158), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (225) all_27_0_35 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (225) can reduce 87 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (87) ~ (all_27_0_35 = 0) % 16.04/4.44 | (276) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (159), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (225) all_27_0_35 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (225) can reduce 87 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (87) ~ (all_27_0_35 = 0) % 16.04/4.44 | (280) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (197), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (225) all_27_0_35 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (225) can reduce 87 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (87) ~ (all_27_0_35 = 0) % 16.04/4.44 | (284) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (198), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (225) all_27_0_35 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (225) can reduce 87 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (87) ~ (all_27_0_35 = 0) % 16.04/4.44 | (288) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (164), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (225) all_27_0_35 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (225) can reduce 87 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (87) ~ (all_27_0_35 = 0) % 16.04/4.44 | (292) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (193), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (213) all_20_0_28 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (213) can reduce 74 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (74) ~ (all_20_0_28 = 0) % 16.04/4.44 | (296) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (194), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (213) all_20_0_28 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (213) can reduce 74 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (74) ~ (all_20_0_28 = 0) % 16.04/4.44 | (300) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (202), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (217) all_24_0_32 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (217) can reduce 82 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (82) ~ (all_24_0_32 = 0) % 16.04/4.44 | (304) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (168), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (217) all_24_0_32 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (217) can reduce 82 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (82) ~ (all_24_0_32 = 0) % 16.04/4.44 | (308) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (203), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (217) all_24_0_32 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (217) can reduce 82 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (82) ~ (all_24_0_32 = 0) % 16.04/4.44 | (312) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.04/4.44 | % 16.04/4.44 +-Applying beta-rule and splitting (195), into two cases. % 16.04/4.44 |-Branch one: % 16.04/4.44 | (213) all_20_0_28 = 0 % 16.04/4.44 | % 16.04/4.44 | Equations (213) can reduce 74 to: % 16.04/4.44 | (100) $false % 16.04/4.44 | % 16.04/4.44 |-The branch is then unsatisfiable % 16.04/4.44 |-Branch two: % 16.04/4.44 | (74) ~ (all_20_0_28 = 0) % 16.04/4.44 | (316) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (204), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (209) all_22_0_30 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (209) can reduce 78 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (78) ~ (all_22_0_30 = 0) % 16.04/4.45 | (320) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (169), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (217) all_24_0_32 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (217) can reduce 82 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (82) ~ (all_24_0_32 = 0) % 16.04/4.45 | (324) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (170), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (217) all_24_0_32 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (217) can reduce 82 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (82) ~ (all_24_0_32 = 0) % 16.04/4.45 | (328) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (171), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (217) all_24_0_32 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (217) can reduce 82 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (82) ~ (all_24_0_32 = 0) % 16.04/4.45 | (332) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (196), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (225) all_27_0_35 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (225) can reduce 87 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (87) ~ (all_27_0_35 = 0) % 16.04/4.45 | (336) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (199), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (225) all_27_0_35 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (225) can reduce 87 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (87) ~ (all_27_0_35 = 0) % 16.04/4.45 | (340) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (200), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (217) all_24_0_32 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (217) can reduce 82 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (82) ~ (all_24_0_32 = 0) % 16.04/4.45 | (344) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (172), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (217) all_24_0_32 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (217) can reduce 82 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (82) ~ (all_24_0_32 = 0) % 16.04/4.45 | (348) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (175), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (225) all_27_0_35 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (225) can reduce 87 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (87) ~ (all_27_0_35 = 0) % 16.04/4.45 | (352) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (173), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (217) all_24_0_32 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (217) can reduce 82 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (82) ~ (all_24_0_32 = 0) % 16.04/4.45 | (356) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (174), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (217) all_24_0_32 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (217) can reduce 82 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (82) ~ (all_24_0_32 = 0) % 16.04/4.45 | (360) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (176), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (225) all_27_0_35 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (225) can reduce 87 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (87) ~ (all_27_0_35 = 0) % 16.04/4.45 | (364) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (179), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (209) all_22_0_30 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (209) can reduce 78 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (78) ~ (all_22_0_30 = 0) % 16.04/4.45 | (368) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (185), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (225) all_27_0_35 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (225) can reduce 87 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (87) ~ (all_27_0_35 = 0) % 16.04/4.45 | (372) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (186), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (225) all_27_0_35 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (225) can reduce 87 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (87) ~ (all_27_0_35 = 0) % 16.04/4.45 | (376) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.04/4.45 | % 16.04/4.45 +-Applying beta-rule and splitting (187), into two cases. % 16.04/4.45 |-Branch one: % 16.04/4.45 | (217) all_24_0_32 = 0 % 16.04/4.45 | % 16.04/4.45 | Equations (217) can reduce 82 to: % 16.04/4.45 | (100) $false % 16.04/4.45 | % 16.04/4.45 |-The branch is then unsatisfiable % 16.04/4.45 |-Branch two: % 16.04/4.45 | (82) ~ (all_24_0_32 = 0) % 16.04/4.45 | (380) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (180), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (209) all_22_0_30 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (209) can reduce 78 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (78) ~ (all_22_0_30 = 0) % 16.04/4.46 | (384) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (181), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (209) all_22_0_30 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (209) can reduce 78 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (78) ~ (all_22_0_30 = 0) % 16.04/4.46 | (388) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (182), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (209) all_22_0_30 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (209) can reduce 78 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (78) ~ (all_22_0_30 = 0) % 16.04/4.46 | (392) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (184), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (225) all_27_0_35 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (225) can reduce 87 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (87) ~ (all_27_0_35 = 0) % 16.04/4.46 | (396) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (188), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (217) all_24_0_32 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (217) can reduce 82 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (82) ~ (all_24_0_32 = 0) % 16.04/4.46 | (400) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (244), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (99) all_0_0_0 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (99) can reduce 35 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (35) ~ (all_0_0_0 = 0) % 16.04/4.46 | (404) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (252), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (209) all_22_0_30 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (209) can reduce 78 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (78) ~ (all_22_0_30 = 0) % 16.04/4.46 | (408) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (256), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (114) all_0_1_1 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (114) can reduce 20 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (20) ~ (all_0_1_1 = 0) % 16.04/4.46 | (412) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (268), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (99) all_0_0_0 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (99) can reduce 35 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (35) ~ (all_0_0_0 = 0) % 16.04/4.46 | (416) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (276), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (99) all_0_0_0 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (99) can reduce 35 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (35) ~ (all_0_0_0 = 0) % 16.04/4.46 | (420) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 16.04/4.46 | % 16.04/4.46 | Instantiating (420) with all_282_0_368 yields: % 16.04/4.46 | (421) (all_282_0_368 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_282_0_368 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (all_282_0_368 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_368) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (300), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (114) all_0_1_1 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (114) can reduce 20 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (20) ~ (all_0_1_1 = 0) % 16.04/4.46 | (425) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (421), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (426) (all_282_0_368 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_282_0_368 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (426), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (427) all_282_0_368 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0 % 16.04/4.46 | % 16.04/4.46 | Applying alpha-rule on (427) yields: % 16.04/4.46 | (428) all_282_0_368 = 0 % 16.04/4.46 | (429) apart_point_and_line(all_0_7_7, all_0_2_2) = 0 % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (260), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (114) all_0_1_1 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (114) can reduce 20 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (20) ~ (all_0_1_1 = 0) % 16.04/4.46 | (433) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (264), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (114) all_0_1_1 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (114) can reduce 20 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (20) ~ (all_0_1_1 = 0) % 16.04/4.46 | (437) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (292), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (114) all_0_1_1 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (114) can reduce 20 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (20) ~ (all_0_1_1 = 0) % 16.04/4.46 | (441) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (316), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (114) all_0_1_1 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (114) can reduce 20 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (20) ~ (all_0_1_1 = 0) % 16.04/4.46 | (445) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (332), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (114) all_0_1_1 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (114) can reduce 20 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (20) ~ (all_0_1_1 = 0) % 16.04/4.46 | (449) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 16.04/4.46 | % 16.04/4.46 +-Applying beta-rule and splitting (348), into two cases. % 16.04/4.46 |-Branch one: % 16.04/4.46 | (114) all_0_1_1 = 0 % 16.04/4.46 | % 16.04/4.46 | Equations (114) can reduce 20 to: % 16.04/4.46 | (100) $false % 16.04/4.46 | % 16.04/4.46 |-The branch is then unsatisfiable % 16.04/4.46 |-Branch two: % 16.04/4.46 | (20) ~ (all_0_1_1 = 0) % 16.04/4.46 | (453) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (356), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (114) all_0_1_1 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (114) can reduce 20 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (20) ~ (all_0_1_1 = 0) % 16.04/4.47 | (457) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (360), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (114) all_0_1_1 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (114) can reduce 20 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (20) ~ (all_0_1_1 = 0) % 16.04/4.47 | (461) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (388), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (114) all_0_1_1 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (114) can reduce 20 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (20) ~ (all_0_1_1 = 0) % 16.04/4.47 | (465) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (392), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (114) all_0_1_1 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (114) can reduce 20 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (20) ~ (all_0_1_1 = 0) % 16.04/4.47 | (469) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.47 | % 16.04/4.47 | Instantiating formula (25) with all_0_7_7, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields: % 16.04/4.47 | (114) all_0_1_1 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (114) can reduce 20 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (472) all_282_0_368 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0 % 16.04/4.47 | % 16.04/4.47 | Applying alpha-rule on (472) yields: % 16.04/4.47 | (428) all_282_0_368 = 0 % 16.04/4.47 | (474) apart_point_and_line(all_0_7_7, all_0_5_5) = 0 % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (352), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (217) all_24_0_32 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (217) can reduce 82 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (82) ~ (all_24_0_32 = 0) % 16.04/4.47 | (478) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (364), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (217) all_24_0_32 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (217) can reduce 82 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (82) ~ (all_24_0_32 = 0) % 16.04/4.47 | (482) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.04/4.47 | % 16.04/4.47 | Instantiating formula (25) with all_0_7_7, all_0_5_5, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_7_7, all_0_5_5) = 0, yields: % 16.04/4.47 | (217) all_24_0_32 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (217) can reduce 82 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (485) ~ (all_282_0_368 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_368 % 16.04/4.47 | % 16.04/4.47 | Applying alpha-rule on (485) yields: % 16.04/4.47 | (486) ~ (all_282_0_368 = 0) % 16.04/4.47 | (487) distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_368 % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (240), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (209) all_22_0_30 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (209) can reduce 78 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (78) ~ (all_22_0_30 = 0) % 16.04/4.47 | (491) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (272), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (209) all_22_0_30 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (209) can reduce 78 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (78) ~ (all_22_0_30 = 0) % 16.04/4.47 | (495) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (372), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (209) all_22_0_30 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (209) can reduce 78 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (78) ~ (all_22_0_30 = 0) % 16.04/4.47 | (499) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (376), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (209) all_22_0_30 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (209) can reduce 78 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (78) ~ (all_22_0_30 = 0) % 16.04/4.47 | (503) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (380), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (209) all_22_0_30 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (209) can reduce 78 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (78) ~ (all_22_0_30 = 0) % 16.04/4.47 | (507) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (396), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (209) all_22_0_30 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (209) can reduce 78 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (78) ~ (all_22_0_30 = 0) % 16.04/4.47 | (511) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (400), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (209) all_22_0_30 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (209) can reduce 78 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (78) ~ (all_22_0_30 = 0) % 16.04/4.47 | (515) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.04/4.47 | % 16.04/4.47 | Instantiating formula (33) with all_22_0_30, all_282_0_368, all_0_2_2, all_0_5_5, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_368, yields: % 16.04/4.47 | (516) all_282_0_368 = 0 | all_22_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_5_5) = v0) % 16.04/4.47 | % 16.04/4.47 | Instantiating formula (23) with all_282_0_368, all_0_2_2, all_0_5_5, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = 0, distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_368, yields: % 16.04/4.47 | (517) all_282_0_368 = 0 | apart_point_and_line(all_0_8_8, all_0_2_2) = 0 % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (517), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (518) apart_point_and_line(all_0_8_8, all_0_2_2) = 0 % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (516), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (428) all_282_0_368 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (428) can reduce 486 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (486) ~ (all_282_0_368 = 0) % 16.04/4.47 | (522) all_22_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_5_5) = v0) % 16.04/4.47 | % 16.04/4.47 +-Applying beta-rule and splitting (522), into two cases. % 16.04/4.47 |-Branch one: % 16.04/4.47 | (209) all_22_0_30 = 0 % 16.04/4.47 | % 16.04/4.47 | Equations (209) can reduce 78 to: % 16.04/4.47 | (100) $false % 16.04/4.47 | % 16.04/4.47 |-The branch is then unsatisfiable % 16.04/4.47 |-Branch two: % 16.04/4.47 | (78) ~ (all_22_0_30 = 0) % 16.04/4.47 | (526) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_5_5) = v0) % 16.04/4.47 | % 16.04/4.47 | Instantiating formula (25) with all_0_8_8, all_0_2_2, 0, all_22_0_30 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_22_0_30, apart_point_and_line(all_0_8_8, all_0_2_2) = 0, yields: % 16.04/4.48 | (209) all_22_0_30 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (209) can reduce 78 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (529) ~ (apart_point_and_line(all_0_8_8, all_0_2_2) = 0) % 16.04/4.48 | (428) all_282_0_368 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (428) can reduce 486 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (532) all_0_4_4 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0 % 16.04/4.48 | % 16.04/4.48 | Applying alpha-rule on (532) yields: % 16.04/4.48 | (533) all_0_4_4 = 0 % 16.04/4.48 | (534) apart_point_and_line(all_0_9_9, all_0_5_5) = 0 % 16.04/4.48 | % 16.04/4.48 +-Applying beta-rule and splitting (191), into two cases. % 16.04/4.48 |-Branch one: % 16.04/4.48 | (209) all_22_0_30 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (209) can reduce 78 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (78) ~ (all_22_0_30 = 0) % 16.04/4.48 | (212) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0)) % 16.04/4.48 | % 16.04/4.48 +-Applying beta-rule and splitting (205), into two cases. % 16.04/4.48 |-Branch one: % 16.04/4.48 | (213) all_20_0_28 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (213) can reduce 74 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (74) ~ (all_20_0_28 = 0) % 16.04/4.48 | (216) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0)) % 16.04/4.48 | % 16.04/4.48 +-Applying beta-rule and splitting (177), into two cases. % 16.04/4.48 |-Branch one: % 16.04/4.48 | (217) all_24_0_32 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (217) can reduce 82 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (82) ~ (all_24_0_32 = 0) % 16.04/4.48 | (220) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 16.04/4.48 | % 16.04/4.48 +-Applying beta-rule and splitting (178), into two cases. % 16.04/4.48 |-Branch one: % 16.04/4.48 | (217) all_24_0_32 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (217) can reduce 82 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (82) ~ (all_24_0_32 = 0) % 16.04/4.48 | (224) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.04/4.48 | % 16.04/4.48 +-Applying beta-rule and splitting (165), into two cases. % 16.04/4.48 |-Branch one: % 16.04/4.48 | (225) all_27_0_35 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (225) can reduce 87 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (87) ~ (all_27_0_35 = 0) % 16.04/4.48 | (228) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 16.04/4.48 | % 16.04/4.48 +-Applying beta-rule and splitting (166), into two cases. % 16.04/4.48 |-Branch one: % 16.04/4.48 | (225) all_27_0_35 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (225) can reduce 87 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (87) ~ (all_27_0_35 = 0) % 16.04/4.48 | (232) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 16.04/4.48 | % 16.04/4.48 +-Applying beta-rule and splitting (160), into two cases. % 16.04/4.48 |-Branch one: % 16.04/4.48 | (225) all_27_0_35 = 0 % 16.04/4.48 | % 16.04/4.48 | Equations (225) can reduce 87 to: % 16.04/4.48 | (100) $false % 16.04/4.48 | % 16.04/4.48 |-The branch is then unsatisfiable % 16.04/4.48 |-Branch two: % 16.04/4.48 | (87) ~ (all_27_0_35 = 0) % 16.04/4.48 | (236) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (183), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (225) all_27_0_35 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (225) can reduce 87 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (87) ~ (all_27_0_35 = 0) % 16.41/4.48 | (240) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (157), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (225) all_27_0_35 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (225) can reduce 87 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (87) ~ (all_27_0_35 = 0) % 16.41/4.48 | (244) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (201), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (217) all_24_0_32 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (217) can reduce 82 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (82) ~ (all_24_0_32 = 0) % 16.41/4.48 | (248) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (189), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (217) all_24_0_32 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (217) can reduce 82 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (82) ~ (all_24_0_32 = 0) % 16.41/4.48 | (252) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (161), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (225) all_27_0_35 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (225) can reduce 87 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (87) ~ (all_27_0_35 = 0) % 16.41/4.48 | (256) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (162), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (225) all_27_0_35 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (225) can reduce 87 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (87) ~ (all_27_0_35 = 0) % 16.41/4.48 | (260) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (163), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (225) all_27_0_35 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (225) can reduce 87 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (87) ~ (all_27_0_35 = 0) % 16.41/4.48 | (264) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (167), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (217) all_24_0_32 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (217) can reduce 82 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (82) ~ (all_24_0_32 = 0) % 16.41/4.48 | (268) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.48 | % 16.41/4.48 +-Applying beta-rule and splitting (190), into two cases. % 16.41/4.48 |-Branch one: % 16.41/4.48 | (217) all_24_0_32 = 0 % 16.41/4.48 | % 16.41/4.48 | Equations (217) can reduce 82 to: % 16.41/4.48 | (100) $false % 16.41/4.48 | % 16.41/4.48 |-The branch is then unsatisfiable % 16.41/4.48 |-Branch two: % 16.41/4.48 | (82) ~ (all_24_0_32 = 0) % 16.41/4.48 | (272) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (158), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (276) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (159), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (280) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (197), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (284) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (198), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (288) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (164), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (292) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (193), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (213) all_20_0_28 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (213) can reduce 74 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (74) ~ (all_20_0_28 = 0) % 16.41/4.49 | (296) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (194), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (213) all_20_0_28 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (213) can reduce 74 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (74) ~ (all_20_0_28 = 0) % 16.41/4.49 | (300) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (202), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (304) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (168), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (308) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (203), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (312) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (195), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (213) all_20_0_28 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (213) can reduce 74 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (74) ~ (all_20_0_28 = 0) % 16.41/4.49 | (316) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (204), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (209) all_22_0_30 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (209) can reduce 78 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (78) ~ (all_22_0_30 = 0) % 16.41/4.49 | (320) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (169), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (324) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (170), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (328) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (171), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (332) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (196), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (336) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (199), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (340) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (200), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (344) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (172), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (348) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (175), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (352) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (173), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (356) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (174), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (217) all_24_0_32 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (217) can reduce 82 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (82) ~ (all_24_0_32 = 0) % 16.41/4.49 | (360) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (176), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (225) all_27_0_35 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (225) can reduce 87 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (87) ~ (all_27_0_35 = 0) % 16.41/4.49 | (364) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.41/4.49 | % 16.41/4.49 +-Applying beta-rule and splitting (179), into two cases. % 16.41/4.49 |-Branch one: % 16.41/4.49 | (209) all_22_0_30 = 0 % 16.41/4.49 | % 16.41/4.49 | Equations (209) can reduce 78 to: % 16.41/4.49 | (100) $false % 16.41/4.49 | % 16.41/4.49 |-The branch is then unsatisfiable % 16.41/4.49 |-Branch two: % 16.41/4.49 | (78) ~ (all_22_0_30 = 0) % 16.41/4.49 | (368) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (187), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (217) all_24_0_32 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (217) can reduce 82 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (82) ~ (all_24_0_32 = 0) % 16.41/4.50 | (380) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (180), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (209) all_22_0_30 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (209) can reduce 78 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (78) ~ (all_22_0_30 = 0) % 16.41/4.50 | (384) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (181), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (209) all_22_0_30 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (209) can reduce 78 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (78) ~ (all_22_0_30 = 0) % 16.41/4.50 | (388) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (182), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (209) all_22_0_30 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (209) can reduce 78 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (78) ~ (all_22_0_30 = 0) % 16.41/4.50 | (392) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (188), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (217) all_24_0_32 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (217) can reduce 82 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (82) ~ (all_24_0_32 = 0) % 16.41/4.50 | (400) all_22_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (192), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (213) all_20_0_28 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (213) can reduce 74 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (74) ~ (all_20_0_28 = 0) % 16.41/4.50 | (718) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (244), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (99) all_0_0_0 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (99) can reduce 35 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (35) ~ (all_0_0_0 = 0) % 16.41/4.50 | (404) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (248), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (213) all_20_0_28 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (213) can reduce 74 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (74) ~ (all_20_0_28 = 0) % 16.41/4.50 | (726) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (256), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (412) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (268), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (99) all_0_0_0 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (99) can reduce 35 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (35) ~ (all_0_0_0 = 0) % 16.41/4.50 | (416) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (276), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (99) all_0_0_0 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (99) can reduce 35 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (35) ~ (all_0_0_0 = 0) % 16.41/4.50 | (420) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 16.41/4.50 | % 16.41/4.50 | Instantiating (420) with all_282_0_892 yields: % 16.41/4.50 | (739) (all_282_0_892 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_282_0_892 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (all_282_0_892 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_892) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (284), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (213) all_20_0_28 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (213) can reduce 74 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (74) ~ (all_20_0_28 = 0) % 16.41/4.50 | (743) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (288), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (213) all_20_0_28 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (213) can reduce 74 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (74) ~ (all_20_0_28 = 0) % 16.41/4.50 | (747) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (300), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (425) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (304), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (213) all_20_0_28 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (213) can reduce 74 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (74) ~ (all_20_0_28 = 0) % 16.41/4.50 | (755) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (336), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (213) all_20_0_28 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (213) can reduce 74 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (74) ~ (all_20_0_28 = 0) % 16.41/4.50 | (759) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (739), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (760) (all_282_0_892 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_282_0_892 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (760), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (761) all_282_0_892 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0 % 16.41/4.50 | % 16.41/4.50 | Applying alpha-rule on (761) yields: % 16.41/4.50 | (762) all_282_0_892 = 0 % 16.41/4.50 | (429) apart_point_and_line(all_0_7_7, all_0_2_2) = 0 % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (260), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (433) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (264), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (437) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (292), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (441) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (316), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (445) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (332), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (449) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (348), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (453) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0)) % 16.41/4.50 | % 16.41/4.50 +-Applying beta-rule and splitting (356), into two cases. % 16.41/4.50 |-Branch one: % 16.41/4.50 | (114) all_0_1_1 = 0 % 16.41/4.50 | % 16.41/4.50 | Equations (114) can reduce 20 to: % 16.41/4.50 | (100) $false % 16.41/4.50 | % 16.41/4.50 |-The branch is then unsatisfiable % 16.41/4.50 |-Branch two: % 16.41/4.50 | (20) ~ (all_0_1_1 = 0) % 16.41/4.50 | (457) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (360), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (114) all_0_1_1 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (114) can reduce 20 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (20) ~ (all_0_1_1 = 0) % 16.41/4.51 | (461) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0)) % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (388), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (114) all_0_1_1 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (114) can reduce 20 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (20) ~ (all_0_1_1 = 0) % 16.41/4.51 | (465) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0)) % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (392), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (114) all_0_1_1 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (114) can reduce 20 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (20) ~ (all_0_1_1 = 0) % 16.41/4.51 | (469) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0)) % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (25) with all_0_7_7, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields: % 16.41/4.51 | (114) all_0_1_1 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (114) can reduce 20 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (806) all_282_0_892 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0 % 16.41/4.51 | % 16.41/4.51 | Applying alpha-rule on (806) yields: % 16.41/4.51 | (762) all_282_0_892 = 0 % 16.41/4.51 | (474) apart_point_and_line(all_0_7_7, all_0_5_5) = 0 % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (352), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (217) all_24_0_32 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (217) can reduce 82 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (82) ~ (all_24_0_32 = 0) % 16.41/4.51 | (478) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0)) % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (364), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (217) all_24_0_32 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (217) can reduce 82 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (82) ~ (all_24_0_32 = 0) % 16.41/4.51 | (482) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)) % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (25) with all_0_7_7, all_0_5_5, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_24_0_32, apart_point_and_line(all_0_7_7, all_0_5_5) = 0, yields: % 16.41/4.51 | (217) all_24_0_32 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (217) can reduce 82 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (819) ~ (all_282_0_892 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_892 % 16.41/4.51 | % 16.41/4.51 | Applying alpha-rule on (819) yields: % 16.41/4.51 | (820) ~ (all_282_0_892 = 0) % 16.41/4.51 | (821) distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_892 % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (312), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (213) all_20_0_28 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (213) can reduce 74 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (74) ~ (all_20_0_28 = 0) % 16.41/4.51 | (825) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0)) % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (320), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (213) all_20_0_28 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (213) can reduce 74 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (74) ~ (all_20_0_28 = 0) % 16.41/4.51 | (829) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0)) % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (340), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (213) all_20_0_28 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (213) can reduce 74 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (74) ~ (all_20_0_28 = 0) % 16.41/4.51 | (833) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0)) % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (344), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (213) all_20_0_28 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (213) can reduce 74 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (74) ~ (all_20_0_28 = 0) % 16.41/4.51 | (837) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0)) % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (33) with all_20_0_28, all_282_0_892, all_0_2_2, all_0_5_5, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_892, yields: % 16.41/4.51 | (838) all_282_0_892 = 0 | all_20_0_28 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_5_5) = v0) % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (23) with all_282_0_892, all_0_2_2, all_0_5_5, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_5_5) = 0, distinct_lines(all_0_5_5, all_0_2_2) = all_282_0_892, yields: % 16.41/4.51 | (839) all_282_0_892 = 0 | apart_point_and_line(all_0_9_9, all_0_2_2) = 0 % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (839), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (840) apart_point_and_line(all_0_9_9, all_0_2_2) = 0 % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (838), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (762) all_282_0_892 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (762) can reduce 820 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (820) ~ (all_282_0_892 = 0) % 16.41/4.51 | (844) all_20_0_28 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_5_5) = v0) % 16.41/4.51 | % 16.41/4.51 +-Applying beta-rule and splitting (844), into two cases. % 16.41/4.51 |-Branch one: % 16.41/4.51 | (213) all_20_0_28 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (213) can reduce 74 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (74) ~ (all_20_0_28 = 0) % 16.41/4.51 | (848) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_5_5) = v0) % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (25) with all_0_9_9, all_0_2_2, 0, all_20_0_28 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_20_0_28, apart_point_and_line(all_0_9_9, all_0_2_2) = 0, yields: % 16.41/4.51 | (213) all_20_0_28 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (213) can reduce 74 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (851) ~ (apart_point_and_line(all_0_9_9, all_0_2_2) = 0) % 16.41/4.51 | (762) all_282_0_892 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (762) can reduce 820 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (854) ~ (all_31_0_39 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_31_0_39 % 16.41/4.51 | % 16.41/4.51 | Applying alpha-rule on (854) yields: % 16.41/4.51 | (127) ~ (all_31_0_39 = 0) % 16.41/4.51 | (856) distinct_points(all_0_7_7, all_0_6_6) = all_31_0_39 % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (36) with all_0_7_7, all_0_6_6, all_31_0_39, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_31_0_39, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 16.41/4.51 | (857) all_31_0_39 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (857) can reduce 127 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (859) ~ (all_29_0_37 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_29_0_37 % 16.41/4.51 | % 16.41/4.51 | Applying alpha-rule on (859) yields: % 16.41/4.51 | (112) ~ (all_29_0_37 = 0) % 16.41/4.51 | (861) distinct_points(all_0_9_9, all_0_8_8) = all_29_0_37 % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (36) with all_0_9_9, all_0_8_8, all_29_0_37, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_29_0_37, distinct_points(all_0_9_9, all_0_8_8) = 0, yields: % 16.41/4.51 | (862) all_29_0_37 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (862) can reduce 112 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (864) ~ (all_26_0_34 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_26_0_34 % 16.41/4.51 | % 16.41/4.51 | Applying alpha-rule on (864) yields: % 16.41/4.51 | (97) ~ (all_26_0_34 = 0) % 16.41/4.51 | (866) distinct_points(all_0_9_9, all_0_8_8) = all_26_0_34 % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (36) with all_0_9_9, all_0_8_8, all_26_0_34, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_26_0_34, distinct_points(all_0_9_9, all_0_8_8) = 0, yields: % 16.41/4.51 | (867) all_26_0_34 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (867) can reduce 97 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 |-Branch two: % 16.41/4.51 | (869) ~ (all_30_0_38 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_30_0_38 % 16.41/4.51 | % 16.41/4.51 | Applying alpha-rule on (869) yields: % 16.41/4.51 | (94) ~ (all_30_0_38 = 0) % 16.41/4.51 | (871) distinct_points(all_0_7_7, all_0_6_6) = all_30_0_38 % 16.41/4.51 | % 16.41/4.51 | Instantiating formula (36) with all_0_7_7, all_0_6_6, all_30_0_38, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_30_0_38, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 16.41/4.51 | (872) all_30_0_38 = 0 % 16.41/4.51 | % 16.41/4.51 | Equations (872) can reduce 94 to: % 16.41/4.51 | (100) $false % 16.41/4.51 | % 16.41/4.51 |-The branch is then unsatisfiable % 16.41/4.51 % SZS output end Proof for theBenchmark % 16.41/4.51 % 16.41/4.51 3915ms %------------------------------------------------------------------------------