%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO197+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 03:48:33 EDT 2022 % Result : Theorem 5.63s 1.94s % Output : Proof 24.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO197+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n019.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 10:20:39 EDT 2022 % 0.12/0.33 % CPUTime : % 0.49/0.58 ____ _ % 0.49/0.58 ___ / __ \_____(_)___ ________ __________ % 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.58 % 0.49/0.58 A Theorem Prover for First-Order Logic % 0.49/0.58 (ePrincess v.1.0) % 0.49/0.58 % 0.49/0.58 (c) Philipp Rümmer, 2009-2015 % 0.49/0.58 (c) Peter Backeman, 2014-2015 % 0.49/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.58 Bug reports to peter@backeman.se % 0.49/0.58 % 0.49/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.58 % 0.49/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.49/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.42/0.92 Prover 0: Preprocessing ... % 1.83/1.05 Prover 0: Warning: ignoring some quantifiers % 1.98/1.07 Prover 0: Constructing countermodel ... % 3.11/1.37 Prover 0: gave up % 3.11/1.37 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.11/1.40 Prover 1: Preprocessing ... % 3.47/1.48 Prover 1: Constructing countermodel ... % 3.47/1.52 Prover 1: gave up % 3.47/1.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.78/1.54 Prover 2: Preprocessing ... % 3.99/1.64 Prover 2: Warning: ignoring some quantifiers % 3.99/1.65 Prover 2: Constructing countermodel ... % 5.63/1.94 Prover 2: proved (427ms) % 5.63/1.94 % 5.63/1.94 No countermodel exists, formula is valid % 5.63/1.94 % SZS status Theorem for theBenchmark % 5.63/1.94 % 5.63/1.94 Generating proof ... Warning: ignoring some quantifiers % 23.37/7.12 found it (size 403) % 23.37/7.12 % 23.37/7.12 % SZS output start Proof for theBenchmark % 23.37/7.12 Assumed formulas after preprocessing and simplification: % 23.37/7.12 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & intersection_point(v2, v1) = v5 & intersection_point(v0, v1) = v3 & apart_point_and_line(v5, v0) = 0 & apart_point_and_line(v3, v2) = v4 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8) % 23.83/7.17 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 23.83/7.17 | (1) ~ (all_0_1_1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_0_0_0 & intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1 & convergent_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 23.83/7.19 | % 23.83/7.19 | Applying alpha-rule on (1) yields: % 23.83/7.19 | (2) intersection_point(all_0_3_3, all_0_4_4) = all_0_0_0 % 23.83/7.19 | (3) ! [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))) % 23.83/7.19 | (4) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 23.83/7.19 | (5) ! [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)) % 23.83/7.19 | (6) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 23.83/7.19 | (7) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 23.83/7.19 | (8) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 23.83/7.19 | (9) ! [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))) % 23.83/7.19 | (10) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 23.83/7.19 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 23.83/7.19 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 23.83/7.19 | (13) ! [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)) % 23.83/7.19 | (14) ! [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)) % 23.83/7.20 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 23.83/7.20 | (16) ! [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))) % 23.83/7.20 | (17) convergent_lines(all_0_5_5, all_0_4_4) = 0 % 23.83/7.20 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 23.83/7.20 | (19) ! [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) % 23.95/7.20 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 23.95/7.20 | (21) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 23.95/7.20 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 23.95/7.20 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 23.95/7.20 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 23.95/7.20 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 23.95/7.20 | (26) ! [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))) % 23.95/7.20 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 23.95/7.20 | (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)) % 23.95/7.20 | (29) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 23.95/7.20 | (30) convergent_lines(all_0_3_3, all_0_4_4) = 0 % 23.95/7.20 | (31) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 23.95/7.20 | (32) ~ (all_0_1_1 = 0) % 23.95/7.20 | (33) ! [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) % 23.95/7.20 | (34) apart_point_and_line(all_0_0_0, all_0_5_5) = 0 % 23.95/7.20 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 23.95/7.20 | (36) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 23.95/7.20 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 23.95/7.20 | (38) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 23.95/7.20 | (39) ! [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))) % 23.95/7.20 | (40) intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 % 23.95/7.20 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 23.95/7.20 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 23.95/7.20 | (43) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 23.95/7.21 | (44) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 23.95/7.21 | (45) ! [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))) % 23.95/7.21 | (46) ! [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)) % 23.95/7.21 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 23.95/7.21 | (48) ! [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) % 23.95/7.21 | (49) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 23.95/7.21 | (50) apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1 % 23.95/7.21 | (51) ! [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))) % 23.95/7.21 | (52) ! [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)) % 23.95/7.21 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 23.95/7.21 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 23.95/7.21 | (55) ! [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) % 23.95/7.21 | (56) convergent_lines(all_0_5_5, all_0_3_3) = 0 % 23.95/7.21 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 23.95/7.21 | % 23.95/7.21 | Instantiating formula (23) with all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_0_0_0, yields: % 23.95/7.21 | (58) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_0_0, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 23.95/7.21 | % 23.95/7.21 | Instantiating formula (3) with all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_0_0_0, yields: % 23.95/7.21 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 23.95/7.21 | % 23.95/7.21 | Instantiating formula (23) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 23.95/7.21 | (60) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0)) % 23.95/7.21 | % 23.95/7.21 | Instantiating formula (3) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 23.95/7.21 | (61) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0)) % 23.95/7.21 | % 23.95/7.21 | Instantiating formula (51) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 23.95/7.21 | (62) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 23.95/7.21 | % 23.95/7.21 | Instantiating formula (31) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 23.95/7.21 | (63) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1) % 23.95/7.21 | % 23.95/7.21 | Instantiating formula (49) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 23.95/7.21 | (64) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_3_3) = v1) % 23.95/7.21 | % 23.95/7.21 | Instantiating formula (31) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields: % 23.95/7.21 | (65) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_3_3) = v1) % 23.95/7.22 | % 23.95/7.22 | Instantiating formula (49) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields: % 23.95/7.22 | (66) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_5_5) = v1) % 23.95/7.22 | % 23.95/7.22 | Instantiating formula (31) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 23.95/7.22 | (67) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1) % 23.95/7.22 | % 23.95/7.22 | Instantiating formula (49) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 23.95/7.22 | (68) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_5_5) = v1) % 23.95/7.22 | % 23.95/7.22 | Instantiating (68) with all_20_0_24, all_20_1_25 yields: % 23.95/7.22 | (69) ~ (all_20_0_24 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25 & apart_point_and_line(all_20_1_25, all_0_5_5) = all_20_0_24 % 23.95/7.22 | % 23.95/7.22 | Applying alpha-rule on (69) yields: % 23.95/7.22 | (70) ~ (all_20_0_24 = 0) % 23.95/7.22 | (71) intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25 % 23.95/7.22 | (72) apart_point_and_line(all_20_1_25, all_0_5_5) = all_20_0_24 % 23.95/7.22 | % 23.95/7.22 | Instantiating (65) with all_22_0_26, all_22_1_27 yields: % 23.95/7.22 | (73) ~ (all_22_0_26 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27 & apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26 % 23.95/7.22 | % 23.95/7.22 | Applying alpha-rule on (73) yields: % 23.95/7.22 | (74) ~ (all_22_0_26 = 0) % 23.95/7.22 | (75) intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27 % 23.95/7.22 | (76) apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26 % 23.95/7.22 | % 23.95/7.22 | Instantiating (64) with all_24_0_28, all_24_1_29 yields: % 23.95/7.22 | (77) ~ (all_24_0_28 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29 & apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28 % 23.95/7.22 | % 23.95/7.22 | Applying alpha-rule on (77) yields: % 23.95/7.22 | (78) ~ (all_24_0_28 = 0) % 23.95/7.22 | (79) intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29 % 23.95/7.22 | (80) apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28 % 23.95/7.22 | % 23.95/7.22 | Instantiating (63) with all_26_0_30, all_26_1_31 yields: % 23.95/7.22 | (81) ~ (all_26_0_30 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31 & apart_point_and_line(all_26_1_31, all_0_4_4) = all_26_0_30 % 24.06/7.22 | % 24.06/7.22 | Applying alpha-rule on (81) yields: % 24.06/7.22 | (82) ~ (all_26_0_30 = 0) % 24.06/7.22 | (83) intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31 % 24.06/7.22 | (84) apart_point_and_line(all_26_1_31, all_0_4_4) = all_26_0_30 % 24.06/7.22 | % 24.06/7.22 | Instantiating (67) with all_28_0_32, all_28_1_33 yields: % 24.06/7.22 | (85) ~ (all_28_0_32 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33 & apart_point_and_line(all_28_1_33, all_0_4_4) = all_28_0_32 % 24.06/7.22 | % 24.06/7.22 | Applying alpha-rule on (85) yields: % 24.06/7.22 | (86) ~ (all_28_0_32 = 0) % 24.06/7.22 | (87) intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33 % 24.06/7.22 | (88) apart_point_and_line(all_28_1_33, all_0_4_4) = all_28_0_32 % 24.06/7.22 | % 24.06/7.22 | Instantiating (61) with all_30_0_34 yields: % 24.06/7.22 | (89) ( ~ (all_30_0_34 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34) | ( ~ (all_30_0_34 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34) % 24.06/7.22 | % 24.06/7.22 | Instantiating (60) with all_31_0_35 yields: % 24.06/7.22 | (90) ( ~ (all_31_0_35 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35) | ( ~ (all_31_0_35 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35) % 24.06/7.22 | % 24.06/7.22 | Instantiating (66) with all_32_0_36, all_32_1_37 yields: % 24.06/7.22 | (91) ~ (all_32_0_36 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37 & apart_point_and_line(all_32_1_37, all_0_5_5) = all_32_0_36 % 24.06/7.22 | % 24.06/7.22 | Applying alpha-rule on (91) yields: % 24.06/7.22 | (92) ~ (all_32_0_36 = 0) % 24.06/7.22 | (93) intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37 % 24.06/7.22 | (94) apart_point_and_line(all_32_1_37, all_0_5_5) = all_32_0_36 % 24.06/7.22 | % 24.06/7.22 | Instantiating (59) with all_34_0_38 yields: % 24.06/7.22 | (95) ( ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = all_34_0_38) | ( ~ (all_34_0_38 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38) % 24.06/7.22 | % 24.06/7.22 | Instantiating (58) with all_35_0_39 yields: % 24.06/7.22 | (96) ( ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_0_0, all_0_4_4) = all_35_0_39) | ( ~ (all_35_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39) % 24.06/7.22 | % 24.06/7.22 +-Applying beta-rule and splitting (96), into two cases. % 24.06/7.22 |-Branch one: % 24.06/7.22 | (97) ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_0_0, all_0_4_4) = all_35_0_39 % 24.06/7.22 | % 24.06/7.22 | Applying alpha-rule on (97) yields: % 24.06/7.22 | (98) ~ (all_35_0_39 = 0) % 24.06/7.22 | (99) apart_point_and_line(all_0_0_0, all_0_4_4) = all_35_0_39 % 24.06/7.22 | % 24.06/7.22 +-Applying beta-rule and splitting (62), into two cases. % 24.06/7.22 |-Branch one: % 24.06/7.22 | (100) all_0_1_1 = 0 % 24.06/7.22 | % 24.06/7.22 | Equations (100) can reduce 32 to: % 24.06/7.22 | (101) $false % 24.06/7.22 | % 24.06/7.22 |-The branch is then unsatisfiable % 24.06/7.22 |-Branch two: % 24.06/7.22 | (32) ~ (all_0_1_1 = 0) % 24.06/7.22 | (103) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.23 | % 24.06/7.23 +-Applying beta-rule and splitting (89), into two cases. % 24.06/7.23 |-Branch one: % 24.06/7.23 | (104) ~ (all_30_0_34 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34 % 24.06/7.23 | % 24.06/7.23 | Applying alpha-rule on (104) yields: % 24.06/7.23 | (105) ~ (all_30_0_34 = 0) % 24.06/7.23 | (106) apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34 % 24.06/7.23 | % 24.06/7.23 +-Applying beta-rule and splitting (95), into two cases. % 24.06/7.23 |-Branch one: % 24.06/7.23 | (107) ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = all_34_0_38 % 24.06/7.23 | % 24.06/7.23 | Applying alpha-rule on (107) yields: % 24.06/7.23 | (108) ~ (all_34_0_38 = 0) % 24.06/7.23 | (109) apart_point_and_line(all_0_0_0, all_0_3_3) = all_34_0_38 % 24.06/7.23 | % 24.06/7.23 +-Applying beta-rule and splitting (90), into two cases. % 24.06/7.23 |-Branch one: % 24.06/7.23 | (110) ~ (all_31_0_35 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35 % 24.06/7.23 | % 24.06/7.23 | Applying alpha-rule on (110) yields: % 24.06/7.23 | (111) ~ (all_31_0_35 = 0) % 24.06/7.23 | (112) apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (20) with all_0_3_3, all_0_4_4, all_26_1_31, all_0_0_0 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31, intersection_point(all_0_3_3, all_0_4_4) = all_0_0_0, yields: % 24.06/7.23 | (113) all_26_1_31 = all_0_0_0 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (20) with all_0_3_3, all_0_4_4, all_24_1_29, all_26_1_31 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31, intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29, yields: % 24.06/7.23 | (114) all_26_1_31 = all_24_1_29 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (20) with all_0_5_5, all_0_3_3, all_22_1_27, all_32_1_37 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37, intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27, yields: % 24.06/7.23 | (115) all_32_1_37 = all_22_1_27 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (20) with all_0_5_5, all_0_4_4, all_28_1_33, all_0_2_2 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33, intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 24.06/7.23 | (116) all_28_1_33 = all_0_2_2 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (20) with all_0_5_5, all_0_4_4, all_20_1_25, all_28_1_33 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33, intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25, yields: % 24.06/7.23 | (117) all_28_1_33 = all_20_1_25 % 24.06/7.23 | % 24.06/7.23 | Combining equations (116,117) yields a new equation: % 24.06/7.23 | (118) all_20_1_25 = all_0_2_2 % 24.06/7.23 | % 24.06/7.23 | Combining equations (114,113) yields a new equation: % 24.06/7.23 | (119) all_24_1_29 = all_0_0_0 % 24.06/7.23 | % 24.06/7.23 | Simplifying 119 yields: % 24.06/7.23 | (120) all_24_1_29 = all_0_0_0 % 24.06/7.23 | % 24.06/7.23 | Combining equations (118,117) yields a new equation: % 24.06/7.23 | (116) all_28_1_33 = all_0_2_2 % 24.06/7.23 | % 24.06/7.23 | From (115) and (94) follows: % 24.06/7.23 | (122) apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36 % 24.06/7.23 | % 24.06/7.23 | From (116) and (88) follows: % 24.06/7.23 | (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32 % 24.06/7.23 | % 24.06/7.23 | From (113) and (84) follows: % 24.06/7.23 | (124) apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30 % 24.06/7.23 | % 24.06/7.23 | From (120) and (80) follows: % 24.06/7.23 | (125) apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28 % 24.06/7.23 | % 24.06/7.23 | From (118) and (72) follows: % 24.06/7.23 | (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (41) with all_0_0_0, all_0_3_3, all_24_0_28, all_34_0_38 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_34_0_38, apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, yields: % 24.06/7.23 | (127) all_34_0_38 = all_24_0_28 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (41) with all_0_0_0, all_0_4_4, all_26_0_30, all_35_0_39 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_35_0_39, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.23 | (128) all_35_0_39 = all_26_0_30 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (41) with all_0_2_2, all_0_4_4, all_28_0_32, all_31_0_35 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.23 | (129) all_31_0_35 = all_28_0_32 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (41) with all_0_2_2, all_0_5_5, all_20_0_24, all_30_0_34 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.23 | (130) all_30_0_34 = all_20_0_24 % 24.06/7.23 | % 24.06/7.23 | Equations (128) can reduce 98 to: % 24.06/7.23 | (82) ~ (all_26_0_30 = 0) % 24.06/7.23 | % 24.06/7.23 | Equations (127) can reduce 108 to: % 24.06/7.23 | (78) ~ (all_24_0_28 = 0) % 24.06/7.23 | % 24.06/7.23 | Equations (129) can reduce 111 to: % 24.06/7.23 | (86) ~ (all_28_0_32 = 0) % 24.06/7.23 | % 24.06/7.23 | Equations (130) can reduce 105 to: % 24.06/7.23 | (70) ~ (all_20_0_24 = 0) % 24.06/7.23 | % 24.06/7.23 | From (127) and (109) follows: % 24.06/7.23 | (125) apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28 % 24.06/7.23 | % 24.06/7.23 | From (128) and (99) follows: % 24.06/7.23 | (124) apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30 % 24.06/7.23 | % 24.06/7.23 | From (129) and (112) follows: % 24.06/7.23 | (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32 % 24.06/7.23 | % 24.06/7.23 | From (130) and (106) follows: % 24.06/7.23 | (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24 % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (51) with all_22_0_26, all_0_1_1, all_0_3_3, all_0_3_3, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.23 | (139) all_22_0_26 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.23 | % 24.06/7.23 | Instantiating formula (51) with all_0_1_1, all_22_0_26, all_0_3_3, all_0_3_3, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.23 | (140) all_22_0_26 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_22_0_26, all_22_0_26, all_0_3_3, all_0_3_3, all_22_1_27, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, yields: % 24.06/7.24 | (141) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_32_0_36, all_0_1_1, all_0_5_5, all_0_3_3, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.24 | (142) all_32_0_36 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (26) with all_32_0_36, all_0_1_1, all_0_3_3, all_0_5_5, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.24 | (143) all_32_0_36 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (26) with all_0_1_1, all_32_0_36, all_0_5_5, all_0_3_3, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.24 | (144) all_32_0_36 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_32_0_36, all_22_0_26, all_0_5_5, all_0_3_3, all_22_1_27, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, yields: % 24.06/7.24 | (145) all_32_0_36 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_22_0_26, all_32_0_36, all_0_3_3, all_0_5_5, all_22_1_27, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, yields: % 24.06/7.24 | (146) all_32_0_36 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_32_0_36, all_32_0_36, all_0_5_5, all_0_5_5, all_22_1_27, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, yields: % 24.06/7.24 | (147) all_32_0_36 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_24_0_28, all_0_1_1, all_0_3_3, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.24 | (148) all_24_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_0_1_1, all_24_0_28, all_0_3_3, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.24 | (149) all_24_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_24_0_28, all_22_0_26, all_0_3_3, all_0_3_3, all_0_0_0, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, yields: % 24.06/7.24 | (150) all_24_0_28 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_24_0_28, all_32_0_36, all_0_3_3, all_0_5_5, all_0_0_0, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, yields: % 24.06/7.24 | (151) all_32_0_36 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_32_0_36, all_24_0_28, all_0_5_5, all_0_3_3, all_22_1_27, all_0_0_0 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, yields: % 24.06/7.24 | (152) all_32_0_36 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (26) with all_24_0_28, all_32_0_36, all_0_5_5, all_0_3_3, all_0_0_0, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, yields: % 24.06/7.24 | (153) all_32_0_36 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_24_0_28, all_24_0_28, all_0_3_3, all_0_3_3, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, yields: % 24.06/7.24 | (154) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 24.06/7.24 | % 24.06/7.24 | Instantiating formula (51) with all_26_0_30, all_0_1_1, all_0_4_4, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.24 | (155) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_0_1_1, all_26_0_30, all_0_3_3, all_0_4_4, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.25 | (156) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (26) with all_26_0_30, all_0_1_1, all_0_3_3, all_0_4_4, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.25 | (157) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (26) with all_0_1_1, all_26_0_30, all_0_4_4, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 24.06/7.25 | (158) all_26_0_30 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_26_0_30, all_22_0_26, all_0_4_4, all_0_3_3, all_0_0_0, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (159) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_22_0_26, all_26_0_30, all_0_3_3, all_0_4_4, all_22_1_27, all_0_0_0 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (160) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (26) with all_26_0_30, all_22_0_26, all_0_3_3, all_0_4_4, all_0_0_0, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (161) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (26) with all_22_0_26, all_26_0_30, all_0_4_4, all_0_3_3, all_22_1_27, all_0_0_0 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (162) all_26_0_30 = 0 | all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_26_0_30, all_32_0_36, all_0_4_4, all_0_5_5, all_0_0_0, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (163) all_32_0_36 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_32_0_36, all_26_0_30, all_0_5_5, all_0_4_4, all_22_1_27, all_0_0_0 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (164) all_32_0_36 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (26) with all_26_0_30, all_32_0_36, all_0_5_5, all_0_4_4, all_0_0_0, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (165) all_32_0_36 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_26_0_30, all_24_0_28, all_0_4_4, all_0_3_3, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (166) all_26_0_30 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_24_0_28, all_26_0_30, all_0_3_3, all_0_4_4, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (167) all_26_0_30 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_26_0_30, all_26_0_30, all_0_4_4, all_0_4_4, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, yields: % 24.06/7.25 | (168) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_28_0_32, all_0_1_1, all_0_4_4, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.25 | (169) all_28_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_0_1_1, all_28_0_32, all_0_3_3, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.25 | (170) all_28_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_28_0_32, all_32_0_36, all_0_4_4, all_0_5_5, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.25 | (171) all_32_0_36 = 0 | all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (51) with all_32_0_36, all_28_0_32, all_0_5_5, all_0_4_4, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.25 | (172) all_32_0_36 = 0 | all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.25 | % 24.06/7.25 | Instantiating formula (26) with all_28_0_32, all_32_0_36, all_0_5_5, all_0_4_4, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.25 | (173) all_32_0_36 = 0 | all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (26) with all_32_0_36, all_28_0_32, all_0_4_4, all_0_5_5, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.26 | (174) all_32_0_36 = 0 | all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_28_0_32, all_24_0_28, all_0_4_4, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.26 | (175) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_24_0_28, all_28_0_32, all_0_3_3, all_0_4_4, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.26 | (176) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (26) with all_28_0_32, all_24_0_28, all_0_3_3, all_0_4_4, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.26 | (177) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (26) with all_24_0_28, all_28_0_32, all_0_4_4, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.26 | (178) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_28_0_32, all_26_0_30, all_0_4_4, all_0_4_4, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.26 | (179) all_28_0_32 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_26_0_30, all_28_0_32, all_0_4_4, all_0_4_4, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.26 | (180) all_28_0_32 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_28_0_32, all_28_0_32, all_0_4_4, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 24.06/7.26 | (181) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (19) with all_20_0_24, all_0_2_2, all_0_5_5, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = 0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (182) all_20_0_24 = 0 | distinct_points(all_0_0_0, all_0_2_2) = 0 % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_20_0_24, all_0_1_1, all_0_5_5, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (183) all_20_0_24 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_0_1_1, all_20_0_24, all_0_3_3, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (184) all_20_0_24 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_20_0_24, all_22_0_26, all_0_5_5, all_0_3_3, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (185) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_22_0_26, all_20_0_24, all_0_3_3, all_0_5_5, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (186) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (26) with all_20_0_24, all_22_0_26, all_0_3_3, all_0_5_5, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (187) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (26) with all_22_0_26, all_20_0_24, all_0_5_5, all_0_3_3, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (188) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_20_0_24, all_32_0_36, all_0_5_5, all_0_5_5, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (189) all_32_0_36 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_32_0_36, all_20_0_24, all_0_5_5, all_0_5_5, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (190) all_32_0_36 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_20_0_24, all_24_0_28, all_0_5_5, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (191) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_24_0_28, all_20_0_24, all_0_3_3, all_0_5_5, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (192) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (26) with all_24_0_28, all_20_0_24, all_0_5_5, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.26 | (193) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.26 | % 24.06/7.26 | Instantiating formula (51) with all_20_0_24, all_26_0_30, all_0_5_5, all_0_4_4, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.27 | (194) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 | Instantiating formula (51) with all_26_0_30, all_20_0_24, all_0_4_4, all_0_5_5, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.27 | (195) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.27 | % 24.06/7.27 | Instantiating formula (26) with all_26_0_30, all_20_0_24, all_0_5_5, all_0_4_4, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 24.06/7.27 | (196) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (141), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (197) all_22_0_26 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (197) can reduce 74 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (74) ~ (all_22_0_26 = 0) % 24.06/7.27 | (200) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (147), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (201) all_32_0_36 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (201) can reduce 92 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (92) ~ (all_32_0_36 = 0) % 24.06/7.27 | (204) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (181), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (205) all_28_0_32 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (205) can reduce 86 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (86) ~ (all_28_0_32 = 0) % 24.06/7.27 | (208) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (145), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (201) all_32_0_36 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (201) can reduce 92 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (92) ~ (all_32_0_36 = 0) % 24.06/7.27 | (212) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (144), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (201) all_32_0_36 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (201) can reduce 92 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (92) ~ (all_32_0_36 = 0) % 24.06/7.27 | (216) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (140), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (197) all_22_0_26 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (197) can reduce 74 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (74) ~ (all_22_0_26 = 0) % 24.06/7.27 | (220) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (182), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (221) distinct_points(all_0_0_0, all_0_2_2) = 0 % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (168), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (222) all_26_0_30 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (222) can reduce 82 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (82) ~ (all_26_0_30 = 0) % 24.06/7.27 | (225) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (183), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (226) all_20_0_24 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (226) can reduce 70 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (70) ~ (all_20_0_24 = 0) % 24.06/7.27 | (229) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (184), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (226) all_20_0_24 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (226) can reduce 70 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (70) ~ (all_20_0_24 = 0) % 24.06/7.27 | (233) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (185), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (197) all_22_0_26 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (197) can reduce 74 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (74) ~ (all_22_0_26 = 0) % 24.06/7.27 | (237) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (186), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (197) all_22_0_26 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (197) can reduce 74 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (74) ~ (all_22_0_26 = 0) % 24.06/7.27 | (241) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (149), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (242) all_24_0_28 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (242) can reduce 78 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (78) ~ (all_24_0_28 = 0) % 24.06/7.27 | (245) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (150), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (242) all_24_0_28 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (242) can reduce 78 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (78) ~ (all_24_0_28 = 0) % 24.06/7.27 | (249) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (189), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (201) all_32_0_36 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (201) can reduce 92 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (92) ~ (all_32_0_36 = 0) % 24.06/7.27 | (253) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (179), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (205) all_28_0_32 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (205) can reduce 86 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (86) ~ (all_28_0_32 = 0) % 24.06/7.27 | (257) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (180), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (205) all_28_0_32 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (205) can reduce 86 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (86) ~ (all_28_0_32 = 0) % 24.06/7.27 | (261) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (187), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (197) all_22_0_26 = 0 % 24.06/7.27 | % 24.06/7.27 | Equations (197) can reduce 74 to: % 24.06/7.27 | (101) $false % 24.06/7.27 | % 24.06/7.27 |-The branch is then unsatisfiable % 24.06/7.27 |-Branch two: % 24.06/7.27 | (74) ~ (all_22_0_26 = 0) % 24.06/7.27 | (265) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.27 | % 24.06/7.27 +-Applying beta-rule and splitting (188), into two cases. % 24.06/7.27 |-Branch one: % 24.06/7.27 | (197) all_22_0_26 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (197) can reduce 74 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (74) ~ (all_22_0_26 = 0) % 24.06/7.28 | (269) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (190), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (201) all_32_0_36 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (201) can reduce 92 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (92) ~ (all_32_0_36 = 0) % 24.06/7.28 | (273) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (146), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (201) all_32_0_36 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (201) can reduce 92 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (92) ~ (all_32_0_36 = 0) % 24.06/7.28 | (277) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (148), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (242) all_24_0_28 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (242) can reduce 78 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (78) ~ (all_24_0_28 = 0) % 24.06/7.28 | (281) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (220), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (100) all_0_1_1 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (100) can reduce 32 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (32) ~ (all_0_1_1 = 0) % 24.06/7.28 | (285) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (154), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (242) all_24_0_28 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (242) can reduce 78 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (78) ~ (all_24_0_28 = 0) % 24.06/7.28 | (289) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (281), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (100) all_0_1_1 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (100) can reduce 32 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (32) ~ (all_0_1_1 = 0) % 24.06/7.28 | (293) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (169), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (205) all_28_0_32 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (205) can reduce 86 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (86) ~ (all_28_0_32 = 0) % 24.06/7.28 | (297) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (170), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (205) all_28_0_32 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (205) can reduce 86 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (86) ~ (all_28_0_32 = 0) % 24.06/7.28 | (301) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (177), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (205) all_28_0_32 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (205) can reduce 86 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (86) ~ (all_28_0_32 = 0) % 24.06/7.28 | (305) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (175), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (205) all_28_0_32 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (205) can reduce 86 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (86) ~ (all_28_0_32 = 0) % 24.06/7.28 | (309) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (176), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (205) all_28_0_32 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (205) can reduce 86 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (86) ~ (all_28_0_32 = 0) % 24.06/7.28 | (313) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (178), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (205) all_28_0_32 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (205) can reduce 86 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (86) ~ (all_28_0_32 = 0) % 24.06/7.28 | (317) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (171), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (201) all_32_0_36 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (201) can reduce 92 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (92) ~ (all_32_0_36 = 0) % 24.06/7.28 | (321) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (172), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (201) all_32_0_36 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (201) can reduce 92 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (92) ~ (all_32_0_36 = 0) % 24.06/7.28 | (325) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (194), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (222) all_26_0_30 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (222) can reduce 82 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (82) ~ (all_26_0_30 = 0) % 24.06/7.28 | (329) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (195), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (222) all_26_0_30 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (222) can reduce 82 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (82) ~ (all_26_0_30 = 0) % 24.06/7.28 | (333) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (191), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (242) all_24_0_28 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (242) can reduce 78 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (78) ~ (all_24_0_28 = 0) % 24.06/7.28 | (337) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (192), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (242) all_24_0_28 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (242) can reduce 78 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (78) ~ (all_24_0_28 = 0) % 24.06/7.28 | (341) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.28 | % 24.06/7.28 +-Applying beta-rule and splitting (193), into two cases. % 24.06/7.28 |-Branch one: % 24.06/7.28 | (242) all_24_0_28 = 0 % 24.06/7.28 | % 24.06/7.28 | Equations (242) can reduce 78 to: % 24.06/7.28 | (101) $false % 24.06/7.28 | % 24.06/7.28 |-The branch is then unsatisfiable % 24.06/7.28 |-Branch two: % 24.06/7.28 | (78) ~ (all_24_0_28 = 0) % 24.06/7.28 | (345) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.28 | % 24.06/7.29 +-Applying beta-rule and splitting (196), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (222) all_26_0_30 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (222) can reduce 82 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (82) ~ (all_26_0_30 = 0) % 24.06/7.29 | (349) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (173), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (201) all_32_0_36 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (201) can reduce 92 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (92) ~ (all_32_0_36 = 0) % 24.06/7.29 | (353) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (174), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (201) all_32_0_36 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (201) can reduce 92 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (92) ~ (all_32_0_36 = 0) % 24.06/7.29 | (357) all_28_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (216), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (100) all_0_1_1 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (100) can reduce 32 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (32) ~ (all_0_1_1 = 0) % 24.06/7.29 | (361) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (229), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (100) all_0_1_1 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (100) can reduce 32 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (32) ~ (all_0_1_1 = 0) % 24.06/7.29 | (365) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (261), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (222) all_26_0_30 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (222) can reduce 82 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (82) ~ (all_26_0_30 = 0) % 24.06/7.29 | (369) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (277), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (197) all_22_0_26 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (197) can reduce 74 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (74) ~ (all_22_0_26 = 0) % 24.06/7.29 | (373) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (317), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (242) all_24_0_28 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (242) can reduce 78 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (78) ~ (all_24_0_28 = 0) % 24.06/7.29 | (377) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (156), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (222) all_26_0_30 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (222) can reduce 82 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (82) ~ (all_26_0_30 = 0) % 24.06/7.29 | (381) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (157), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (222) all_26_0_30 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (222) can reduce 82 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (82) ~ (all_26_0_30 = 0) % 24.06/7.29 | (385) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (158), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (222) all_26_0_30 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (222) can reduce 82 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (82) ~ (all_26_0_30 = 0) % 24.06/7.29 | (389) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (159), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (222) all_26_0_30 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (222) can reduce 82 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (82) ~ (all_26_0_30 = 0) % 24.06/7.29 | (393) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (162), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (222) all_26_0_30 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (222) can reduce 82 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (82) ~ (all_26_0_30 = 0) % 24.06/7.29 | (397) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (152), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (201) all_32_0_36 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (201) can reduce 92 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (92) ~ (all_32_0_36 = 0) % 24.06/7.29 | (401) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (151), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (201) all_32_0_36 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (201) can reduce 92 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (92) ~ (all_32_0_36 = 0) % 24.06/7.29 | (405) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (153), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (201) all_32_0_36 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (201) can reduce 92 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (92) ~ (all_32_0_36 = 0) % 24.06/7.29 | (409) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (143), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (201) all_32_0_36 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (201) can reduce 92 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (92) ~ (all_32_0_36 = 0) % 24.06/7.29 | (413) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (139), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (197) all_22_0_26 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (197) can reduce 74 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (74) ~ (all_22_0_26 = 0) % 24.06/7.29 | (417) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (142), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (201) all_32_0_36 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (201) can reduce 92 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (92) ~ (all_32_0_36 = 0) % 24.06/7.29 | (421) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.29 | % 24.06/7.29 +-Applying beta-rule and splitting (164), into two cases. % 24.06/7.29 |-Branch one: % 24.06/7.29 | (201) all_32_0_36 = 0 % 24.06/7.29 | % 24.06/7.29 | Equations (201) can reduce 92 to: % 24.06/7.29 | (101) $false % 24.06/7.29 | % 24.06/7.29 |-The branch is then unsatisfiable % 24.06/7.29 |-Branch two: % 24.06/7.29 | (92) ~ (all_32_0_36 = 0) % 24.06/7.29 | (425) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (165), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (201) all_32_0_36 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (201) can reduce 92 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (92) ~ (all_32_0_36 = 0) % 24.06/7.30 | (429) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (166), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (433) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (167), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (437) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (155), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (441) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (160), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (445) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (161), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (449) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (163), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (201) all_32_0_36 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (201) can reduce 92 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (92) ~ (all_32_0_36 = 0) % 24.06/7.30 | (453) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (233), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (100) all_0_1_1 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (100) can reduce 32 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (32) ~ (all_0_1_1 = 0) % 24.06/7.30 | (457) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (257), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (461) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (297), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (100) all_0_1_1 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (100) can reduce 32 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (32) ~ (all_0_1_1 = 0) % 24.06/7.30 | (465) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (301), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (100) all_0_1_1 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (100) can reduce 32 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (32) ~ (all_0_1_1 = 0) % 24.06/7.30 | (469) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (305), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (242) all_24_0_28 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (242) can reduce 78 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (78) ~ (all_24_0_28 = 0) % 24.06/7.30 | (473) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.30 | % 24.06/7.30 | Instantiating (473) with all_376_0_1222 yields: % 24.06/7.30 | (474) (all_376_0_1222 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (all_376_0_1222 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_376_0_1222 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = all_376_0_1222) | ( ~ (all_376_0_1222 = 0) & distinct_points(all_0_0_0, all_0_2_2) = all_376_0_1222) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (474), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (475) (all_376_0_1222 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (all_376_0_1222 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_376_0_1222 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = all_376_0_1222) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (475), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (476) (all_376_0_1222 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (all_376_0_1222 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (476), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (477) all_376_0_1222 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0 % 24.06/7.30 | % 24.06/7.30 | Applying alpha-rule on (477) yields: % 24.06/7.30 | (478) all_376_0_1222 = 0 % 24.06/7.30 | (479) apart_point_and_line(all_0_0_0, all_0_4_4) = 0 % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (425), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (483) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_22_1_27) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (429), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (487) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (453), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (82) ~ (all_26_0_30 = 0) % 24.06/7.30 | (491) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_0_0) = v0)) % 24.06/7.30 | % 24.06/7.30 | Instantiating formula (41) with all_0_0_0, all_0_4_4, 0, all_26_0_30 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_0_0, all_0_4_4) = 0, yields: % 24.06/7.30 | (222) all_26_0_30 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (222) can reduce 82 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (494) all_376_0_1222 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0 % 24.06/7.30 | % 24.06/7.30 | Applying alpha-rule on (494) yields: % 24.06/7.30 | (478) all_376_0_1222 = 0 % 24.06/7.30 | (496) apart_point_and_line(all_0_2_2, all_0_3_3) = 0 % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (381), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (100) all_0_1_1 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (100) can reduce 32 to: % 24.06/7.30 | (101) $false % 24.06/7.30 | % 24.06/7.30 |-The branch is then unsatisfiable % 24.06/7.30 |-Branch two: % 24.06/7.30 | (32) ~ (all_0_1_1 = 0) % 24.06/7.30 | (500) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.30 | % 24.06/7.30 +-Applying beta-rule and splitting (385), into two cases. % 24.06/7.30 |-Branch one: % 24.06/7.30 | (100) all_0_1_1 = 0 % 24.06/7.30 | % 24.06/7.30 | Equations (100) can reduce 32 to: % 24.06/7.30 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (32) ~ (all_0_1_1 = 0) % 24.06/7.31 | (504) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.31 | % 24.06/7.31 +-Applying beta-rule and splitting (389), into two cases. % 24.06/7.31 |-Branch one: % 24.06/7.31 | (100) all_0_1_1 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (100) can reduce 32 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (32) ~ (all_0_1_1 = 0) % 24.06/7.31 | (508) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0)) % 24.06/7.31 | % 24.06/7.31 +-Applying beta-rule and splitting (413), into two cases. % 24.06/7.31 |-Branch one: % 24.06/7.31 | (100) all_0_1_1 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (100) can reduce 32 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (32) ~ (all_0_1_1 = 0) % 24.06/7.31 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.31 | % 24.06/7.31 +-Applying beta-rule and splitting (417), into two cases. % 24.06/7.31 |-Branch one: % 24.06/7.31 | (100) all_0_1_1 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (100) can reduce 32 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (32) ~ (all_0_1_1 = 0) % 24.06/7.31 | (516) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.31 | % 24.06/7.31 +-Applying beta-rule and splitting (421), into two cases. % 24.06/7.31 |-Branch one: % 24.06/7.31 | (100) all_0_1_1 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (100) can reduce 32 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (32) ~ (all_0_1_1 = 0) % 24.06/7.31 | (520) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0)) % 24.06/7.31 | % 24.06/7.31 +-Applying beta-rule and splitting (441), into two cases. % 24.06/7.31 |-Branch one: % 24.06/7.31 | (100) all_0_1_1 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (100) can reduce 32 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (32) ~ (all_0_1_1 = 0) % 24.06/7.31 | (524) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0)) % 24.06/7.31 | % 24.06/7.31 | Instantiating formula (41) with all_0_2_2, all_0_3_3, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_3_3) = 0, yields: % 24.06/7.31 | (100) all_0_1_1 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (100) can reduce 32 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (527) ~ (all_376_0_1222 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = all_376_0_1222 % 24.06/7.31 | % 24.06/7.31 | Applying alpha-rule on (527) yields: % 24.06/7.31 | (528) ~ (all_376_0_1222 = 0) % 24.06/7.31 | (529) distinct_lines(all_0_4_4, all_0_3_3) = all_376_0_1222 % 24.06/7.31 | % 24.06/7.31 | Instantiating formula (18) with all_376_0_1222, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_3_3) = all_376_0_1222, yields: % 24.06/7.31 | (530) all_376_0_1222 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0 % 24.06/7.31 | % 24.06/7.31 +-Applying beta-rule and splitting (530), into two cases. % 24.06/7.31 |-Branch one: % 24.06/7.31 | (531) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 24.06/7.31 | % 24.06/7.31 | Instantiating formula (7) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 24.06/7.31 | (532) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (533) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0) % 24.06/7.31 | (478) all_376_0_1222 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (478) can reduce 528 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (536) ~ (all_376_0_1222 = 0) & distinct_points(all_0_0_0, all_0_2_2) = all_376_0_1222 % 24.06/7.31 | % 24.06/7.31 | Applying alpha-rule on (536) yields: % 24.06/7.31 | (528) ~ (all_376_0_1222 = 0) % 24.06/7.31 | (538) distinct_points(all_0_0_0, all_0_2_2) = all_376_0_1222 % 24.06/7.31 | % 24.06/7.31 | Instantiating formula (24) with all_0_0_0, all_0_2_2, 0, all_376_0_1222 and discharging atoms distinct_points(all_0_0_0, all_0_2_2) = all_376_0_1222, distinct_points(all_0_0_0, all_0_2_2) = 0, yields: % 24.06/7.31 | (478) all_376_0_1222 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (478) can reduce 528 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (541) ~ (distinct_points(all_0_0_0, all_0_2_2) = 0) % 24.06/7.31 | (226) all_20_0_24 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (226) can reduce 70 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (544) ~ (all_31_0_35 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35 % 24.06/7.31 | % 24.06/7.31 | Applying alpha-rule on (544) yields: % 24.06/7.31 | (111) ~ (all_31_0_35 = 0) % 24.06/7.31 | (546) convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35 % 24.06/7.31 | % 24.06/7.31 | Instantiating formula (27) with all_0_5_5, all_0_4_4, all_31_0_35, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 24.06/7.31 | (547) all_31_0_35 = 0 % 24.06/7.31 | % 24.06/7.31 | Equations (547) can reduce 111 to: % 24.06/7.31 | (101) $false % 24.06/7.31 | % 24.06/7.31 |-The branch is then unsatisfiable % 24.06/7.31 |-Branch two: % 24.06/7.31 | (549) ~ (all_34_0_38 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38 % 24.06/7.31 | % 24.06/7.31 | Applying alpha-rule on (549) yields: % 24.06/7.31 | (108) ~ (all_34_0_38 = 0) % 24.06/7.31 | (551) convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38 % 24.06/7.31 | % 24.06/7.31 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_34_0_38, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 24.06/7.31 | (552) all_34_0_38 = 0 % 24.06/7.32 | % 24.06/7.32 | Equations (552) can reduce 108 to: % 24.06/7.32 | (101) $false % 24.06/7.32 | % 24.06/7.32 |-The branch is then unsatisfiable % 24.06/7.32 |-Branch two: % 24.06/7.32 | (554) ~ (all_30_0_34 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34 % 24.06/7.32 | % 24.06/7.32 | Applying alpha-rule on (554) yields: % 24.06/7.32 | (105) ~ (all_30_0_34 = 0) % 24.06/7.32 | (556) convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34 % 24.06/7.32 | % 24.06/7.32 | Instantiating formula (27) with all_0_5_5, all_0_4_4, all_30_0_34, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 24.06/7.32 | (557) all_30_0_34 = 0 % 24.06/7.32 | % 24.06/7.32 | Equations (557) can reduce 105 to: % 24.06/7.32 | (101) $false % 24.06/7.32 | % 24.06/7.32 |-The branch is then unsatisfiable % 24.06/7.32 |-Branch two: % 24.06/7.32 | (559) ~ (all_35_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39 % 24.06/7.32 | % 24.06/7.32 | Applying alpha-rule on (559) yields: % 24.06/7.32 | (98) ~ (all_35_0_39 = 0) % 24.06/7.32 | (561) convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39 % 24.06/7.32 | % 24.06/7.32 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_35_0_39, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 24.06/7.32 | (562) all_35_0_39 = 0 % 24.06/7.32 | % 24.06/7.32 | Equations (562) can reduce 98 to: % 24.06/7.32 | (101) $false % 24.06/7.32 | % 24.06/7.32 |-The branch is then unsatisfiable % 24.06/7.32 % SZS output end Proof for theBenchmark % 24.06/7.32 % 24.06/7.32 6726ms %------------------------------------------------------------------------------