%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO193+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 03:48:29 EDT 2022 % Result : Theorem 5.69s 1.98s % Output : Proof 32.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.14/0.14 % Problem : GEO193+1 : TPTP v8.1.0. Released v3.3.0. % 0.14/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.36 % Computer : n017.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Fri Jun 17 18:52:57 EDT 2022 % 0.15/0.36 % CPUTime : % 0.53/0.62 ____ _ % 0.53/0.62 ___ / __ \_____(_)___ ________ __________ % 0.53/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.62 % 0.53/0.62 A Theorem Prover for First-Order Logic % 0.53/0.62 (ePrincess v.1.0) % 0.53/0.62 % 0.53/0.62 (c) Philipp Rümmer, 2009-2015 % 0.53/0.62 (c) Peter Backeman, 2014-2015 % 0.53/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.62 Bug reports to peter@backeman.se % 0.53/0.62 % 0.53/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.62 % 0.53/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.72/0.95 Prover 0: Preprocessing ... % 2.04/1.08 Prover 0: Warning: ignoring some quantifiers % 2.04/1.10 Prover 0: Constructing countermodel ... % 3.03/1.41 Prover 0: gave up % 3.03/1.41 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.03/1.43 Prover 1: Preprocessing ... % 3.56/1.51 Prover 1: Constructing countermodel ... % 3.74/1.55 Prover 1: gave up % 3.74/1.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.74/1.57 Prover 2: Preprocessing ... % 4.39/1.68 Prover 2: Warning: ignoring some quantifiers % 4.39/1.68 Prover 2: Constructing countermodel ... % 5.69/1.98 Prover 2: proved (424ms) % 5.69/1.98 % 5.69/1.98 No countermodel exists, formula is valid % 5.69/1.98 % SZS status Theorem for theBenchmark % 5.69/1.98 % 5.69/1.98 Generating proof ... Warning: ignoring some quantifiers % 31.37/10.82 found it (size 438) % 31.37/10.82 % 31.37/10.82 % SZS output start Proof for theBenchmark % 31.37/10.82 Assumed formulas after preprocessing and simplification: % 31.37/10.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v1) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v0) = v5 & apart_point_and_line(v3, v2) = 0 & 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) % 31.82/10.88 | 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: % 31.82/10.88 | (1) ~ (all_0_0_0 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1 & intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0 & 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 % 31.82/10.89 | % 31.82/10.89 | Applying alpha-rule on (1) yields: % 31.82/10.90 | (2) ! [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))) % 31.82/10.90 | (3) apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0 % 31.82/10.90 | (4) intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 % 31.82/10.90 | (5) intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1 % 31.82/10.90 | (6) ! [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) % 31.82/10.90 | (7) ! [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))) % 31.82/10.90 | (8) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 31.82/10.90 | (9) convergent_lines(all_0_5_5, all_0_4_4) = 0 % 31.82/10.90 | (10) ! [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)) % 31.82/10.90 | (11) ! [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))) % 31.82/10.90 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 31.82/10.90 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 31.82/10.90 | (14) ! [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))) % 31.82/10.90 | (15) apart_point_and_line(all_0_2_2, all_0_3_3) = 0 % 31.82/10.90 | (16) ! [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)) % 31.82/10.90 | (17) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 31.82/10.90 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 31.82/10.90 | (19) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 31.82/10.90 | (20) convergent_lines(all_0_5_5, all_0_3_3) = 0 % 31.82/10.90 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 31.82/10.90 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 31.82/10.90 | (23) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 31.82/10.90 | (24) ! [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))) % 31.82/10.90 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 31.82/10.90 | (26) convergent_lines(all_0_3_3, all_0_4_4) = 0 % 31.82/10.90 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 31.82/10.90 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 31.82/10.90 | (29) ! [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))) % 31.82/10.91 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 31.82/10.91 | (31) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 31.82/10.91 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 31.82/10.91 | (33) ! [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)) % 31.82/10.91 | (34) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 31.82/10.91 | (35) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 31.82/10.91 | (36) ! [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)) % 31.82/10.91 | (37) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 31.82/10.91 | (38) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 31.82/10.91 | (39) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 31.82/10.91 | (40) ! [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))) % 31.82/10.91 | (41) ! [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) % 31.82/10.91 | (42) ! [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) % 31.82/10.91 | (43) ! [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))) % 31.82/10.91 | (44) ! [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))) % 31.82/10.91 | (45) ! [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) % 31.82/10.91 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 31.82/10.91 | (47) ! [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)) % 31.82/10.91 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 31.82/10.91 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 31.82/10.91 | (50) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 31.82/10.91 | (51) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 31.82/10.91 | (52) ! [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))) % 31.82/10.91 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 31.82/10.91 | (54) ! [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)) % 31.82/10.92 | (55) ! [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))) % 31.82/10.92 | (56) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 31.82/10.92 | (57) ~ (all_0_0_0 = 0) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (52) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields: % 31.82/10.92 | (58) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (7) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields: % 31.82/10.92 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (52) 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: % 31.82/10.92 | (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)) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (7) 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: % 31.82/10.92 | (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)) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (14) with all_0_0_0, all_0_0_0, all_0_5_5, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 31.82/10.92 | (62) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (50) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 31.82/10.92 | (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) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (19) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 31.82/10.92 | (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) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (50) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields: % 31.82/10.92 | (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) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (19) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields: % 31.82/10.92 | (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) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (50) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 31.82/10.92 | (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) % 31.82/10.92 | % 31.82/10.92 | Instantiating formula (19) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 31.82/10.92 | (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) % 31.82/10.92 | % 31.82/10.92 | Instantiating (68) with all_20_0_24, all_20_1_25 yields: % 31.82/10.92 | (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 % 31.82/10.92 | % 32.09/10.92 | Applying alpha-rule on (69) yields: % 32.09/10.92 | (70) ~ (all_20_0_24 = 0) % 32.09/10.92 | (71) intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25 % 32.09/10.92 | (72) apart_point_and_line(all_20_1_25, all_0_5_5) = all_20_0_24 % 32.09/10.92 | % 32.09/10.92 | Instantiating (65) with all_22_0_26, all_22_1_27 yields: % 32.09/10.92 | (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 % 32.09/10.92 | % 32.09/10.92 | Applying alpha-rule on (73) yields: % 32.09/10.92 | (74) ~ (all_22_0_26 = 0) % 32.09/10.92 | (75) intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27 % 32.09/10.92 | (76) apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26 % 32.09/10.92 | % 32.09/10.92 | Instantiating (64) with all_24_0_28, all_24_1_29 yields: % 32.09/10.92 | (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 % 32.09/10.92 | % 32.09/10.92 | Applying alpha-rule on (77) yields: % 32.09/10.92 | (78) ~ (all_24_0_28 = 0) % 32.09/10.92 | (79) intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29 % 32.09/10.92 | (80) apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28 % 32.09/10.92 | % 32.09/10.92 | Instantiating (63) with all_26_0_30, all_26_1_31 yields: % 32.09/10.92 | (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 % 32.09/10.93 | % 32.09/10.93 | Applying alpha-rule on (81) yields: % 32.09/10.93 | (82) ~ (all_26_0_30 = 0) % 32.09/10.93 | (83) intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31 % 32.09/10.93 | (84) apart_point_and_line(all_26_1_31, all_0_4_4) = all_26_0_30 % 32.09/10.93 | % 32.09/10.93 | Instantiating (67) with all_28_0_32, all_28_1_33 yields: % 32.09/10.93 | (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 % 32.09/10.93 | % 32.09/10.93 | Applying alpha-rule on (85) yields: % 32.09/10.93 | (86) ~ (all_28_0_32 = 0) % 32.09/10.93 | (87) intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33 % 32.09/10.93 | (88) apart_point_and_line(all_28_1_33, all_0_4_4) = all_28_0_32 % 32.09/10.93 | % 32.09/10.93 | Instantiating (61) with all_30_0_34 yields: % 32.09/10.93 | (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) % 32.09/10.93 | % 32.09/10.93 | Instantiating (60) with all_31_0_35 yields: % 32.09/10.93 | (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) % 32.09/10.93 | % 32.09/10.93 | Instantiating (66) with all_32_0_36, all_32_1_37 yields: % 32.09/10.93 | (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 % 32.09/10.93 | % 32.09/10.93 | Applying alpha-rule on (91) yields: % 32.09/10.93 | (92) ~ (all_32_0_36 = 0) % 32.09/10.93 | (93) intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37 % 32.09/10.93 | (94) apart_point_and_line(all_32_1_37, all_0_5_5) = all_32_0_36 % 32.09/10.93 | % 32.09/10.93 | Instantiating (59) with all_34_0_38 yields: % 32.09/10.93 | (95) ( ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_1_1, 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) % 32.09/10.93 | % 32.09/10.93 | Instantiating (58) with all_35_0_39 yields: % 32.09/10.93 | (96) ( ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_1_1, 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) % 32.09/10.93 | % 32.09/10.93 +-Applying beta-rule and splitting (96), into two cases. % 32.09/10.93 |-Branch one: % 32.09/10.93 | (97) ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_35_0_39 % 32.09/10.93 | % 32.09/10.93 | Applying alpha-rule on (97) yields: % 32.09/10.93 | (98) ~ (all_35_0_39 = 0) % 32.09/10.93 | (99) apart_point_and_line(all_0_1_1, all_0_4_4) = all_35_0_39 % 32.09/10.93 | % 32.09/10.93 +-Applying beta-rule and splitting (62), into two cases. % 32.09/10.93 |-Branch one: % 32.09/10.93 | (100) all_0_0_0 = 0 % 32.09/10.93 | % 32.09/10.93 | Equations (100) can reduce 57 to: % 32.09/10.93 | (101) $false % 32.09/10.93 | % 32.09/10.93 |-The branch is then unsatisfiable % 32.09/10.93 |-Branch two: % 32.09/10.93 | (57) ~ (all_0_0_0 = 0) % 32.09/10.93 | (103) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.93 | % 32.09/10.93 +-Applying beta-rule and splitting (89), into two cases. % 32.09/10.93 |-Branch one: % 32.09/10.93 | (104) ~ (all_30_0_34 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34 % 32.09/10.93 | % 32.09/10.93 | Applying alpha-rule on (104) yields: % 32.09/10.93 | (105) ~ (all_30_0_34 = 0) % 32.09/10.93 | (106) apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34 % 32.09/10.93 | % 32.09/10.93 +-Applying beta-rule and splitting (95), into two cases. % 32.09/10.93 |-Branch one: % 32.09/10.93 | (107) ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_34_0_38 % 32.09/10.93 | % 32.09/10.93 | Applying alpha-rule on (107) yields: % 32.09/10.93 | (108) ~ (all_34_0_38 = 0) % 32.09/10.93 | (109) apart_point_and_line(all_0_1_1, all_0_3_3) = all_34_0_38 % 32.09/10.93 | % 32.09/10.93 +-Applying beta-rule and splitting (90), into two cases. % 32.09/10.93 |-Branch one: % 32.09/10.93 | (110) ~ (all_31_0_35 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35 % 32.09/10.93 | % 32.09/10.93 | Applying alpha-rule on (110) yields: % 32.09/10.93 | (111) ~ (all_31_0_35 = 0) % 32.09/10.93 | (112) apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35 % 32.09/10.93 | % 32.09/10.93 | Instantiating formula (22) with all_0_3_3, all_0_4_4, all_26_1_31, all_0_1_1 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_1_1, yields: % 32.09/10.93 | (113) all_26_1_31 = all_0_1_1 % 32.09/10.93 | % 32.09/10.93 | Instantiating formula (22) 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: % 32.09/10.93 | (114) all_26_1_31 = all_24_1_29 % 32.09/10.93 | % 32.09/10.93 | Instantiating formula (22) 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: % 32.09/10.93 | (115) all_32_1_37 = all_22_1_27 % 32.09/10.93 | % 32.09/10.93 | Instantiating formula (22) 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: % 32.09/10.93 | (116) all_28_1_33 = all_0_2_2 % 32.09/10.93 | % 32.09/10.93 | Instantiating formula (22) 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: % 32.09/10.93 | (117) all_28_1_33 = all_20_1_25 % 32.09/10.93 | % 32.09/10.94 | Combining equations (116,117) yields a new equation: % 32.09/10.94 | (118) all_20_1_25 = all_0_2_2 % 32.09/10.94 | % 32.09/10.94 | Combining equations (114,113) yields a new equation: % 32.09/10.94 | (119) all_24_1_29 = all_0_1_1 % 32.09/10.94 | % 32.09/10.94 | Simplifying 119 yields: % 32.09/10.94 | (120) all_24_1_29 = all_0_1_1 % 32.09/10.94 | % 32.09/10.94 | Combining equations (118,117) yields a new equation: % 32.09/10.94 | (116) all_28_1_33 = all_0_2_2 % 32.09/10.94 | % 32.09/10.94 | From (115) and (94) follows: % 32.09/10.94 | (122) apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36 % 32.09/10.94 | % 32.09/10.94 | From (116) and (88) follows: % 32.09/10.94 | (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32 % 32.09/10.94 | % 32.09/10.94 | From (113) and (84) follows: % 32.09/10.94 | (124) apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30 % 32.09/10.94 | % 32.09/10.94 | From (120) and (80) follows: % 32.09/10.94 | (125) apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28 % 32.09/10.94 | % 32.09/10.94 | From (118) and (72) follows: % 32.09/10.94 | (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24 % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (21) with all_0_1_1, all_0_3_3, all_24_0_28, all_34_0_38 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_34_0_38, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, yields: % 32.09/10.94 | (127) all_34_0_38 = all_24_0_28 % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (21) with all_0_1_1, all_0_4_4, all_26_0_30, all_35_0_39 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_35_0_39, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields: % 32.09/10.94 | (128) all_35_0_39 = all_26_0_30 % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (21) 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: % 32.09/10.94 | (129) all_31_0_35 = all_28_0_32 % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (21) 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: % 32.09/10.94 | (130) all_30_0_34 = all_20_0_24 % 32.09/10.94 | % 32.09/10.94 | Equations (128) can reduce 98 to: % 32.09/10.94 | (82) ~ (all_26_0_30 = 0) % 32.09/10.94 | % 32.09/10.94 | Equations (127) can reduce 108 to: % 32.09/10.94 | (78) ~ (all_24_0_28 = 0) % 32.09/10.94 | % 32.09/10.94 | Equations (129) can reduce 111 to: % 32.09/10.94 | (86) ~ (all_28_0_32 = 0) % 32.09/10.94 | % 32.09/10.94 | Equations (130) can reduce 105 to: % 32.09/10.94 | (70) ~ (all_20_0_24 = 0) % 32.09/10.94 | % 32.09/10.94 | From (127) and (109) follows: % 32.09/10.94 | (125) apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28 % 32.09/10.94 | % 32.09/10.94 | From (128) and (99) follows: % 32.09/10.94 | (124) apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30 % 32.09/10.94 | % 32.09/10.94 | From (129) and (112) follows: % 32.09/10.94 | (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32 % 32.09/10.94 | % 32.09/10.94 | From (130) and (106) follows: % 32.09/10.94 | (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24 % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (14) with all_22_0_26, all_0_0_0, all_0_3_3, all_0_5_5, all_22_1_27, all_0_1_1 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_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.94 | (139) all_22_0_26 = 0 | all_0_0_0 = 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_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (14) with all_0_0_0, all_22_0_26, all_0_5_5, all_0_3_3, all_0_1_1, 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_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.94 | (140) all_22_0_26 = 0 | all_0_0_0 = 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_1_1, 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_1_1) = v0)) % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (44) with all_22_0_26, all_0_0_0, all_0_5_5, all_0_3_3, all_22_1_27, all_0_1_1 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_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.94 | (141) all_22_0_26 = 0 | all_0_0_0 = 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_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (44) with all_0_0_0, all_22_0_26, all_0_3_3, all_0_5_5, all_0_1_1, 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_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.94 | (142) all_22_0_26 = 0 | all_0_0_0 = 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_1_1, 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_1_1) = v0)) % 32.09/10.94 | % 32.09/10.94 | Instantiating formula (14) 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: % 32.09/10.94 | (143) 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)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) with all_32_0_36, all_0_0_0, all_0_5_5, all_0_5_5, all_22_1_27, all_0_1_1 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_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.95 | (144) all_32_0_36 = 0 | all_0_0_0 = 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_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) with all_0_0_0, all_32_0_36, all_0_5_5, all_0_5_5, all_0_1_1, 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_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.95 | (145) all_32_0_36 = 0 | all_0_0_0 = 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_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) 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: % 32.09/10.95 | (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_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) 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: % 32.09/10.95 | (147) 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)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) 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: % 32.09/10.95 | (148) 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)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) with all_24_0_28, all_0_0_0, all_0_3_3, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.95 | (149) all_24_0_28 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) with all_0_0_0, all_24_0_28, all_0_5_5, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.95 | (150) all_24_0_28 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (42) with all_24_0_28, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_3_3) = 0, yields: % 32.09/10.95 | (151) all_24_0_28 = 0 | distinct_points(all_0_2_2, all_0_1_1) = 0 % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) with all_24_0_28, all_22_0_26, all_0_3_3, all_0_3_3, all_0_1_1, 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_1_1, all_0_3_3) = all_24_0_28, yields: % 32.09/10.95 | (152) 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_1_1, 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_1_1) = v0)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) with all_24_0_28, all_24_0_28, all_0_3_3, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, yields: % 32.09/10.95 | (153) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) with all_26_0_30, all_0_0_0, all_0_4_4, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.95 | (154) all_26_0_30 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.95 | % 32.09/10.95 | Instantiating formula (14) with all_0_0_0, all_26_0_30, all_0_5_5, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 32.09/10.95 | (155) all_26_0_30 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (14) with all_26_0_30, all_22_0_26, all_0_4_4, all_0_3_3, all_0_1_1, 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_1_1, all_0_4_4) = all_26_0_30, yields: % 32.09/10.96 | (156) 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_1_1, 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_1_1) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (14) with all_22_0_26, all_26_0_30, all_0_3_3, all_0_4_4, all_22_1_27, all_0_1_1 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_1_1, all_0_4_4) = all_26_0_30, yields: % 32.09/10.96 | (157) 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_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (44) with all_26_0_30, all_22_0_26, all_0_3_3, all_0_4_4, all_0_1_1, 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_1_1, all_0_4_4) = all_26_0_30, yields: % 32.09/10.96 | (158) 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_1_1, 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_1_1) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (44) with all_22_0_26, all_26_0_30, all_0_4_4, all_0_3_3, all_22_1_27, all_0_1_1 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_1_1, all_0_4_4) = all_26_0_30, yields: % 32.09/10.96 | (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_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (14) with all_26_0_30, all_24_0_28, all_0_4_4, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields: % 32.09/10.96 | (160) all_26_0_30 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (14) with all_24_0_28, all_26_0_30, all_0_3_3, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields: % 32.09/10.96 | (161) all_26_0_30 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (14) with all_26_0_30, all_26_0_30, all_0_4_4, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields: % 32.09/10.96 | (162) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (14) with all_28_0_32, all_0_0_0, all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 32.09/10.96 | (163) all_28_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (14) with all_0_0_0, all_28_0_32, all_0_5_5, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 32.09/10.96 | (164) all_28_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_0_1_1) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (44) with all_28_0_32, all_0_0_0, all_0_5_5, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 32.09/10.96 | (165) all_28_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.09/10.96 | % 32.09/10.96 | Instantiating formula (44) with all_0_0_0, all_28_0_32, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 32.09/10.96 | (166) all_28_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_0_1_1) = v0)) % 32.09/10.97 | % 32.09/10.97 | Instantiating formula (14) with all_28_0_32, all_22_0_26, all_0_4_4, 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_4_4) = all_28_0_32, yields: % 32.09/10.97 | (167) all_28_0_32 = 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_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_22_1_27, all_0_2_2) = v0)) % 32.09/10.97 | % 32.09/10.97 | Instantiating formula (14) with all_22_0_26, all_28_0_32, all_0_3_3, 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_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 32.09/10.97 | (168) all_28_0_32 = 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_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_22_1_27) = v0)) % 32.09/10.97 | % 32.09/10.97 | Instantiating formula (44) with all_28_0_32, all_22_0_26, all_0_3_3, 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_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields: % 32.09/10.97 | (169) all_28_0_32 = 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_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_22_1_27, all_0_2_2) = v0)) % 32.09/10.97 | % 32.09/10.97 | Instantiating formula (44) with all_22_0_26, all_28_0_32, all_0_4_4, 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_4_4) = all_28_0_32, yields: % 32.09/10.97 | (170) all_28_0_32 = 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_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_22_1_27) = v0)) % 32.09/10.97 | % 32.09/10.97 | Instantiating formula (14) 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: % 32.33/10.97 | (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)) % 32.33/10.97 | % 32.33/10.97 | Instantiating formula (14) 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: % 32.33/10.97 | (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)) % 32.33/10.97 | % 32.33/10.97 | Instantiating formula (44) 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: % 32.33/10.97 | (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)) % 32.33/10.97 | % 32.33/10.97 | Instantiating formula (44) 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: % 32.33/10.97 | (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)) % 32.33/10.97 | % 32.33/10.97 | Instantiating formula (14) with all_28_0_32, all_24_0_28, all_0_4_4, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, 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: % 32.33/10.97 | (175) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) with all_24_0_28, all_28_0_32, all_0_3_3, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, 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: % 32.33/10.98 | (176) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (44) with all_28_0_32, all_24_0_28, all_0_3_3, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, 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: % 32.33/10.98 | (177) all_28_0_32 = 0 | all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) with all_28_0_32, all_26_0_30, all_0_4_4, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, 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: % 32.33/10.98 | (178) all_28_0_32 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) with all_26_0_30, all_28_0_32, all_0_4_4, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, 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: % 32.33/10.98 | (179) all_28_0_32 = 0 | all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) 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: % 32.33/10.98 | (180) 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)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) with all_20_0_24, all_0_0_0, all_0_5_5, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 32.33/10.98 | (181) all_20_0_24 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (44) 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: % 32.33/10.98 | (182) 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)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (44) 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: % 32.33/10.98 | (183) 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)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) 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: % 32.33/10.98 | (184) 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)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) 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: % 32.33/10.98 | (185) 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)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) with all_20_0_24, all_24_0_28, all_0_5_5, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, 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: % 32.33/10.98 | (186) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) with all_24_0_28, all_20_0_24, all_0_3_3, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 32.33/10.98 | (187) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (44) with all_20_0_24, all_24_0_28, all_0_3_3, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 32.33/10.98 | (188) all_24_0_28 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/10.98 | % 32.33/10.98 | Instantiating formula (14) with all_20_0_24, all_26_0_30, all_0_5_5, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, 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: % 32.33/10.98 | (189) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/10.99 | % 32.33/10.99 | Instantiating formula (14) with all_26_0_30, all_20_0_24, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 32.33/10.99 | (190) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1) = v0)) % 32.33/10.99 | % 32.33/10.99 | Instantiating formula (44) with all_20_0_24, all_26_0_30, all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 32.33/10.99 | (191) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/10.99 | % 32.33/10.99 | Instantiating formula (44) with all_26_0_30, all_20_0_24, all_0_5_5, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, 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: % 32.33/10.99 | (192) all_26_0_30 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1) = v0)) % 32.33/10.99 | % 32.33/10.99 | Instantiating formula (14) with all_20_0_24, all_28_0_32, all_0_5_5, 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, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 32.33/10.99 | (193) all_28_0_32 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, 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_0_2_2) = v0)) % 32.33/10.99 | % 32.33/10.99 | Instantiating formula (14) with all_28_0_32, all_20_0_24, all_0_4_4, 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_4_4) = all_28_0_32, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields: % 32.33/10.99 | (194) all_28_0_32 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, 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_0_2_2) = v0)) % 32.33/10.99 | % 32.33/10.99 | Instantiating formula (14) with all_20_0_24, all_20_0_24, all_0_5_5, 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_5_5) = all_20_0_24, yields: % 32.33/10.99 | (195) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (148), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (196) all_32_0_36 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (196) can reduce 92 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (92) ~ (all_32_0_36 = 0) % 32.33/10.99 | (199) ? [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)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (180), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (200) all_28_0_32 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (200) can reduce 86 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (86) ~ (all_28_0_32 = 0) % 32.33/10.99 | (203) ? [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)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (145), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (196) all_32_0_36 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (196) can reduce 92 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (92) ~ (all_32_0_36 = 0) % 32.33/10.99 | (207) all_0_0_0 = 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_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (140), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (208) all_22_0_26 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (208) can reduce 74 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (74) ~ (all_22_0_26 = 0) % 32.33/10.99 | (211) all_0_0_0 = 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_1_1, 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_1_1) = v0)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (141), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (208) all_22_0_26 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (208) can reduce 74 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (74) ~ (all_22_0_26 = 0) % 32.33/10.99 | (215) all_0_0_0 = 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_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (146), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (196) all_32_0_36 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (196) can reduce 92 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (92) ~ (all_32_0_36 = 0) % 32.33/10.99 | (219) 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)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (151), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (220) distinct_points(all_0_2_2, all_0_1_1) = 0 % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (162), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (221) all_26_0_30 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (221) can reduce 82 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (82) ~ (all_26_0_30 = 0) % 32.33/10.99 | (224) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (147), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (196) all_32_0_36 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (196) can reduce 92 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (92) ~ (all_32_0_36 = 0) % 32.33/10.99 | (228) 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)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (152), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (229) all_24_0_28 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (229) can reduce 78 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (78) ~ (all_24_0_28 = 0) % 32.33/10.99 | (232) 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_1_1, 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_1_1) = v0)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (182), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (208) all_22_0_26 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (208) can reduce 74 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (74) ~ (all_22_0_26 = 0) % 32.33/10.99 | (236) 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)) % 32.33/10.99 | % 32.33/10.99 +-Applying beta-rule and splitting (149), into two cases. % 32.33/10.99 |-Branch one: % 32.33/10.99 | (229) all_24_0_28 = 0 % 32.33/10.99 | % 32.33/10.99 | Equations (229) can reduce 78 to: % 32.33/10.99 | (101) $false % 32.33/10.99 | % 32.33/10.99 |-The branch is then unsatisfiable % 32.33/10.99 |-Branch two: % 32.33/10.99 | (78) ~ (all_24_0_28 = 0) % 32.33/10.99 | (240) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (150), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (229) all_24_0_28 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (229) can reduce 78 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (78) ~ (all_24_0_28 = 0) % 32.33/11.00 | (244) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (183), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (208) all_22_0_26 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (208) can reduce 74 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (74) ~ (all_22_0_26 = 0) % 32.33/11.00 | (248) 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)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (184), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (196) all_32_0_36 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (196) can reduce 92 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (92) ~ (all_32_0_36 = 0) % 32.33/11.00 | (252) 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)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (185), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (196) all_32_0_36 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (196) can reduce 92 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (92) ~ (all_32_0_36 = 0) % 32.33/11.00 | (256) 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)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (207), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (100) all_0_0_0 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (100) can reduce 57 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (57) ~ (all_0_0_0 = 0) % 32.33/11.00 | (260) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (211), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (100) all_0_0_0 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (100) can reduce 57 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (57) ~ (all_0_0_0 = 0) % 32.33/11.00 | (264) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (215), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (100) all_0_0_0 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (100) can reduce 57 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (57) ~ (all_0_0_0 = 0) % 32.33/11.00 | (268) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (219), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (208) all_22_0_26 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (208) can reduce 74 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (74) ~ (all_22_0_26 = 0) % 32.33/11.00 | (272) ? [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)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (236), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (273) all_20_0_24 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (273) can reduce 70 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (70) ~ (all_20_0_24 = 0) % 32.33/11.00 | (276) ? [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)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (143), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (208) all_22_0_26 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (208) can reduce 74 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (74) ~ (all_22_0_26 = 0) % 32.33/11.00 | (280) ? [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)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (153), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (229) all_24_0_28 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (229) can reduce 78 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (78) ~ (all_24_0_28 = 0) % 32.33/11.00 | (284) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (195), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (273) all_20_0_24 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (273) can reduce 70 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (70) ~ (all_20_0_24 = 0) % 32.33/11.00 | (288) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (186), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (229) all_24_0_28 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (229) can reduce 78 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (78) ~ (all_24_0_28 = 0) % 32.33/11.00 | (292) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (187), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (229) all_24_0_28 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (229) can reduce 78 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (78) ~ (all_24_0_28 = 0) % 32.33/11.00 | (296) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (188), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (229) all_24_0_28 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (229) can reduce 78 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (78) ~ (all_24_0_28 = 0) % 32.33/11.00 | (300) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (191), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (221) all_26_0_30 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (221) can reduce 82 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (82) ~ (all_26_0_30 = 0) % 32.33/11.00 | (304) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (189), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (221) all_26_0_30 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (221) can reduce 82 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (82) ~ (all_26_0_30 = 0) % 32.33/11.00 | (308) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/11.00 | % 32.33/11.00 +-Applying beta-rule and splitting (190), into two cases. % 32.33/11.00 |-Branch one: % 32.33/11.00 | (221) all_26_0_30 = 0 % 32.33/11.00 | % 32.33/11.00 | Equations (221) can reduce 82 to: % 32.33/11.00 | (101) $false % 32.33/11.00 | % 32.33/11.00 |-The branch is then unsatisfiable % 32.33/11.00 |-Branch two: % 32.33/11.00 | (82) ~ (all_26_0_30 = 0) % 32.33/11.00 | (312) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (160), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (221) all_26_0_30 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (221) can reduce 82 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (82) ~ (all_26_0_30 = 0) % 32.33/11.01 | (316) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (161), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (221) all_26_0_30 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (221) can reduce 82 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (82) ~ (all_26_0_30 = 0) % 32.33/11.01 | (320) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (172), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (196) all_32_0_36 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (196) can reduce 92 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (92) ~ (all_32_0_36 = 0) % 32.33/11.01 | (324) 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)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (192), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (221) all_26_0_30 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (221) can reduce 82 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (82) ~ (all_26_0_30 = 0) % 32.33/11.01 | (328) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (167), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (200) all_28_0_32 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (200) can reduce 86 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (86) ~ (all_28_0_32 = 0) % 32.33/11.01 | (332) 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_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_22_1_27, all_0_2_2) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (168), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (200) all_28_0_32 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (200) can reduce 86 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (86) ~ (all_28_0_32 = 0) % 32.33/11.01 | (336) 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_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_22_1_27) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (169), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (200) all_28_0_32 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (200) can reduce 86 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (86) ~ (all_28_0_32 = 0) % 32.33/11.01 | (340) 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_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_22_1_27, all_0_2_2) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (170), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (200) all_28_0_32 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (200) can reduce 86 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (86) ~ (all_28_0_32 = 0) % 32.33/11.01 | (344) 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_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_22_1_27) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (173), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (196) all_32_0_36 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (196) can reduce 92 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (92) ~ (all_32_0_36 = 0) % 32.33/11.01 | (348) 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)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (171), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (196) all_32_0_36 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (196) can reduce 92 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (92) ~ (all_32_0_36 = 0) % 32.33/11.01 | (352) 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)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (174), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (196) all_32_0_36 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (196) can reduce 92 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (92) ~ (all_32_0_36 = 0) % 32.33/11.01 | (356) 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)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (228), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (208) all_22_0_26 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (208) can reduce 74 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (74) ~ (all_22_0_26 = 0) % 32.33/11.01 | (360) ? [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)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (232), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (208) all_22_0_26 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (208) can reduce 74 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (74) ~ (all_22_0_26 = 0) % 32.33/11.01 | (364) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (240), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (100) all_0_0_0 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (100) can reduce 57 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (57) ~ (all_0_0_0 = 0) % 32.33/11.01 | (368) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (244), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (100) all_0_0_0 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (100) can reduce 57 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (57) ~ (all_0_0_0 = 0) % 32.33/11.01 | (372) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (252), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (273) all_20_0_24 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (273) can reduce 70 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (70) ~ (all_20_0_24 = 0) % 32.33/11.01 | (376) ? [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)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (256), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (273) all_20_0_24 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (273) can reduce 70 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (70) ~ (all_20_0_24 = 0) % 32.33/11.01 | (380) ? [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)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (304), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (273) all_20_0_24 = 0 % 32.33/11.01 | % 32.33/11.01 | Equations (273) can reduce 70 to: % 32.33/11.01 | (101) $false % 32.33/11.01 | % 32.33/11.01 |-The branch is then unsatisfiable % 32.33/11.01 |-Branch two: % 32.33/11.01 | (70) ~ (all_20_0_24 = 0) % 32.33/11.01 | (384) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.01 | % 32.33/11.01 +-Applying beta-rule and splitting (308), into two cases. % 32.33/11.01 |-Branch one: % 32.33/11.01 | (273) all_20_0_24 = 0 % 32.33/11.01 | % 32.33/11.02 | Equations (273) can reduce 70 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (70) ~ (all_20_0_24 = 0) % 32.33/11.02 | (388) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (336), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (208) all_22_0_26 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (208) can reduce 74 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (74) ~ (all_22_0_26 = 0) % 32.33/11.02 | (392) ? [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_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_22_1_27) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (352), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (200) all_28_0_32 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (200) can reduce 86 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (86) ~ (all_28_0_32 = 0) % 32.33/11.02 | (396) ? [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)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (356), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (200) all_28_0_32 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (200) can reduce 86 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (86) ~ (all_28_0_32 = 0) % 32.33/11.02 | (400) ? [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)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (139), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (208) all_22_0_26 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (208) can reduce 74 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (74) ~ (all_22_0_26 = 0) % 32.33/11.02 | (404) all_0_0_0 = 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_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (144), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (196) all_32_0_36 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (196) can reduce 92 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (92) ~ (all_32_0_36 = 0) % 32.33/11.02 | (408) all_0_0_0 = 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_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (165), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (200) all_28_0_32 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (200) can reduce 86 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (86) ~ (all_28_0_32 = 0) % 32.33/11.02 | (412) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (177), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (200) all_28_0_32 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (200) can reduce 86 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (86) ~ (all_28_0_32 = 0) % 32.33/11.02 | (416) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (175), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (200) all_28_0_32 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (200) can reduce 86 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (86) ~ (all_28_0_32 = 0) % 32.33/11.02 | (420) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (176), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (200) all_28_0_32 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (200) can reduce 86 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (86) ~ (all_28_0_32 = 0) % 32.33/11.02 | (424) all_24_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (181), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (273) all_20_0_24 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (273) can reduce 70 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (70) ~ (all_20_0_24 = 0) % 32.33/11.02 | (428) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_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_1_1, all_0_2_2) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (142), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (208) all_22_0_26 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (208) can reduce 74 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (74) ~ (all_22_0_26 = 0) % 32.33/11.02 | (432) all_0_0_0 = 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_1_1, 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_1_1) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (292), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (273) all_20_0_24 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (273) can reduce 70 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (70) ~ (all_20_0_24 = 0) % 32.33/11.02 | (436) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (296), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (273) all_20_0_24 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (273) can reduce 70 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (70) ~ (all_20_0_24 = 0) % 32.33/11.02 | (440) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (300), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (273) all_20_0_24 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (273) can reduce 70 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (70) ~ (all_20_0_24 = 0) % 32.33/11.02 | (444) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (324), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (200) all_28_0_32 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (200) can reduce 86 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (86) ~ (all_28_0_32 = 0) % 32.33/11.02 | (448) ? [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)) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (328), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (273) all_20_0_24 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (273) can reduce 70 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (70) ~ (all_20_0_24 = 0) % 32.33/11.02 | (452) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/11.02 | % 32.33/11.02 | Instantiating (452) with all_345_0_5202 yields: % 32.33/11.02 | (453) (all_345_0_5202 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_345_0_5202 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_345_0_5202 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202) | ( ~ (all_345_0_5202 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_345_0_5202) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (453), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (454) (all_345_0_5202 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_345_0_5202 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_345_0_5202 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (454), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (455) (all_345_0_5202 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_345_0_5202 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (455), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (456) all_345_0_5202 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0 % 32.33/11.02 | % 32.33/11.02 | Applying alpha-rule on (456) yields: % 32.33/11.02 | (457) all_345_0_5202 = 0 % 32.33/11.02 | (458) apart_point_and_line(all_0_1_1, all_0_5_5) = 0 % 32.33/11.02 | % 32.33/11.02 +-Applying beta-rule and splitting (164), into two cases. % 32.33/11.02 |-Branch one: % 32.33/11.02 | (200) all_28_0_32 = 0 % 32.33/11.02 | % 32.33/11.02 | Equations (200) can reduce 86 to: % 32.33/11.02 | (101) $false % 32.33/11.02 | % 32.33/11.02 |-The branch is then unsatisfiable % 32.33/11.02 |-Branch two: % 32.33/11.02 | (86) ~ (all_28_0_32 = 0) % 32.33/11.02 | (462) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_0_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (163), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (200) all_28_0_32 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (200) can reduce 86 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (86) ~ (all_28_0_32 = 0) % 32.33/11.03 | (466) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (166), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (200) all_28_0_32 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (200) can reduce 86 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (86) ~ (all_28_0_32 = 0) % 32.33/11.03 | (470) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_0_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (156), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (221) all_26_0_30 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (221) can reduce 82 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (82) ~ (all_26_0_30 = 0) % 32.33/11.03 | (474) 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_1_1, 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_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (157), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (221) all_26_0_30 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (221) can reduce 82 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (82) ~ (all_26_0_30 = 0) % 32.33/11.03 | (478) 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_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (158), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (221) all_26_0_30 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (221) can reduce 82 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (82) ~ (all_26_0_30 = 0) % 32.33/11.03 | (482) 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_1_1, 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_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (159), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (221) all_26_0_30 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (221) can reduce 82 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (82) ~ (all_26_0_30 = 0) % 32.33/11.03 | (486) 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_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (154), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (221) all_26_0_30 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (221) can reduce 82 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (82) ~ (all_26_0_30 = 0) % 32.33/11.03 | (490) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (155), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (221) all_26_0_30 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (221) can reduce 82 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (82) ~ (all_26_0_30 = 0) % 32.33/11.03 | (494) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (404), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (498) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (408), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (502) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (412), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (506) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (428), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (510) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (432), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (514) ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (462), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (518) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_0_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (466), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (522) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (470), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (526) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_0_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (490), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (530) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 +-Applying beta-rule and splitting (494), into two cases. % 32.33/11.03 |-Branch one: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (57) ~ (all_0_0_0 = 0) % 32.33/11.03 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 32.33/11.03 | % 32.33/11.03 | Instantiating formula (21) with all_0_1_1, all_0_5_5, 0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_1_1, all_0_5_5) = 0, yields: % 32.33/11.03 | (100) all_0_0_0 = 0 % 32.33/11.03 | % 32.33/11.03 | Equations (100) can reduce 57 to: % 32.33/11.03 | (101) $false % 32.33/11.03 | % 32.33/11.03 |-The branch is then unsatisfiable % 32.33/11.03 |-Branch two: % 32.33/11.03 | (537) all_345_0_5202 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0 % 32.33/11.04 | % 32.33/11.04 | Applying alpha-rule on (537) yields: % 32.33/11.04 | (457) all_345_0_5202 = 0 % 32.33/11.04 | (539) apart_point_and_line(all_0_2_2, all_0_4_4) = 0 % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (164), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (86) ~ (all_28_0_32 = 0) % 32.33/11.04 | (462) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_0_1_1) = v0)) % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (163), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (86) ~ (all_28_0_32 = 0) % 32.33/11.04 | (466) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (166), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (86) ~ (all_28_0_32 = 0) % 32.33/11.04 | (470) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_0_1_1) = v0)) % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (178), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (86) ~ (all_28_0_32 = 0) % 32.33/11.04 | (555) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0)) % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (179), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (86) ~ (all_28_0_32 = 0) % 32.33/11.04 | (559) all_26_0_30 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0)) % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (193), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (86) ~ (all_28_0_32 = 0) % 32.33/11.04 | (563) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, 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_0_2_2) = v0)) % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (194), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (86) ~ (all_28_0_32 = 0) % 32.33/11.04 | (567) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, 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_0_2_2) = v0)) % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (348), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (86) ~ (all_28_0_32 = 0) % 32.33/11.04 | (571) ? [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)) % 32.33/11.04 | % 32.33/11.04 | Instantiating formula (21) with all_0_2_2, all_0_4_4, 0, all_28_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, apart_point_and_line(all_0_2_2, all_0_4_4) = 0, yields: % 32.33/11.04 | (200) all_28_0_32 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (200) can reduce 86 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (574) ~ (all_345_0_5202 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202 % 32.33/11.04 | % 32.33/11.04 | Applying alpha-rule on (574) yields: % 32.33/11.04 | (575) ~ (all_345_0_5202 = 0) % 32.33/11.04 | (576) distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202 % 32.33/11.04 | % 32.33/11.04 | Instantiating formula (25) with all_345_0_5202, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202, yields: % 32.33/11.04 | (577) all_345_0_5202 = 0 | convergent_lines(all_0_5_5, all_0_5_5) = 0 % 32.33/11.04 | % 32.33/11.04 +-Applying beta-rule and splitting (577), into two cases. % 32.33/11.04 |-Branch one: % 32.33/11.04 | (578) convergent_lines(all_0_5_5, all_0_5_5) = 0 % 32.33/11.04 | % 32.33/11.04 | Instantiating formula (38) with all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_5_5) = 0, yields: % 32.33/11.04 | (579) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (580) ~ (convergent_lines(all_0_5_5, all_0_5_5) = 0) % 32.33/11.04 | (457) all_345_0_5202 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (457) can reduce 575 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (583) ~ (all_345_0_5202 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_345_0_5202 % 32.33/11.04 | % 32.33/11.04 | Applying alpha-rule on (583) yields: % 32.33/11.04 | (575) ~ (all_345_0_5202 = 0) % 32.33/11.04 | (585) distinct_points(all_0_2_2, all_0_1_1) = all_345_0_5202 % 32.33/11.04 | % 32.33/11.04 | Instantiating formula (53) with all_0_2_2, all_0_1_1, 0, all_345_0_5202 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_345_0_5202, distinct_points(all_0_2_2, all_0_1_1) = 0, yields: % 32.33/11.04 | (457) all_345_0_5202 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (457) can reduce 575 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (588) ~ (distinct_points(all_0_2_2, all_0_1_1) = 0) % 32.33/11.04 | (229) all_24_0_28 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (229) can reduce 78 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (591) ~ (all_31_0_35 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35 % 32.33/11.04 | % 32.33/11.04 | Applying alpha-rule on (591) yields: % 32.33/11.04 | (111) ~ (all_31_0_35 = 0) % 32.33/11.04 | (593) convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35 % 32.33/11.04 | % 32.33/11.04 | Instantiating formula (18) 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: % 32.33/11.04 | (594) all_31_0_35 = 0 % 32.33/11.04 | % 32.33/11.04 | Equations (594) can reduce 111 to: % 32.33/11.04 | (101) $false % 32.33/11.04 | % 32.33/11.04 |-The branch is then unsatisfiable % 32.33/11.04 |-Branch two: % 32.33/11.04 | (596) ~ (all_34_0_38 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38 % 32.33/11.05 | % 32.33/11.05 | Applying alpha-rule on (596) yields: % 32.33/11.05 | (108) ~ (all_34_0_38 = 0) % 32.33/11.05 | (598) convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38 % 32.33/11.05 | % 32.33/11.05 | Instantiating formula (18) 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: % 32.33/11.05 | (599) all_34_0_38 = 0 % 32.33/11.05 | % 32.33/11.05 | Equations (599) can reduce 108 to: % 32.33/11.05 | (101) $false % 32.33/11.05 | % 32.33/11.05 |-The branch is then unsatisfiable % 32.33/11.05 |-Branch two: % 32.33/11.05 | (601) ~ (all_30_0_34 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34 % 32.33/11.05 | % 32.33/11.05 | Applying alpha-rule on (601) yields: % 32.33/11.05 | (105) ~ (all_30_0_34 = 0) % 32.33/11.05 | (603) convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34 % 32.67/11.05 | % 32.67/11.05 | Instantiating formula (18) 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: % 32.67/11.05 | (604) all_30_0_34 = 0 % 32.67/11.05 | % 32.67/11.05 | Equations (604) can reduce 105 to: % 32.67/11.05 | (101) $false % 32.67/11.05 | % 32.67/11.05 |-The branch is then unsatisfiable % 32.67/11.05 |-Branch two: % 32.67/11.05 | (606) ~ (all_35_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39 % 32.67/11.05 | % 32.67/11.05 | Applying alpha-rule on (606) yields: % 32.67/11.05 | (98) ~ (all_35_0_39 = 0) % 32.67/11.05 | (608) convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39 % 32.67/11.05 | % 32.67/11.05 | Instantiating formula (18) 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: % 32.67/11.05 | (609) all_35_0_39 = 0 % 32.67/11.05 | % 32.67/11.05 | Equations (609) can reduce 98 to: % 32.67/11.05 | (101) $false % 32.67/11.05 | % 32.67/11.05 |-The branch is then unsatisfiable % 32.67/11.05 % SZS output end Proof for theBenchmark % 32.67/11.05 % 32.67/11.05 10416ms %------------------------------------------------------------------------------