%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO191+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 03:48:27 EDT 2022 % Result : Theorem 5.65s 2.00s % Output : Proof 27.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GEO191+1 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n008.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jun 17 15:15:07 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.65/0.93 Prover 0: Preprocessing ... % 2.00/1.07 Prover 0: Warning: ignoring some quantifiers % 2.00/1.09 Prover 0: Constructing countermodel ... % 3.13/1.40 Prover 0: gave up % 3.13/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.13/1.43 Prover 1: Preprocessing ... % 3.57/1.51 Prover 1: Constructing countermodel ... % 3.69/1.56 Prover 1: gave up % 3.69/1.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.69/1.58 Prover 2: Preprocessing ... % 4.39/1.69 Prover 2: Warning: ignoring some quantifiers % 4.39/1.70 Prover 2: Constructing countermodel ... % 5.65/2.00 Prover 2: proved (442ms) % 5.65/2.00 % 5.65/2.00 No countermodel exists, formula is valid % 5.65/2.00 % SZS status Theorem for theBenchmark % 5.65/2.00 % 5.65/2.00 Generating proof ... Warning: ignoring some quantifiers % 26.06/9.29 found it (size 731) % 26.06/9.29 % 26.06/9.29 % SZS output start Proof for theBenchmark % 26.06/9.29 Assumed formulas after preprocessing and simplification: % 26.06/9.29 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & intersection_point(v2, v3) = v7 & intersection_point(v0, v1) = v4 & apart_point_and_line(v7, v1) = v9 & apart_point_and_line(v7, v0) = v8 & convergent_lines(v2, v3) = 0 & convergent_lines(v0, v1) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v11, v12) = v14) | ~ (distinct_points(v10, v11) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v10, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v10, v13) = v14) | ~ (distinct_lines(v12, v13) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v12) = v15) | ~ (apart_point_and_line(v10, v13) = v14) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v12) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v12, v13) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v10, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_points(v10, v11) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v11, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v12, v11) = v14) | ~ (distinct_points(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (convergent_lines(v11, v12) = v14) | ~ (convergent_lines(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (convergent_lines(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (distinct_lines(v11, v12) = v14) | ~ (distinct_lines(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & distinct_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (distinct_points(v11, v12) = v14) | ~ (distinct_points(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & distinct_points(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v12, v11) = v13) | ~ (apart_point_and_line(v10, v11) = 0) | distinct_points(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v12) = v13) | ~ (apart_point_and_line(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = 0) | ~ (distinct_lines(v11, v12) = v13) | apart_point_and_line(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = 0) | ~ (distinct_points(v10, v12) = v13) | apart_point_and_line(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v11, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v11) = 0) | ~ (distinct_lines(v11, v12) = v13) | convergent_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_lines(v11, v12) = v13) | ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_lines(v10, v12) = v13) | ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_points(v11, v12) = v13) | ~ (distinct_points(v10, v11) = 0) | distinct_points(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_points(v10, v12) = v13) | ~ (distinct_points(v10, v11) = 0) | distinct_points(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (intersection_point(v13, v12) = v11) | ~ (intersection_point(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (line_connecting(v13, v12) = v11) | ~ (line_connecting(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (apart_point_and_line(v13, v12) = v11) | ~ (apart_point_and_line(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (convergent_lines(v13, v12) = v11) | ~ (convergent_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (distinct_lines(v13, v12) = v11) | ~ (distinct_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (distinct_points(v13, v12) = v11) | ~ (distinct_points(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (distinct_lines(v12, v13) = 0) | ~ (distinct_points(v10, v11) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v11, v13) = 0) | (v14 = 0 & apart_point_and_line(v11, v12) = 0) | (v14 = 0 & apart_point_and_line(v10, v13) = 0) | (v14 = 0 & apart_point_and_line(v10, v12) = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v11) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v11, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v10, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v11) = v13)) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v10) = v13)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v11, v12) = v13)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v10, v12) = v13)) & ! [v10] : ~ (convergent_lines(v10, v10) = 0) & ! [v10] : ~ (distinct_lines(v10, v10) = 0) & ! [v10] : ~ (distinct_points(v10, v10) = 0) & ? [v10] : ? [v11] : ? [v12] : intersection_point(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : line_connecting(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : apart_point_and_line(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : convergent_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : distinct_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : distinct_points(v11, v10) = v12 & ((v6 = 0 & apart_point_and_line(v4, v3) = 0) | (v5 = 0 & apart_point_and_line(v4, v2) = 0))) % 26.06/9.35 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields: % 26.06/9.35 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5 & apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0 & apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1 & convergent_lines(all_0_7_7, all_0_6_6) = 0 & convergent_lines(all_0_9_9, all_0_8_8) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ((all_0_3_3 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (all_0_4_4 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)) % 26.06/9.37 | % 26.06/9.37 | Applying alpha-rule on (1) yields: % 26.06/9.37 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 26.06/9.37 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 26.06/9.37 | (4) ! [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) % 26.06/9.37 | (5) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 26.06/9.37 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 26.06/9.37 | (7) intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 % 26.06/9.37 | (8) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 26.06/9.37 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 26.06/9.37 | (10) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 26.06/9.37 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 26.06/9.37 | (12) ! [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))) % 26.06/9.37 | (13) ! [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))) % 26.06/9.37 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 26.06/9.37 | (15) ! [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))) % 26.06/9.37 | (16) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 26.06/9.37 | (17) ~ (all_0_0_0 = 0) % 26.06/9.37 | (18) intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5 % 26.06/9.37 | (19) ! [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))) % 26.06/9.37 | (20) (all_0_3_3 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (all_0_4_4 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) % 26.06/9.37 | (21) ! [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)) % 26.06/9.37 | (22) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 26.06/9.37 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 26.06/9.38 | (24) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 26.06/9.38 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 26.06/9.38 | (26) ! [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)) % 26.06/9.38 | (27) ! [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) % 26.06/9.38 | (28) ! [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))) % 26.06/9.38 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 26.06/9.38 | (30) ! [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))) % 26.06/9.38 | (31) ! [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))) % 26.06/9.38 | (32) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 26.06/9.38 | (33) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 26.06/9.38 | (34) ! [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) % 26.06/9.38 | (35) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 26.48/9.38 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 26.48/9.38 | (37) apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0 % 26.48/9.38 | (38) ! [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))) % 26.48/9.38 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 26.48/9.38 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 26.48/9.38 | (41) ! [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) % 26.48/9.38 | (42) ! [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)) % 26.48/9.38 | (43) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 26.48/9.38 | (44) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 26.48/9.38 | (45) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 26.48/9.38 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 26.48/9.38 | (47) ! [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)) % 26.48/9.39 | (48) ~ (all_0_1_1 = 0) % 26.48/9.39 | (49) convergent_lines(all_0_7_7, all_0_6_6) = 0 % 26.48/9.39 | (50) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 26.48/9.39 | (51) convergent_lines(all_0_9_9, all_0_8_8) = 0 % 26.48/9.39 | (52) ! [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))) % 26.48/9.39 | (53) ! [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)) % 26.48/9.39 | (54) ! [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)) % 26.48/9.39 | (55) ! [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))) % 26.48/9.39 | (56) apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1 % 26.48/9.39 | (57) ! [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))) % 26.53/9.39 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 26.53/9.39 | % 26.53/9.39 | Instantiating formula (31) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 26.53/9.39 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = v0)) % 26.53/9.39 | % 26.53/9.39 | Instantiating formula (13) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 26.53/9.39 | (60) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = v0)) % 26.53/9.39 | % 26.53/9.39 | Instantiating formula (31) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields: % 26.53/9.39 | (61) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = v0)) % 26.53/9.39 | % 26.53/9.39 | Instantiating formula (13) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields: % 26.53/9.39 | (62) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = v0)) % 26.53/9.39 | % 26.53/9.39 | Instantiating formula (38) with all_0_0_0, all_0_0_0, all_0_8_8, all_0_8_8, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, yields: % 26.53/9.39 | (63) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.39 | % 26.53/9.39 | Instantiating formula (38) with all_0_1_1, all_0_0_0, all_0_9_9, all_0_8_8, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, yields: % 26.53/9.39 | (64) all_0_0_0 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.40 | % 26.53/9.40 | Instantiating formula (38) with all_0_0_0, all_0_1_1, all_0_8_8, all_0_9_9, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, yields: % 26.53/9.40 | (65) all_0_0_0 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.40 | % 26.53/9.40 | Instantiating formula (38) with all_0_1_1, all_0_1_1, all_0_9_9, all_0_9_9, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, yields: % 26.53/9.40 | (66) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.40 | % 26.53/9.40 | Instantiating formula (22) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields: % 26.53/9.40 | (67) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(v0, all_0_6_6) = v1) % 26.53/9.40 | % 26.53/9.40 | Instantiating formula (33) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields: % 26.53/9.40 | (68) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(v0, all_0_7_7) = v1) % 26.53/9.40 | % 26.53/9.40 | Instantiating formula (22) with all_0_8_8, all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = 0, yields: % 26.53/9.40 | (69) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(v0, all_0_8_8) = v1) % 26.53/9.40 | % 26.53/9.40 | Instantiating formula (33) with all_0_8_8, all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = 0, yields: % 26.53/9.40 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(v0, all_0_9_9) = v1) % 26.53/9.40 | % 26.53/9.40 | Instantiating (70) with all_20_0_28, all_20_1_29 yields: % 26.53/9.40 | (71) ~ (all_20_0_28 = 0) & intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29 & apart_point_and_line(all_20_1_29, all_0_9_9) = all_20_0_28 % 26.53/9.40 | % 26.53/9.40 | Applying alpha-rule on (71) yields: % 26.53/9.40 | (72) ~ (all_20_0_28 = 0) % 26.53/9.40 | (73) intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29 % 26.53/9.40 | (74) apart_point_and_line(all_20_1_29, all_0_9_9) = all_20_0_28 % 26.53/9.40 | % 26.53/9.40 | Instantiating (62) with all_22_0_30 yields: % 26.53/9.40 | (75) ( ~ (all_22_0_30 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30) | ( ~ (all_22_0_30 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30) % 26.53/9.40 | % 26.53/9.40 | Instantiating (61) with all_23_0_31 yields: % 26.53/9.40 | (76) ( ~ (all_23_0_31 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31) | ( ~ (all_23_0_31 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31) % 26.53/9.40 | % 26.53/9.40 | Instantiating (59) with all_24_0_32 yields: % 26.53/9.40 | (77) ( ~ (all_24_0_32 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32) | ( ~ (all_24_0_32 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32) % 26.53/9.40 | % 26.53/9.40 | Instantiating (60) with all_25_0_33 yields: % 26.53/9.40 | (78) ( ~ (all_25_0_33 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33) | ( ~ (all_25_0_33 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33) % 26.53/9.40 | % 26.53/9.40 | Instantiating (69) with all_26_0_34, all_26_1_35 yields: % 26.53/9.40 | (79) ~ (all_26_0_34 = 0) & intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35 & apart_point_and_line(all_26_1_35, all_0_8_8) = all_26_0_34 % 26.53/9.40 | % 26.53/9.40 | Applying alpha-rule on (79) yields: % 26.53/9.40 | (80) ~ (all_26_0_34 = 0) % 26.53/9.40 | (81) intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35 % 26.53/9.40 | (82) apart_point_and_line(all_26_1_35, all_0_8_8) = all_26_0_34 % 26.53/9.40 | % 26.53/9.40 | Instantiating (67) with all_28_0_36, all_28_1_37 yields: % 26.53/9.40 | (83) ~ (all_28_0_36 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37 & apart_point_and_line(all_28_1_37, all_0_6_6) = all_28_0_36 % 26.53/9.40 | % 26.53/9.40 | Applying alpha-rule on (83) yields: % 26.53/9.40 | (84) ~ (all_28_0_36 = 0) % 26.53/9.40 | (85) intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37 % 26.53/9.40 | (86) apart_point_and_line(all_28_1_37, all_0_6_6) = all_28_0_36 % 26.53/9.40 | % 26.53/9.40 | Instantiating (68) with all_30_0_38, all_30_1_39 yields: % 26.53/9.40 | (87) ~ (all_30_0_38 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39 & apart_point_and_line(all_30_1_39, all_0_7_7) = all_30_0_38 % 26.53/9.40 | % 26.53/9.40 | Applying alpha-rule on (87) yields: % 26.53/9.40 | (88) ~ (all_30_0_38 = 0) % 26.53/9.40 | (89) intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39 % 26.53/9.40 | (90) apart_point_and_line(all_30_1_39, all_0_7_7) = all_30_0_38 % 26.53/9.40 | % 26.53/9.40 +-Applying beta-rule and splitting (75), into two cases. % 26.53/9.40 |-Branch one: % 26.53/9.40 | (91) ~ (all_22_0_30 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30 % 26.53/9.40 | % 26.53/9.40 | Applying alpha-rule on (91) yields: % 26.53/9.40 | (92) ~ (all_22_0_30 = 0) % 26.53/9.40 | (93) apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30 % 26.53/9.40 | % 26.53/9.40 +-Applying beta-rule and splitting (76), into two cases. % 26.53/9.40 |-Branch one: % 26.53/9.40 | (94) ~ (all_23_0_31 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31 % 26.53/9.40 | % 26.53/9.40 | Applying alpha-rule on (94) yields: % 26.53/9.40 | (95) ~ (all_23_0_31 = 0) % 26.53/9.40 | (96) apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31 % 26.53/9.40 | % 26.53/9.40 +-Applying beta-rule and splitting (77), into two cases. % 26.53/9.40 |-Branch one: % 26.53/9.40 | (97) ~ (all_24_0_32 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32 % 26.53/9.40 | % 26.53/9.40 | Applying alpha-rule on (97) yields: % 26.53/9.40 | (98) ~ (all_24_0_32 = 0) % 26.53/9.40 | (99) apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32 % 26.53/9.40 | % 26.53/9.40 +-Applying beta-rule and splitting (66), into two cases. % 26.53/9.40 |-Branch one: % 26.53/9.40 | (100) all_0_1_1 = 0 % 26.53/9.40 | % 26.53/9.41 | Equations (100) can reduce 48 to: % 26.53/9.41 | (101) $false % 26.53/9.41 | % 26.53/9.41 |-The branch is then unsatisfiable % 26.53/9.41 |-Branch two: % 26.53/9.41 | (48) ~ (all_0_1_1 = 0) % 26.53/9.41 | (103) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.41 | % 26.53/9.41 +-Applying beta-rule and splitting (78), into two cases. % 26.53/9.41 |-Branch one: % 26.53/9.41 | (104) ~ (all_25_0_33 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33 % 26.53/9.41 | % 26.53/9.41 | Applying alpha-rule on (104) yields: % 26.53/9.41 | (105) ~ (all_25_0_33 = 0) % 26.53/9.41 | (106) apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33 % 26.53/9.41 | % 26.53/9.41 +-Applying beta-rule and splitting (63), into two cases. % 26.53/9.41 |-Branch one: % 26.53/9.41 | (107) all_0_0_0 = 0 % 26.53/9.41 | % 26.53/9.41 | Equations (107) can reduce 17 to: % 26.53/9.41 | (101) $false % 26.53/9.41 | % 26.53/9.41 |-The branch is then unsatisfiable % 26.53/9.41 |-Branch two: % 26.53/9.41 | (17) ~ (all_0_0_0 = 0) % 26.53/9.41 | (110) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.41 | % 26.53/9.41 +-Applying beta-rule and splitting (64), into two cases. % 26.53/9.41 |-Branch one: % 26.53/9.41 | (107) all_0_0_0 = 0 % 26.53/9.41 | % 26.53/9.41 | Equations (107) can reduce 17 to: % 26.53/9.41 | (101) $false % 26.53/9.41 | % 26.53/9.41 |-The branch is then unsatisfiable % 26.53/9.41 |-Branch two: % 26.53/9.41 | (17) ~ (all_0_0_0 = 0) % 26.53/9.41 | (114) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.41 | % 26.53/9.41 +-Applying beta-rule and splitting (65), into two cases. % 26.53/9.41 |-Branch one: % 26.53/9.41 | (107) all_0_0_0 = 0 % 26.53/9.41 | % 26.53/9.41 | Equations (107) can reduce 17 to: % 26.53/9.41 | (101) $false % 26.53/9.41 | % 26.53/9.41 |-The branch is then unsatisfiable % 26.53/9.41 |-Branch two: % 26.53/9.41 | (17) ~ (all_0_0_0 = 0) % 26.53/9.41 | (118) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.41 | % 26.53/9.41 +-Applying beta-rule and splitting (114), into two cases. % 26.53/9.41 |-Branch one: % 26.53/9.41 | (100) all_0_1_1 = 0 % 26.53/9.41 | % 26.53/9.41 | Equations (100) can reduce 48 to: % 26.53/9.41 | (101) $false % 26.53/9.41 | % 26.53/9.41 |-The branch is then unsatisfiable % 26.53/9.41 |-Branch two: % 26.53/9.41 | (48) ~ (all_0_1_1 = 0) % 26.53/9.41 | (122) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.41 | % 26.53/9.41 +-Applying beta-rule and splitting (118), into two cases. % 26.53/9.41 |-Branch one: % 26.53/9.41 | (100) all_0_1_1 = 0 % 26.53/9.41 | % 26.53/9.41 | Equations (100) can reduce 48 to: % 26.53/9.41 | (101) $false % 26.53/9.41 | % 26.53/9.41 |-The branch is then unsatisfiable % 26.53/9.41 |-Branch two: % 26.53/9.41 | (48) ~ (all_0_1_1 = 0) % 26.53/9.41 | (126) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.41 | % 26.53/9.41 | Instantiating formula (11) with all_0_7_7, all_0_6_6, all_30_1_39, all_0_2_2 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39, intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 26.53/9.41 | (127) all_30_1_39 = all_0_2_2 % 26.53/9.41 | % 26.53/9.41 | Instantiating formula (11) with all_0_7_7, all_0_6_6, all_28_1_37, all_30_1_39 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39, intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37, yields: % 26.53/9.41 | (128) all_30_1_39 = all_28_1_37 % 26.53/9.41 | % 26.53/9.41 | Instantiating formula (11) with all_0_9_9, all_0_8_8, all_26_1_35, all_0_5_5 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35, intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields: % 26.53/9.41 | (129) all_26_1_35 = all_0_5_5 % 26.53/9.41 | % 26.53/9.41 | Instantiating formula (11) with all_0_9_9, all_0_8_8, all_20_1_29, all_26_1_35 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35, intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29, yields: % 26.53/9.41 | (130) all_26_1_35 = all_20_1_29 % 26.53/9.41 | % 26.53/9.41 | Combining equations (127,128) yields a new equation: % 26.53/9.41 | (131) all_28_1_37 = all_0_2_2 % 26.53/9.41 | % 26.53/9.41 | Combining equations (130,129) yields a new equation: % 26.53/9.41 | (132) all_20_1_29 = all_0_5_5 % 26.53/9.41 | % 26.53/9.41 | Simplifying 132 yields: % 26.53/9.41 | (133) all_20_1_29 = all_0_5_5 % 26.53/9.41 | % 26.53/9.41 | Combining equations (131,128) yields a new equation: % 26.53/9.41 | (127) all_30_1_39 = all_0_2_2 % 26.53/9.41 | % 26.53/9.41 | From (127) and (90) follows: % 26.53/9.41 | (135) apart_point_and_line(all_0_2_2, all_0_7_7) = all_30_0_38 % 26.53/9.41 | % 26.53/9.41 | From (131) and (86) follows: % 26.53/9.41 | (136) apart_point_and_line(all_0_2_2, all_0_6_6) = all_28_0_36 % 26.53/9.41 | % 26.53/9.41 | From (129) and (82) follows: % 26.53/9.41 | (137) apart_point_and_line(all_0_5_5, all_0_8_8) = all_26_0_34 % 26.53/9.41 | % 26.53/9.41 | From (133) and (74) follows: % 26.53/9.41 | (138) apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28 % 26.53/9.41 | % 26.53/9.41 | Instantiating formula (2) with all_0_2_2, all_0_6_6, all_28_0_36, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_28_0_36, apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, yields: % 26.53/9.41 | (139) all_28_0_36 = all_24_0_32 % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (2) with all_0_2_2, all_0_7_7, all_30_0_38, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_30_0_38, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields: % 26.53/9.42 | (140) all_30_0_38 = all_25_0_33 % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (2) with all_0_5_5, all_0_8_8, all_26_0_34, all_23_0_31 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_26_0_34, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.53/9.42 | (141) all_26_0_34 = all_23_0_31 % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (2) with all_0_5_5, all_0_9_9, all_20_0_28, all_22_0_30 and discharging atoms apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.53/9.42 | (142) all_22_0_30 = all_20_0_28 % 26.53/9.42 | % 26.53/9.42 | Equations (140) can reduce 88 to: % 26.53/9.42 | (105) ~ (all_25_0_33 = 0) % 26.53/9.42 | % 26.53/9.42 | Equations (139) can reduce 84 to: % 26.53/9.42 | (98) ~ (all_24_0_32 = 0) % 26.53/9.42 | % 26.53/9.42 | Equations (141) can reduce 80 to: % 26.53/9.42 | (95) ~ (all_23_0_31 = 0) % 26.53/9.42 | % 26.53/9.42 | Equations (142) can reduce 92 to: % 26.53/9.42 | (72) ~ (all_20_0_28 = 0) % 26.53/9.42 | % 26.53/9.42 | From (139) and (136) follows: % 26.53/9.42 | (99) apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32 % 26.53/9.42 | % 26.53/9.42 | From (140) and (135) follows: % 26.53/9.42 | (106) apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33 % 26.53/9.42 | % 26.53/9.42 | From (141) and (137) follows: % 26.53/9.42 | (96) apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31 % 26.53/9.42 | % 26.53/9.42 | From (142) and (93) follows: % 26.53/9.42 | (138) apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28 % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_24_0_32, all_0_0_0, all_0_6_6, all_0_8_8, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, yields: % 26.53/9.42 | (151) all_24_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_0_0_0, all_24_0_32, all_0_8_8, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, yields: % 26.53/9.42 | (152) all_24_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_24_0_32, all_0_1_1, all_0_6_6, all_0_9_9, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, yields: % 26.53/9.42 | (153) all_24_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_0_1_1, all_24_0_32, all_0_9_9, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, yields: % 26.53/9.42 | (154) all_24_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_24_0_32, all_24_0_32, all_0_6_6, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, yields: % 26.53/9.42 | (155) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_25_0_33, all_0_0_0, all_0_7_7, all_0_8_8, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, yields: % 26.53/9.42 | (156) all_25_0_33 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_0_0_0, all_25_0_33, all_0_8_8, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, yields: % 26.53/9.42 | (157) all_25_0_33 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_25_0_33, all_0_1_1, all_0_7_7, all_0_9_9, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, yields: % 26.53/9.42 | (158) all_25_0_33 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_0_1_1, all_25_0_33, all_0_9_9, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, yields: % 26.53/9.42 | (159) all_25_0_33 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.53/9.42 | % 26.53/9.42 | Instantiating formula (38) with all_25_0_33, all_24_0_32, all_0_7_7, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields: % 26.71/9.43 | (160) all_25_0_33 = 0 | all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.71/9.43 | % 26.71/9.43 | Instantiating formula (38) with all_24_0_32, all_25_0_33, all_0_6_6, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields: % 26.71/9.43 | (161) all_25_0_33 = 0 | all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.71/9.43 | % 26.71/9.43 | Instantiating formula (38) with all_25_0_33, all_25_0_33, all_0_7_7, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields: % 26.71/9.43 | (162) all_25_0_33 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.71/9.43 | % 26.71/9.43 | Instantiating formula (38) with all_23_0_31, all_0_0_0, all_0_8_8, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.71/9.43 | (163) all_23_0_31 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.71/9.43 | % 26.71/9.43 | Instantiating formula (38) with all_0_0_0, all_23_0_31, all_0_8_8, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.71/9.43 | (164) all_23_0_31 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.71/9.43 | % 26.71/9.43 | Instantiating formula (38) with all_23_0_31, all_0_1_1, all_0_8_8, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.71/9.43 | (165) all_23_0_31 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.71/9.43 | % 26.71/9.43 | Instantiating formula (38) with all_0_1_1, all_23_0_31, all_0_9_9, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.71/9.43 | (166) all_23_0_31 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.71/9.43 | % 26.71/9.43 | Instantiating formula (30) with all_23_0_31, all_0_1_1, all_0_9_9, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.71/9.43 | (167) all_23_0_31 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.43 | % 26.74/9.43 | Instantiating formula (30) with all_0_1_1, all_23_0_31, all_0_8_8, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.43 | (168) all_23_0_31 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.43 | % 26.74/9.43 | Instantiating formula (38) with all_23_0_31, all_24_0_32, all_0_8_8, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.43 | (169) all_24_0_32 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (38) with all_24_0_32, all_23_0_31, all_0_6_6, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.44 | (170) all_24_0_32 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (30) with all_23_0_31, all_24_0_32, all_0_6_6, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.44 | (171) all_24_0_32 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (30) with all_24_0_32, all_23_0_31, all_0_8_8, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.44 | (172) all_24_0_32 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (38) with all_23_0_31, all_25_0_33, all_0_8_8, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.44 | (173) all_25_0_33 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (38) with all_25_0_33, all_23_0_31, all_0_7_7, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.44 | (174) all_25_0_33 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (30) with all_23_0_31, all_25_0_33, all_0_7_7, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.44 | (175) all_25_0_33 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (30) with all_25_0_33, all_23_0_31, all_0_8_8, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.44 | (176) all_25_0_33 = 0 | all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (38) with all_23_0_31, all_23_0_31, all_0_8_8, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields: % 26.74/9.44 | (177) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (38) with all_20_0_28, all_0_0_0, all_0_9_9, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.44 | (178) all_20_0_28 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (38) with all_0_0_0, all_20_0_28, all_0_8_8, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.44 | (179) all_20_0_28 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (30) with all_20_0_28, all_0_0_0, all_0_8_8, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.44 | (180) all_20_0_28 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (30) with all_0_0_0, all_20_0_28, all_0_9_9, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.44 | (181) all_20_0_28 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.44 | % 26.74/9.44 | Instantiating formula (38) with all_20_0_28, all_0_1_1, all_0_9_9, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.44 | (182) all_20_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (38) with all_0_1_1, all_20_0_28, all_0_9_9, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (183) all_20_0_28 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (38) with all_20_0_28, all_24_0_32, all_0_9_9, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (184) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (38) with all_24_0_32, all_20_0_28, all_0_6_6, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (185) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (30) with all_20_0_28, all_24_0_32, all_0_6_6, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (186) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (30) with all_24_0_32, all_20_0_28, all_0_9_9, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (187) all_24_0_32 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (38) with all_20_0_28, all_25_0_33, all_0_9_9, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (188) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (38) with all_25_0_33, all_20_0_28, all_0_7_7, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (189) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (30) with all_20_0_28, all_25_0_33, all_0_7_7, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (190) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (30) with all_25_0_33, all_20_0_28, all_0_9_9, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (191) all_25_0_33 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (38) with all_20_0_28, all_23_0_31, all_0_9_9, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (192) all_23_0_31 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (38) with all_23_0_31, all_20_0_28, all_0_8_8, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (193) all_23_0_31 = 0 | all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.45 | % 26.74/9.45 | Instantiating formula (38) with all_20_0_28, all_20_0_28, all_0_9_9, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields: % 26.74/9.45 | (194) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.45 | % 26.74/9.45 +-Applying beta-rule and splitting (20), into two cases. % 26.74/9.45 |-Branch one: % 26.74/9.45 | (195) all_0_3_3 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0 % 26.74/9.45 | % 26.74/9.45 | Applying alpha-rule on (195) yields: % 26.74/9.45 | (196) all_0_3_3 = 0 % 26.74/9.45 | (197) apart_point_and_line(all_0_5_5, all_0_6_6) = 0 % 26.74/9.45 | % 26.74/9.45 +-Applying beta-rule and splitting (162), into two cases. % 26.74/9.45 |-Branch one: % 26.74/9.45 | (198) all_25_0_33 = 0 % 26.74/9.45 | % 26.74/9.45 | Equations (198) can reduce 105 to: % 26.74/9.45 | (101) $false % 26.74/9.45 | % 26.74/9.45 |-The branch is then unsatisfiable % 26.74/9.45 |-Branch two: % 26.74/9.45 | (105) ~ (all_25_0_33 = 0) % 26.74/9.45 | (201) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.45 | % 26.74/9.45 +-Applying beta-rule and splitting (155), into two cases. % 26.74/9.45 |-Branch one: % 26.74/9.45 | (202) all_24_0_32 = 0 % 26.74/9.45 | % 26.74/9.45 | Equations (202) can reduce 98 to: % 26.74/9.45 | (101) $false % 26.74/9.45 | % 26.74/9.45 |-The branch is then unsatisfiable % 26.74/9.45 |-Branch two: % 26.74/9.45 | (98) ~ (all_24_0_32 = 0) % 26.74/9.45 | (205) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.45 | % 26.74/9.45 +-Applying beta-rule and splitting (177), into two cases. % 26.74/9.45 |-Branch one: % 26.74/9.46 | (206) all_23_0_31 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (206) can reduce 95 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (95) ~ (all_23_0_31 = 0) % 26.74/9.46 | (209) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (194), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (210) all_20_0_28 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (210) can reduce 72 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (72) ~ (all_20_0_28 = 0) % 26.74/9.46 | (213) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (175), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (198) all_25_0_33 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (198) can reduce 105 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (105) ~ (all_25_0_33 = 0) % 26.74/9.46 | (217) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (176), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (198) all_25_0_33 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (198) can reduce 105 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (105) ~ (all_25_0_33 = 0) % 26.74/9.46 | (221) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (187), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (202) all_24_0_32 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (202) can reduce 98 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (98) ~ (all_24_0_32 = 0) % 26.74/9.46 | (225) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (188), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (198) all_25_0_33 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (198) can reduce 105 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (105) ~ (all_25_0_33 = 0) % 26.74/9.46 | (229) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (191), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (198) all_25_0_33 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (198) can reduce 105 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (105) ~ (all_25_0_33 = 0) % 26.74/9.46 | (233) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (151), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (202) all_24_0_32 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (202) can reduce 98 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (98) ~ (all_24_0_32 = 0) % 26.74/9.46 | (237) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (159), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (198) all_25_0_33 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (198) can reduce 105 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (105) ~ (all_25_0_33 = 0) % 26.74/9.46 | (241) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (160), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (198) all_25_0_33 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (198) can reduce 105 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (105) ~ (all_25_0_33 = 0) % 26.74/9.46 | (245) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (192), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (206) all_23_0_31 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (206) can reduce 95 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (95) ~ (all_23_0_31 = 0) % 26.74/9.46 | (249) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (152), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (202) all_24_0_32 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (202) can reduce 98 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (98) ~ (all_24_0_32 = 0) % 26.74/9.46 | (253) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (153), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (202) all_24_0_32 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (202) can reduce 98 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (98) ~ (all_24_0_32 = 0) % 26.74/9.46 | (257) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (154), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (202) all_24_0_32 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (202) can reduce 98 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (98) ~ (all_24_0_32 = 0) % 26.74/9.46 | (261) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (156), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (198) all_25_0_33 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (198) can reduce 105 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (105) ~ (all_25_0_33 = 0) % 26.74/9.46 | (265) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (157), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (198) all_25_0_33 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (198) can reduce 105 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (105) ~ (all_25_0_33 = 0) % 26.74/9.46 | (269) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.46 | % 26.74/9.46 +-Applying beta-rule and splitting (183), into two cases. % 26.74/9.46 |-Branch one: % 26.74/9.46 | (210) all_20_0_28 = 0 % 26.74/9.46 | % 26.74/9.46 | Equations (210) can reduce 72 to: % 26.74/9.46 | (101) $false % 26.74/9.46 | % 26.74/9.46 |-The branch is then unsatisfiable % 26.74/9.46 |-Branch two: % 26.74/9.46 | (72) ~ (all_20_0_28 = 0) % 26.74/9.46 | (273) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (171), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (202) all_24_0_32 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (202) can reduce 98 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (98) ~ (all_24_0_32 = 0) % 26.74/9.47 | (277) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (184), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (202) all_24_0_32 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (202) can reduce 98 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (98) ~ (all_24_0_32 = 0) % 26.74/9.47 | (281) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (158), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (198) all_25_0_33 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (198) can reduce 105 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (105) ~ (all_25_0_33 = 0) % 26.74/9.47 | (285) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (185), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (202) all_24_0_32 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (202) can reduce 98 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (98) ~ (all_24_0_32 = 0) % 26.74/9.47 | (289) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (186), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (202) all_24_0_32 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (202) can reduce 98 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (98) ~ (all_24_0_32 = 0) % 26.74/9.47 | (293) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (189), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (198) all_25_0_33 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (198) can reduce 105 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (105) ~ (all_25_0_33 = 0) % 26.74/9.47 | (297) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (190), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (198) all_25_0_33 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (198) can reduce 105 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (105) ~ (all_25_0_33 = 0) % 26.74/9.47 | (301) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (172), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (202) all_24_0_32 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (202) can reduce 98 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (98) ~ (all_24_0_32 = 0) % 26.74/9.47 | (305) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (178), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (210) all_20_0_28 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (210) can reduce 72 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (72) ~ (all_20_0_28 = 0) % 26.74/9.47 | (309) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (181), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (210) all_20_0_28 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (210) can reduce 72 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (72) ~ (all_20_0_28 = 0) % 26.74/9.47 | (313) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (179), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (210) all_20_0_28 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (210) can reduce 72 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (72) ~ (all_20_0_28 = 0) % 26.74/9.47 | (317) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (180), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (210) all_20_0_28 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (210) can reduce 72 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (72) ~ (all_20_0_28 = 0) % 26.74/9.47 | (321) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (182), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (210) all_20_0_28 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (210) can reduce 72 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (72) ~ (all_20_0_28 = 0) % 26.74/9.47 | (325) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (193), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (206) all_23_0_31 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (206) can reduce 95 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (95) ~ (all_23_0_31 = 0) % 26.74/9.47 | (329) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (167), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (206) all_23_0_31 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (206) can reduce 95 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (95) ~ (all_23_0_31 = 0) % 26.74/9.47 | (333) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (168), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (206) all_23_0_31 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (206) can reduce 95 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (95) ~ (all_23_0_31 = 0) % 26.74/9.47 | (337) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (169), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (202) all_24_0_32 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (202) can reduce 98 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (98) ~ (all_24_0_32 = 0) % 26.74/9.47 | (341) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (170), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (202) all_24_0_32 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (202) can reduce 98 to: % 26.74/9.47 | (101) $false % 26.74/9.47 | % 26.74/9.47 |-The branch is then unsatisfiable % 26.74/9.47 |-Branch two: % 26.74/9.47 | (98) ~ (all_24_0_32 = 0) % 26.74/9.47 | (345) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.47 | % 26.74/9.47 +-Applying beta-rule and splitting (173), into two cases. % 26.74/9.47 |-Branch one: % 26.74/9.47 | (198) all_25_0_33 = 0 % 26.74/9.47 | % 26.74/9.47 | Equations (198) can reduce 105 to: % 26.74/9.47 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (105) ~ (all_25_0_33 = 0) % 26.74/9.48 | (349) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (174), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (198) all_25_0_33 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (198) can reduce 105 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (105) ~ (all_25_0_33 = 0) % 26.74/9.48 | (353) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (161), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (198) all_25_0_33 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (198) can reduce 105 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (105) ~ (all_25_0_33 = 0) % 26.74/9.48 | (357) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (165), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (206) all_23_0_31 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (206) can reduce 95 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (95) ~ (all_23_0_31 = 0) % 26.74/9.48 | (361) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (163), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (206) all_23_0_31 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (206) can reduce 95 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (95) ~ (all_23_0_31 = 0) % 26.74/9.48 | (365) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (164), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (206) all_23_0_31 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (206) can reduce 95 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (95) ~ (all_23_0_31 = 0) % 26.74/9.48 | (369) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (166), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (206) all_23_0_31 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (206) can reduce 95 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (95) ~ (all_23_0_31 = 0) % 26.74/9.48 | (373) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (217), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (206) all_23_0_31 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (206) can reduce 95 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (95) ~ (all_23_0_31 = 0) % 26.74/9.48 | (377) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (221), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (206) all_23_0_31 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (206) can reduce 95 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (95) ~ (all_23_0_31 = 0) % 26.74/9.48 | (381) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (225), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (210) all_20_0_28 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (210) can reduce 72 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (72) ~ (all_20_0_28 = 0) % 26.74/9.48 | (385) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (229), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (210) all_20_0_28 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (210) can reduce 72 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (72) ~ (all_20_0_28 = 0) % 26.74/9.48 | (389) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (233), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (210) all_20_0_28 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (210) can reduce 72 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (72) ~ (all_20_0_28 = 0) % 26.74/9.48 | (393) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (237), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (107) all_0_0_0 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (107) can reduce 17 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (17) ~ (all_0_0_0 = 0) % 26.74/9.48 | (397) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (241), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (100) all_0_1_1 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (100) can reduce 48 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (48) ~ (all_0_1_1 = 0) % 26.74/9.48 | (401) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (245), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (202) all_24_0_32 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (202) can reduce 98 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (98) ~ (all_24_0_32 = 0) % 26.74/9.48 | (405) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (249), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (210) all_20_0_28 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (210) can reduce 72 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (72) ~ (all_20_0_28 = 0) % 26.74/9.48 | (409) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (253), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (107) all_0_0_0 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (107) can reduce 17 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (17) ~ (all_0_0_0 = 0) % 26.74/9.48 | (413) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (257), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (100) all_0_1_1 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (100) can reduce 48 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (48) ~ (all_0_1_1 = 0) % 26.74/9.48 | (417) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (261), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (100) all_0_1_1 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (100) can reduce 48 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (48) ~ (all_0_1_1 = 0) % 26.74/9.48 | (421) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (265), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (107) all_0_0_0 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (107) can reduce 17 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (17) ~ (all_0_0_0 = 0) % 26.74/9.48 | (425) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.48 | % 26.74/9.48 +-Applying beta-rule and splitting (269), into two cases. % 26.74/9.48 |-Branch one: % 26.74/9.48 | (107) all_0_0_0 = 0 % 26.74/9.48 | % 26.74/9.48 | Equations (107) can reduce 17 to: % 26.74/9.48 | (101) $false % 26.74/9.48 | % 26.74/9.48 |-The branch is then unsatisfiable % 26.74/9.48 |-Branch two: % 26.74/9.48 | (17) ~ (all_0_0_0 = 0) % 26.74/9.49 | (429) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (273), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (100) all_0_1_1 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (100) can reduce 48 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (48) ~ (all_0_1_1 = 0) % 26.74/9.49 | (433) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (277), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (206) all_23_0_31 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (206) can reduce 95 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (95) ~ (all_23_0_31 = 0) % 26.74/9.49 | (437) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (281), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (210) all_20_0_28 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (210) can reduce 72 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (72) ~ (all_20_0_28 = 0) % 26.74/9.49 | (441) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (285), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (100) all_0_1_1 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (100) can reduce 48 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (48) ~ (all_0_1_1 = 0) % 26.74/9.49 | (445) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (289), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (210) all_20_0_28 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (210) can reduce 72 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (72) ~ (all_20_0_28 = 0) % 26.74/9.49 | (449) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (293), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (210) all_20_0_28 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (210) can reduce 72 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (72) ~ (all_20_0_28 = 0) % 26.74/9.49 | (453) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (297), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (210) all_20_0_28 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (210) can reduce 72 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (72) ~ (all_20_0_28 = 0) % 26.74/9.49 | (457) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (301), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (210) all_20_0_28 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (210) can reduce 72 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (72) ~ (all_20_0_28 = 0) % 26.74/9.49 | (461) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (305), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (206) all_23_0_31 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (206) can reduce 95 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (95) ~ (all_23_0_31 = 0) % 26.74/9.49 | (465) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (309), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (107) all_0_0_0 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (107) can reduce 17 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (17) ~ (all_0_0_0 = 0) % 26.74/9.49 | (469) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (313), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (107) all_0_0_0 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (107) can reduce 17 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (17) ~ (all_0_0_0 = 0) % 26.74/9.49 | (473) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 | Instantiating (473) with all_324_0_72 yields: % 26.74/9.49 | (474) (all_324_0_72 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (all_324_0_72 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_324_0_72 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_72) | ( ~ (all_324_0_72 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_324_0_72) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (317), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (107) all_0_0_0 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (107) can reduce 17 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (17) ~ (all_0_0_0 = 0) % 26.74/9.49 | (478) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (321), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (107) all_0_0_0 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (107) can reduce 17 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (17) ~ (all_0_0_0 = 0) % 26.74/9.49 | (482) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (325), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (100) all_0_1_1 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (100) can reduce 48 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (48) ~ (all_0_1_1 = 0) % 26.74/9.49 | (486) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (329), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (210) all_20_0_28 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (210) can reduce 72 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (72) ~ (all_20_0_28 = 0) % 26.74/9.49 | (490) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (333), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (100) all_0_1_1 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (100) can reduce 48 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (48) ~ (all_0_1_1 = 0) % 26.74/9.49 | (494) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (337), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (100) all_0_1_1 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (100) can reduce 48 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (48) ~ (all_0_1_1 = 0) % 26.74/9.49 | (498) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (341), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (206) all_23_0_31 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (206) can reduce 95 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (95) ~ (all_23_0_31 = 0) % 26.74/9.49 | (502) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (345), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (206) all_23_0_31 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (206) can reduce 95 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (95) ~ (all_23_0_31 = 0) % 26.74/9.49 | (506) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (349), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (206) all_23_0_31 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (206) can reduce 95 to: % 26.74/9.49 | (101) $false % 26.74/9.49 | % 26.74/9.49 |-The branch is then unsatisfiable % 26.74/9.49 |-Branch two: % 26.74/9.49 | (95) ~ (all_23_0_31 = 0) % 26.74/9.49 | (510) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.49 | % 26.74/9.49 +-Applying beta-rule and splitting (353), into two cases. % 26.74/9.49 |-Branch one: % 26.74/9.49 | (206) all_23_0_31 = 0 % 26.74/9.49 | % 26.74/9.49 | Equations (206) can reduce 95 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (95) ~ (all_23_0_31 = 0) % 26.74/9.50 | (514) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (357), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (202) all_24_0_32 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (202) can reduce 98 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (98) ~ (all_24_0_32 = 0) % 26.74/9.50 | (518) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (361), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (100) all_0_1_1 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (100) can reduce 48 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (48) ~ (all_0_1_1 = 0) % 26.74/9.50 | (522) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (365), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (107) all_0_0_0 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (107) can reduce 17 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (17) ~ (all_0_0_0 = 0) % 26.74/9.50 | (526) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (369), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (107) all_0_0_0 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (107) can reduce 17 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (17) ~ (all_0_0_0 = 0) % 26.74/9.50 | (530) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (373), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (100) all_0_1_1 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (100) can reduce 48 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (48) ~ (all_0_1_1 = 0) % 26.74/9.50 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 26.74/9.50 | % 26.74/9.50 | Instantiating (534) with all_384_0_87 yields: % 26.74/9.50 | (535) (all_384_0_87 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_384_0_87 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (all_384_0_87 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_87) | ( ~ (all_384_0_87 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_384_0_87) % 26.74/9.50 | % 26.74/9.50 | Instantiating formula (34) with all_24_0_32, all_0_2_2, all_0_6_6, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields: % 26.74/9.50 | (536) all_24_0_32 = 0 | distinct_points(all_0_5_5, all_0_2_2) = 0 % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (536), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (537) distinct_points(all_0_5_5, all_0_2_2) = 0 % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (474), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (538) (all_324_0_72 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (all_324_0_72 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_324_0_72 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_72) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (538), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (539) (all_324_0_72 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (all_324_0_72 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (539), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (540) all_324_0_72 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0 % 26.74/9.50 | % 26.74/9.50 | Applying alpha-rule on (540) yields: % 26.74/9.50 | (541) all_324_0_72 = 0 % 26.74/9.50 | (542) apart_point_and_line(all_0_2_2, all_0_9_9) = 0 % 26.74/9.50 | % 26.74/9.50 | Instantiating formula (2) with all_0_2_2, all_0_9_9, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_9_9) = 0, yields: % 26.74/9.50 | (100) all_0_1_1 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (100) can reduce 48 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (545) all_324_0_72 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0 % 26.74/9.50 | % 26.74/9.50 | Applying alpha-rule on (545) yields: % 26.74/9.50 | (541) all_324_0_72 = 0 % 26.74/9.50 | (547) apart_point_and_line(all_0_5_5, all_0_8_8) = 0 % 26.74/9.50 | % 26.74/9.50 | Instantiating formula (2) with all_0_5_5, all_0_8_8, 0, all_23_0_31 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, apart_point_and_line(all_0_5_5, all_0_8_8) = 0, yields: % 26.74/9.50 | (206) all_23_0_31 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (206) can reduce 95 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (550) ~ (all_324_0_72 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_72 % 26.74/9.50 | % 26.74/9.50 | Applying alpha-rule on (550) yields: % 26.74/9.50 | (551) ~ (all_324_0_72 = 0) % 26.74/9.50 | (552) distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_72 % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (535), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (553) (all_384_0_87 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_384_0_87 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (all_384_0_87 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_87) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (553), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (554) (all_384_0_87 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_384_0_87 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (554), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (555) all_384_0_87 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0 % 26.74/9.50 | % 26.74/9.50 | Applying alpha-rule on (555) yields: % 26.74/9.50 | (556) all_384_0_87 = 0 % 26.74/9.50 | (557) apart_point_and_line(all_0_2_2, all_0_8_8) = 0 % 26.74/9.50 | % 26.74/9.50 | Instantiating formula (2) with all_0_2_2, all_0_8_8, 0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_8_8) = 0, yields: % 26.74/9.50 | (107) all_0_0_0 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (107) can reduce 17 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (560) all_384_0_87 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0 % 26.74/9.50 | % 26.74/9.50 | Applying alpha-rule on (560) yields: % 26.74/9.50 | (556) all_384_0_87 = 0 % 26.74/9.50 | (562) apart_point_and_line(all_0_5_5, all_0_9_9) = 0 % 26.74/9.50 | % 26.74/9.50 | Instantiating formula (2) with all_0_5_5, all_0_9_9, 0, all_20_0_28 and discharging atoms apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, apart_point_and_line(all_0_5_5, all_0_9_9) = 0, yields: % 26.74/9.50 | (210) all_20_0_28 = 0 % 26.74/9.50 | % 26.74/9.50 | Equations (210) can reduce 72 to: % 26.74/9.50 | (101) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (565) ~ (all_384_0_87 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_87 % 26.74/9.50 | % 26.74/9.50 | Applying alpha-rule on (565) yields: % 26.74/9.50 | (566) ~ (all_384_0_87 = 0) % 26.74/9.50 | (567) distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_87 % 26.74/9.50 | % 26.74/9.50 | Instantiating formula (39) with all_0_8_8, all_0_9_9, all_324_0_72, all_384_0_87 and discharging atoms distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_87, distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_72, yields: % 26.74/9.50 | (568) all_384_0_87 = all_324_0_72 % 26.74/9.50 | % 26.74/9.50 | Equations (568) can reduce 566 to: % 26.74/9.50 | (551) ~ (all_324_0_72 = 0) % 26.74/9.50 | % 26.74/9.50 | From (568) and (567) follows: % 26.74/9.50 | (552) distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_72 % 26.74/9.50 | % 26.74/9.50 | Instantiating formula (6) with all_324_0_72, all_0_9_9, all_0_8_8, all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = 0, distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_72, yields: % 26.74/9.50 | (571) all_324_0_72 = 0 | convergent_lines(all_0_9_9, all_0_9_9) = 0 % 26.74/9.50 | % 26.74/9.50 +-Applying beta-rule and splitting (571), into two cases. % 26.74/9.50 |-Branch one: % 26.74/9.50 | (572) convergent_lines(all_0_9_9, all_0_9_9) = 0 % 26.74/9.50 | % 26.74/9.50 | Instantiating formula (32) with all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_9_9) = 0, yields: % 26.74/9.50 | (573) $false % 26.74/9.50 | % 26.74/9.50 |-The branch is then unsatisfiable % 26.74/9.50 |-Branch two: % 26.74/9.50 | (574) ~ (convergent_lines(all_0_9_9, all_0_9_9) = 0) % 26.74/9.50 | (541) all_324_0_72 = 0 % 26.74/9.50 | % 27.09/9.50 | Equations (541) can reduce 551 to: % 27.09/9.50 | (101) $false % 27.09/9.50 | % 27.09/9.50 |-The branch is then unsatisfiable % 27.09/9.50 |-Branch two: % 27.09/9.50 | (577) ~ (all_384_0_87 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_384_0_87 % 27.09/9.50 | % 27.09/9.50 | Applying alpha-rule on (577) yields: % 27.09/9.50 | (566) ~ (all_384_0_87 = 0) % 27.09/9.50 | (579) distinct_points(all_0_5_5, all_0_2_2) = all_384_0_87 % 27.09/9.50 | % 27.09/9.50 | Instantiating formula (46) with all_0_5_5, all_0_2_2, 0, all_384_0_87 and discharging atoms distinct_points(all_0_5_5, all_0_2_2) = all_384_0_87, distinct_points(all_0_5_5, all_0_2_2) = 0, yields: % 27.09/9.50 | (556) all_384_0_87 = 0 % 27.09/9.50 | % 27.09/9.50 | Equations (556) can reduce 566 to: % 27.09/9.50 | (101) $false % 27.09/9.50 | % 27.09/9.50 |-The branch is then unsatisfiable % 27.09/9.50 |-Branch two: % 27.09/9.51 | (582) ~ (all_324_0_72 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_324_0_72 % 27.09/9.51 | % 27.09/9.51 | Applying alpha-rule on (582) yields: % 27.09/9.51 | (551) ~ (all_324_0_72 = 0) % 27.09/9.51 | (584) distinct_points(all_0_5_5, all_0_2_2) = all_324_0_72 % 27.09/9.51 | % 27.09/9.51 | Instantiating formula (46) with all_0_5_5, all_0_2_2, 0, all_324_0_72 and discharging atoms distinct_points(all_0_5_5, all_0_2_2) = all_324_0_72, distinct_points(all_0_5_5, all_0_2_2) = 0, yields: % 27.09/9.51 | (541) all_324_0_72 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (541) can reduce 551 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (587) ~ (distinct_points(all_0_5_5, all_0_2_2) = 0) % 27.09/9.51 | (202) all_24_0_32 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (202) can reduce 98 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (590) all_0_4_4 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0 % 27.09/9.51 | % 27.09/9.51 | Applying alpha-rule on (590) yields: % 27.09/9.51 | (591) all_0_4_4 = 0 % 27.09/9.51 | (592) apart_point_and_line(all_0_5_5, all_0_7_7) = 0 % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (162), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (198) all_25_0_33 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (198) can reduce 105 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (105) ~ (all_25_0_33 = 0) % 27.09/9.51 | (201) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (155), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (202) all_24_0_32 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (202) can reduce 98 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (98) ~ (all_24_0_32 = 0) % 27.09/9.51 | (205) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (177), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (206) all_23_0_31 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (206) can reduce 95 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (95) ~ (all_23_0_31 = 0) % 27.09/9.51 | (209) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (194), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (210) all_20_0_28 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (210) can reduce 72 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (72) ~ (all_20_0_28 = 0) % 27.09/9.51 | (213) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (175), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (198) all_25_0_33 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (198) can reduce 105 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (105) ~ (all_25_0_33 = 0) % 27.09/9.51 | (217) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (176), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (198) all_25_0_33 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (198) can reduce 105 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (105) ~ (all_25_0_33 = 0) % 27.09/9.51 | (221) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (187), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (202) all_24_0_32 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (202) can reduce 98 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (98) ~ (all_24_0_32 = 0) % 27.09/9.51 | (225) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (188), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (198) all_25_0_33 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (198) can reduce 105 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (105) ~ (all_25_0_33 = 0) % 27.09/9.51 | (229) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (191), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (198) all_25_0_33 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (198) can reduce 105 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (105) ~ (all_25_0_33 = 0) % 27.09/9.51 | (233) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (151), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (202) all_24_0_32 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (202) can reduce 98 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (98) ~ (all_24_0_32 = 0) % 27.09/9.51 | (237) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (159), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (198) all_25_0_33 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (198) can reduce 105 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (105) ~ (all_25_0_33 = 0) % 27.09/9.51 | (241) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (160), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (198) all_25_0_33 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (198) can reduce 105 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (105) ~ (all_25_0_33 = 0) % 27.09/9.51 | (245) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (192), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (206) all_23_0_31 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (206) can reduce 95 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (95) ~ (all_23_0_31 = 0) % 27.09/9.51 | (249) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (152), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (202) all_24_0_32 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (202) can reduce 98 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.51 |-The branch is then unsatisfiable % 27.09/9.51 |-Branch two: % 27.09/9.51 | (98) ~ (all_24_0_32 = 0) % 27.09/9.51 | (253) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.51 | % 27.09/9.51 +-Applying beta-rule and splitting (153), into two cases. % 27.09/9.51 |-Branch one: % 27.09/9.51 | (202) all_24_0_32 = 0 % 27.09/9.51 | % 27.09/9.51 | Equations (202) can reduce 98 to: % 27.09/9.51 | (101) $false % 27.09/9.51 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (257) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (154), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (202) all_24_0_32 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (202) can reduce 98 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (261) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (156), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (198) all_25_0_33 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (198) can reduce 105 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (105) ~ (all_25_0_33 = 0) % 27.09/9.52 | (265) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (157), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (198) all_25_0_33 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (198) can reduce 105 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (105) ~ (all_25_0_33 = 0) % 27.09/9.52 | (269) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (183), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (210) all_20_0_28 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (210) can reduce 72 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (72) ~ (all_20_0_28 = 0) % 27.09/9.52 | (273) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (171), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (202) all_24_0_32 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (202) can reduce 98 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (277) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (184), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (202) all_24_0_32 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (202) can reduce 98 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (281) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (158), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (198) all_25_0_33 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (198) can reduce 105 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (105) ~ (all_25_0_33 = 0) % 27.09/9.52 | (285) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (185), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (202) all_24_0_32 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (202) can reduce 98 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (289) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (186), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (202) all_24_0_32 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (202) can reduce 98 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (293) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (189), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (198) all_25_0_33 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (198) can reduce 105 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (105) ~ (all_25_0_33 = 0) % 27.09/9.52 | (297) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (190), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (198) all_25_0_33 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (198) can reduce 105 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (105) ~ (all_25_0_33 = 0) % 27.09/9.52 | (301) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (172), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (202) all_24_0_32 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (202) can reduce 98 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (305) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (178), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (210) all_20_0_28 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (210) can reduce 72 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (72) ~ (all_20_0_28 = 0) % 27.09/9.52 | (309) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (181), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (210) all_20_0_28 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (210) can reduce 72 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (72) ~ (all_20_0_28 = 0) % 27.09/9.52 | (313) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (179), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (210) all_20_0_28 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (210) can reduce 72 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (72) ~ (all_20_0_28 = 0) % 27.09/9.52 | (317) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (180), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (210) all_20_0_28 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (210) can reduce 72 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (72) ~ (all_20_0_28 = 0) % 27.09/9.52 | (321) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (182), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (210) all_20_0_28 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (210) can reduce 72 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (72) ~ (all_20_0_28 = 0) % 27.09/9.52 | (325) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (193), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (206) all_23_0_31 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (206) can reduce 95 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (95) ~ (all_23_0_31 = 0) % 27.09/9.52 | (329) all_20_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (167), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (206) all_23_0_31 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (206) can reduce 95 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (95) ~ (all_23_0_31 = 0) % 27.09/9.52 | (333) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (168), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (206) all_23_0_31 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (206) can reduce 95 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (95) ~ (all_23_0_31 = 0) % 27.09/9.52 | (337) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (169), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (202) all_24_0_32 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (202) can reduce 98 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (341) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.52 | % 27.09/9.52 +-Applying beta-rule and splitting (170), into two cases. % 27.09/9.52 |-Branch one: % 27.09/9.52 | (202) all_24_0_32 = 0 % 27.09/9.52 | % 27.09/9.52 | Equations (202) can reduce 98 to: % 27.09/9.52 | (101) $false % 27.09/9.52 | % 27.09/9.52 |-The branch is then unsatisfiable % 27.09/9.52 |-Branch two: % 27.09/9.52 | (98) ~ (all_24_0_32 = 0) % 27.09/9.52 | (345) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (173), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (198) all_25_0_33 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (198) can reduce 105 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (105) ~ (all_25_0_33 = 0) % 27.09/9.53 | (349) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (174), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (198) all_25_0_33 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (198) can reduce 105 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (105) ~ (all_25_0_33 = 0) % 27.09/9.53 | (353) all_23_0_31 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (161), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (198) all_25_0_33 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (198) can reduce 105 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (105) ~ (all_25_0_33 = 0) % 27.09/9.53 | (357) all_24_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (165), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (206) all_23_0_31 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (206) can reduce 95 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (95) ~ (all_23_0_31 = 0) % 27.09/9.53 | (361) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (163), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (206) all_23_0_31 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (206) can reduce 95 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (95) ~ (all_23_0_31 = 0) % 27.09/9.53 | (365) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (164), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (206) all_23_0_31 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (206) can reduce 95 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (95) ~ (all_23_0_31 = 0) % 27.09/9.53 | (369) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (166), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (206) all_23_0_31 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (206) can reduce 95 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (95) ~ (all_23_0_31 = 0) % 27.09/9.53 | (373) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (217), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (206) all_23_0_31 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (206) can reduce 95 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (95) ~ (all_23_0_31 = 0) % 27.09/9.53 | (377) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (221), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (206) all_23_0_31 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (206) can reduce 95 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (95) ~ (all_23_0_31 = 0) % 27.09/9.53 | (381) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (225), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (210) all_20_0_28 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (210) can reduce 72 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (72) ~ (all_20_0_28 = 0) % 27.09/9.53 | (385) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (229), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (210) all_20_0_28 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (210) can reduce 72 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (72) ~ (all_20_0_28 = 0) % 27.09/9.53 | (389) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (233), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (210) all_20_0_28 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (210) can reduce 72 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (72) ~ (all_20_0_28 = 0) % 27.09/9.53 | (393) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (237), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (107) all_0_0_0 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (107) can reduce 17 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (17) ~ (all_0_0_0 = 0) % 27.09/9.53 | (397) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (241), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (100) all_0_1_1 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (100) can reduce 48 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (48) ~ (all_0_1_1 = 0) % 27.09/9.53 | (401) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (249), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (210) all_20_0_28 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (210) can reduce 72 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (72) ~ (all_20_0_28 = 0) % 27.09/9.53 | (409) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (253), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (107) all_0_0_0 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (107) can reduce 17 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (17) ~ (all_0_0_0 = 0) % 27.09/9.53 | (413) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (257), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (100) all_0_1_1 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (100) can reduce 48 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (48) ~ (all_0_1_1 = 0) % 27.09/9.53 | (417) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (261), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (100) all_0_1_1 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (100) can reduce 48 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (48) ~ (all_0_1_1 = 0) % 27.09/9.53 | (421) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (265), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (107) all_0_0_0 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (107) can reduce 17 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (17) ~ (all_0_0_0 = 0) % 27.09/9.53 | (425) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (269), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (107) all_0_0_0 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (107) can reduce 17 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (17) ~ (all_0_0_0 = 0) % 27.09/9.53 | (429) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (273), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (100) all_0_1_1 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (100) can reduce 48 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (48) ~ (all_0_1_1 = 0) % 27.09/9.53 | (433) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.53 | % 27.09/9.53 +-Applying beta-rule and splitting (277), into two cases. % 27.09/9.53 |-Branch one: % 27.09/9.53 | (206) all_23_0_31 = 0 % 27.09/9.53 | % 27.09/9.53 | Equations (206) can reduce 95 to: % 27.09/9.53 | (101) $false % 27.09/9.53 | % 27.09/9.53 |-The branch is then unsatisfiable % 27.09/9.53 |-Branch two: % 27.09/9.53 | (95) ~ (all_23_0_31 = 0) % 27.09/9.53 | (437) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (281), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (210) all_20_0_28 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (210) can reduce 72 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (72) ~ (all_20_0_28 = 0) % 27.09/9.54 | (441) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (285), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (100) all_0_1_1 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (100) can reduce 48 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (48) ~ (all_0_1_1 = 0) % 27.09/9.54 | (445) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (289), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (210) all_20_0_28 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (210) can reduce 72 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (72) ~ (all_20_0_28 = 0) % 27.09/9.54 | (449) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (293), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (210) all_20_0_28 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (210) can reduce 72 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (72) ~ (all_20_0_28 = 0) % 27.09/9.54 | (453) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (297), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (210) all_20_0_28 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (210) can reduce 72 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (72) ~ (all_20_0_28 = 0) % 27.09/9.54 | (457) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (301), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (210) all_20_0_28 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (210) can reduce 72 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (72) ~ (all_20_0_28 = 0) % 27.09/9.54 | (461) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (305), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (206) all_23_0_31 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (206) can reduce 95 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (95) ~ (all_23_0_31 = 0) % 27.09/9.54 | (465) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (309), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (107) all_0_0_0 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (107) can reduce 17 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (17) ~ (all_0_0_0 = 0) % 27.09/9.54 | (469) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (313), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (107) all_0_0_0 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (107) can reduce 17 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (17) ~ (all_0_0_0 = 0) % 27.09/9.54 | (473) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 | Instantiating (473) with all_324_0_376 yields: % 27.09/9.54 | (865) (all_324_0_376 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (all_324_0_376 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_324_0_376 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_376) | ( ~ (all_324_0_376 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_324_0_376) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (317), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (107) all_0_0_0 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (107) can reduce 17 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (17) ~ (all_0_0_0 = 0) % 27.09/9.54 | (478) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (321), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (107) all_0_0_0 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (107) can reduce 17 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (17) ~ (all_0_0_0 = 0) % 27.09/9.54 | (482) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (325), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (100) all_0_1_1 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (100) can reduce 48 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (48) ~ (all_0_1_1 = 0) % 27.09/9.54 | (486) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (329), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (210) all_20_0_28 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (210) can reduce 72 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (72) ~ (all_20_0_28 = 0) % 27.09/9.54 | (490) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (333), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (100) all_0_1_1 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (100) can reduce 48 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (48) ~ (all_0_1_1 = 0) % 27.09/9.54 | (494) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (337), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (100) all_0_1_1 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (100) can reduce 48 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (48) ~ (all_0_1_1 = 0) % 27.09/9.54 | (498) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (341), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (206) all_23_0_31 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (206) can reduce 95 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (95) ~ (all_23_0_31 = 0) % 27.09/9.54 | (502) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (345), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (206) all_23_0_31 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (206) can reduce 95 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (95) ~ (all_23_0_31 = 0) % 27.09/9.54 | (506) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (349), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (206) all_23_0_31 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (206) can reduce 95 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (95) ~ (all_23_0_31 = 0) % 27.09/9.54 | (510) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (353), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (206) all_23_0_31 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (206) can reduce 95 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (95) ~ (all_23_0_31 = 0) % 27.09/9.54 | (514) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (361), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (100) all_0_1_1 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (100) can reduce 48 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (48) ~ (all_0_1_1 = 0) % 27.09/9.54 | (522) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (365), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (107) all_0_0_0 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (107) can reduce 17 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (17) ~ (all_0_0_0 = 0) % 27.09/9.54 | (526) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (369), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (107) all_0_0_0 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (107) can reduce 17 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (17) ~ (all_0_0_0 = 0) % 27.09/9.54 | (530) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 +-Applying beta-rule and splitting (373), into two cases. % 27.09/9.54 |-Branch one: % 27.09/9.54 | (100) all_0_1_1 = 0 % 27.09/9.54 | % 27.09/9.54 | Equations (100) can reduce 48 to: % 27.09/9.54 | (101) $false % 27.09/9.54 | % 27.09/9.54 |-The branch is then unsatisfiable % 27.09/9.54 |-Branch two: % 27.09/9.54 | (48) ~ (all_0_1_1 = 0) % 27.09/9.54 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0)) % 27.09/9.54 | % 27.09/9.54 | Instantiating (534) with all_384_0_391 yields: % 27.09/9.55 | (922) (all_384_0_391 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_384_0_391 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (all_384_0_391 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_391) | ( ~ (all_384_0_391 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_384_0_391) % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (34) with all_25_0_33, all_0_2_2, all_0_7_7, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields: % 27.09/9.55 | (923) all_25_0_33 = 0 | distinct_points(all_0_5_5, all_0_2_2) = 0 % 27.09/9.55 | % 27.09/9.55 +-Applying beta-rule and splitting (923), into two cases. % 27.09/9.55 |-Branch one: % 27.09/9.55 | (537) distinct_points(all_0_5_5, all_0_2_2) = 0 % 27.09/9.55 | % 27.09/9.55 +-Applying beta-rule and splitting (922), into two cases. % 27.09/9.55 |-Branch one: % 27.09/9.55 | (925) (all_384_0_391 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_384_0_391 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (all_384_0_391 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_391) % 27.09/9.55 | % 27.09/9.55 +-Applying beta-rule and splitting (925), into two cases. % 27.09/9.55 |-Branch one: % 27.09/9.55 | (926) (all_384_0_391 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_384_0_391 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) % 27.09/9.55 | % 27.09/9.55 +-Applying beta-rule and splitting (926), into two cases. % 27.09/9.55 |-Branch one: % 27.09/9.55 | (927) all_384_0_391 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0 % 27.09/9.55 | % 27.09/9.55 | Applying alpha-rule on (927) yields: % 27.09/9.55 | (928) all_384_0_391 = 0 % 27.09/9.55 | (557) apart_point_and_line(all_0_2_2, all_0_8_8) = 0 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (2) with all_0_2_2, all_0_8_8, 0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_8_8) = 0, yields: % 27.09/9.55 | (107) all_0_0_0 = 0 % 27.09/9.55 | % 27.09/9.55 | Equations (107) can reduce 17 to: % 27.09/9.55 | (101) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.55 |-Branch two: % 27.09/9.55 | (932) all_384_0_391 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0 % 27.09/9.55 | % 27.09/9.55 | Applying alpha-rule on (932) yields: % 27.09/9.55 | (928) all_384_0_391 = 0 % 27.09/9.55 | (562) apart_point_and_line(all_0_5_5, all_0_9_9) = 0 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (2) with all_0_5_5, all_0_9_9, 0, all_20_0_28 and discharging atoms apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, apart_point_and_line(all_0_5_5, all_0_9_9) = 0, yields: % 27.09/9.55 | (210) all_20_0_28 = 0 % 27.09/9.55 | % 27.09/9.55 | Equations (210) can reduce 72 to: % 27.09/9.55 | (101) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.55 |-Branch two: % 27.09/9.55 | (937) ~ (all_384_0_391 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_391 % 27.09/9.55 | % 27.09/9.55 | Applying alpha-rule on (937) yields: % 27.09/9.55 | (938) ~ (all_384_0_391 = 0) % 27.09/9.55 | (939) distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_391 % 27.09/9.55 | % 27.09/9.55 +-Applying beta-rule and splitting (865), into two cases. % 27.09/9.55 |-Branch one: % 27.09/9.55 | (940) (all_324_0_376 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (all_324_0_376 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_324_0_376 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_376) % 27.09/9.55 | % 27.09/9.55 +-Applying beta-rule and splitting (940), into two cases. % 27.09/9.55 |-Branch one: % 27.09/9.55 | (941) (all_324_0_376 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (all_324_0_376 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) % 27.09/9.55 | % 27.09/9.55 +-Applying beta-rule and splitting (941), into two cases. % 27.09/9.55 |-Branch one: % 27.09/9.55 | (942) all_324_0_376 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0 % 27.09/9.55 | % 27.09/9.55 | Applying alpha-rule on (942) yields: % 27.09/9.55 | (943) all_324_0_376 = 0 % 27.09/9.55 | (542) apart_point_and_line(all_0_2_2, all_0_9_9) = 0 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (2) with all_0_2_2, all_0_9_9, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_9_9) = 0, yields: % 27.09/9.55 | (100) all_0_1_1 = 0 % 27.09/9.55 | % 27.09/9.55 | Equations (100) can reduce 48 to: % 27.09/9.55 | (101) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.55 |-Branch two: % 27.09/9.55 | (947) all_324_0_376 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0 % 27.09/9.55 | % 27.09/9.55 | Applying alpha-rule on (947) yields: % 27.09/9.55 | (943) all_324_0_376 = 0 % 27.09/9.55 | (547) apart_point_and_line(all_0_5_5, all_0_8_8) = 0 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (2) with all_0_5_5, all_0_8_8, 0, all_23_0_31 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, apart_point_and_line(all_0_5_5, all_0_8_8) = 0, yields: % 27.09/9.55 | (206) all_23_0_31 = 0 % 27.09/9.55 | % 27.09/9.55 | Equations (206) can reduce 95 to: % 27.09/9.55 | (101) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.55 |-Branch two: % 27.09/9.55 | (952) ~ (all_324_0_376 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_376 % 27.09/9.55 | % 27.09/9.55 | Applying alpha-rule on (952) yields: % 27.09/9.55 | (953) ~ (all_324_0_376 = 0) % 27.09/9.55 | (954) distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_376 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (39) with all_0_8_8, all_0_9_9, all_324_0_376, all_384_0_391 and discharging atoms distinct_lines(all_0_8_8, all_0_9_9) = all_384_0_391, distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_376, yields: % 27.09/9.55 | (955) all_384_0_391 = all_324_0_376 % 27.09/9.55 | % 27.09/9.55 | Equations (955) can reduce 938 to: % 27.09/9.55 | (953) ~ (all_324_0_376 = 0) % 27.09/9.55 | % 27.09/9.55 | From (955) and (939) follows: % 27.09/9.55 | (954) distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_376 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (6) with all_324_0_376, all_0_9_9, all_0_8_8, all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = 0, distinct_lines(all_0_8_8, all_0_9_9) = all_324_0_376, yields: % 27.09/9.55 | (958) all_324_0_376 = 0 | convergent_lines(all_0_9_9, all_0_9_9) = 0 % 27.09/9.55 | % 27.09/9.55 +-Applying beta-rule and splitting (958), into two cases. % 27.09/9.55 |-Branch one: % 27.09/9.55 | (572) convergent_lines(all_0_9_9, all_0_9_9) = 0 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (32) with all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_9_9) = 0, yields: % 27.09/9.55 | (573) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.55 |-Branch two: % 27.09/9.55 | (574) ~ (convergent_lines(all_0_9_9, all_0_9_9) = 0) % 27.09/9.55 | (943) all_324_0_376 = 0 % 27.09/9.55 | % 27.09/9.55 | Equations (943) can reduce 953 to: % 27.09/9.55 | (101) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.55 |-Branch two: % 27.09/9.55 | (964) ~ (all_324_0_376 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_324_0_376 % 27.09/9.55 | % 27.09/9.55 | Applying alpha-rule on (964) yields: % 27.09/9.55 | (953) ~ (all_324_0_376 = 0) % 27.09/9.55 | (966) distinct_points(all_0_5_5, all_0_2_2) = all_324_0_376 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (46) with all_0_5_5, all_0_2_2, 0, all_324_0_376 and discharging atoms distinct_points(all_0_5_5, all_0_2_2) = all_324_0_376, distinct_points(all_0_5_5, all_0_2_2) = 0, yields: % 27.09/9.55 | (943) all_324_0_376 = 0 % 27.09/9.55 | % 27.09/9.55 | Equations (943) can reduce 953 to: % 27.09/9.55 | (101) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.55 |-Branch two: % 27.09/9.55 | (969) ~ (all_384_0_391 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_384_0_391 % 27.09/9.55 | % 27.09/9.55 | Applying alpha-rule on (969) yields: % 27.09/9.55 | (938) ~ (all_384_0_391 = 0) % 27.09/9.55 | (971) distinct_points(all_0_5_5, all_0_2_2) = all_384_0_391 % 27.09/9.55 | % 27.09/9.55 | Instantiating formula (46) with all_0_5_5, all_0_2_2, 0, all_384_0_391 and discharging atoms distinct_points(all_0_5_5, all_0_2_2) = all_384_0_391, distinct_points(all_0_5_5, all_0_2_2) = 0, yields: % 27.09/9.55 | (928) all_384_0_391 = 0 % 27.09/9.55 | % 27.09/9.55 | Equations (928) can reduce 938 to: % 27.09/9.55 | (101) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.55 |-Branch two: % 27.09/9.55 | (587) ~ (distinct_points(all_0_5_5, all_0_2_2) = 0) % 27.09/9.55 | (198) all_25_0_33 = 0 % 27.09/9.55 | % 27.09/9.55 | Equations (198) can reduce 105 to: % 27.09/9.55 | (101) $false % 27.09/9.55 | % 27.09/9.55 |-The branch is then unsatisfiable % 27.09/9.56 |-Branch two: % 27.09/9.56 | (977) ~ (all_25_0_33 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33 % 27.09/9.56 | % 27.09/9.56 | Applying alpha-rule on (977) yields: % 27.09/9.56 | (105) ~ (all_25_0_33 = 0) % 27.09/9.56 | (979) convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33 % 27.09/9.56 | % 27.09/9.56 | Instantiating formula (25) with all_0_7_7, all_0_6_6, all_25_0_33, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33, convergent_lines(all_0_7_7, all_0_6_6) = 0, yields: % 27.09/9.56 | (198) all_25_0_33 = 0 % 27.09/9.56 | % 27.09/9.56 | Equations (198) can reduce 105 to: % 27.09/9.56 | (101) $false % 27.09/9.56 | % 27.09/9.56 |-The branch is then unsatisfiable % 27.09/9.56 |-Branch two: % 27.09/9.56 | (982) ~ (all_24_0_32 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32 % 27.09/9.56 | % 27.09/9.56 | Applying alpha-rule on (982) yields: % 27.09/9.56 | (98) ~ (all_24_0_32 = 0) % 27.09/9.56 | (984) convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32 % 27.09/9.56 | % 27.09/9.56 | Instantiating formula (25) with all_0_7_7, all_0_6_6, all_24_0_32, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32, convergent_lines(all_0_7_7, all_0_6_6) = 0, yields: % 27.09/9.56 | (202) all_24_0_32 = 0 % 27.09/9.56 | % 27.09/9.56 | Equations (202) can reduce 98 to: % 27.09/9.56 | (101) $false % 27.09/9.56 | % 27.09/9.56 |-The branch is then unsatisfiable % 27.09/9.56 |-Branch two: % 27.09/9.56 | (987) ~ (all_23_0_31 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31 % 27.09/9.56 | % 27.09/9.56 | Applying alpha-rule on (987) yields: % 27.09/9.56 | (95) ~ (all_23_0_31 = 0) % 27.09/9.56 | (989) convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31 % 27.09/9.56 | % 27.09/9.56 | Instantiating formula (25) with all_0_9_9, all_0_8_8, all_23_0_31, 0 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31, convergent_lines(all_0_9_9, all_0_8_8) = 0, yields: % 27.09/9.56 | (206) all_23_0_31 = 0 % 27.09/9.56 | % 27.09/9.56 | Equations (206) can reduce 95 to: % 27.09/9.56 | (101) $false % 27.09/9.56 | % 27.09/9.56 |-The branch is then unsatisfiable % 27.09/9.56 |-Branch two: % 27.09/9.56 | (992) ~ (all_22_0_30 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30 % 27.09/9.56 | % 27.09/9.56 | Applying alpha-rule on (992) yields: % 27.09/9.56 | (92) ~ (all_22_0_30 = 0) % 27.09/9.56 | (994) convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30 % 27.09/9.56 | % 27.09/9.56 | Instantiating formula (25) with all_0_9_9, all_0_8_8, all_22_0_30, 0 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30, convergent_lines(all_0_9_9, all_0_8_8) = 0, yields: % 27.09/9.56 | (995) all_22_0_30 = 0 % 27.09/9.56 | % 27.09/9.56 | Equations (995) can reduce 92 to: % 27.09/9.56 | (101) $false % 27.09/9.56 | % 27.09/9.56 |-The branch is then unsatisfiable % 27.09/9.56 % SZS output end Proof for theBenchmark % 27.09/9.56 % 27.09/9.56 8965ms %------------------------------------------------------------------------------