%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO188+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.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 03:48:25 EDT 2022 % Result : Theorem 34.17s 9.09s % Output : Proof 42.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO188+3 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 03:54:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.56/0.57 ____ _ % 0.56/0.57 ___ / __ \_____(_)___ ________ __________ % 0.56/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.57 % 0.56/0.57 A Theorem Prover for First-Order Logic % 0.56/0.57 (ePrincess v.1.0) % 0.56/0.57 % 0.56/0.57 (c) Philipp Rümmer, 2009-2015 % 0.56/0.57 (c) Peter Backeman, 2014-2015 % 0.56/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.57 Bug reports to peter@backeman.se % 0.56/0.57 % 0.56/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.57 % 0.56/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.56/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.82/0.95 Prover 0: Preprocessing ... % 2.46/1.18 Prover 0: Warning: ignoring some quantifiers % 2.56/1.21 Prover 0: Constructing countermodel ... % 14.13/3.98 Prover 0: gave up % 14.13/3.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 14.50/4.02 Prover 1: Preprocessing ... % 14.78/4.15 Prover 1: Constructing countermodel ... % 15.32/4.20 Prover 1: gave up % 15.32/4.20 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 15.32/4.23 Prover 2: Preprocessing ... % 16.19/4.39 Prover 2: Warning: ignoring some quantifiers % 16.19/4.40 Prover 2: Constructing countermodel ... % 23.15/6.09 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 23.15/6.14 Prover 3: Preprocessing ... % 23.58/6.18 Prover 3: Warning: ignoring some quantifiers % 23.58/6.18 Prover 3: Constructing countermodel ... % 29.03/7.86 Prover 3: gave up % 29.03/7.86 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 29.03/7.89 Prover 4: Preprocessing ... % 29.61/7.98 Prover 4: Warning: ignoring some quantifiers % 29.61/7.99 Prover 4: Constructing countermodel ... % 32.66/8.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 32.87/8.79 Prover 5: Preprocessing ... % 33.23/8.88 Prover 5: Constructing countermodel ... % 34.17/9.09 Prover 5: proved (339ms) % 34.17/9.09 Prover 4: stopped % 34.17/9.09 Prover 2: stopped % 34.17/9.09 % 34.17/9.09 No countermodel exists, formula is valid % 34.17/9.09 % SZS status Theorem for theBenchmark % 34.17/9.09 % 34.17/9.09 Generating proof ... found it (size 522) % 41.51/10.83 % 41.51/10.83 % SZS output start Proof for theBenchmark % 41.51/10.83 Assumed formulas after preprocessing and simplification: % 41.51/10.83 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 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] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [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] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [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] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [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) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ? [v6] : (convergent_lines(v1, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [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 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : (apart_point_and_line(v0, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [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] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [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, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v1) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 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 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [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] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & orthogonal_through_point(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & parallel_through_point(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (line(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (point(v3) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 & intersection_point(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) & ! [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] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & line_connecting(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) & ! [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] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v2, v3) = 0 & incident_point_and_line(v0, v4) = v5 & line_connecting(v2, v1) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0) % 41.66/10.92 | Applying alpha-rule on (0) yields: % 41.66/10.92 | (1) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) % 41.66/10.92 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 41.66/10.92 | (3) ! [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] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) % 41.66/10.92 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) % 41.66/10.92 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 41.66/10.92 | (6) ! [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)) % 41.66/10.92 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ? [v6] : (convergent_lines(v1, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 41.66/10.92 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 41.66/10.92 | (9) ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 41.66/10.92 | (10) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 41.66/10.93 | (11) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 41.66/10.93 | (12) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 41.66/10.93 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) % 41.66/10.93 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) % 41.66/10.93 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 41.66/10.93 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 41.66/10.93 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 41.66/10.93 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 41.66/10.93 | (19) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 & intersection_point(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) % 42.04/10.93 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) % 42.04/10.93 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 42.04/10.93 | (22) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & parallel_through_point(v0, v1) = v2)) % 42.04/10.93 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 42.04/10.93 | (24) ! [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) % 42.04/10.93 | (25) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 42.04/10.93 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 42.04/10.93 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) % 42.04/10.93 | (28) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 42.04/10.93 | (29) ! [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)) % 42.04/10.93 | (30) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) % 42.04/10.93 | (31) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 42.04/10.93 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 42.04/10.93 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) % 42.04/10.93 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : (apart_point_and_line(v0, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 42.04/10.94 | (35) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 42.04/10.94 | (36) ! [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)) % 42.04/10.94 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) % 42.04/10.94 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 42.04/10.94 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 42.04/10.94 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 42.04/10.94 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 42.04/10.94 | (42) ! [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) % 42.04/10.94 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 42.04/10.94 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 42.04/10.94 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ? [v6] : (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 42.04/10.94 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0))) % 42.04/10.94 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 42.04/10.94 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) % 42.04/10.94 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) % 42.04/10.94 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 42.04/10.94 | (51) ! [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)) % 42.04/10.94 | (52) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) % 42.04/10.94 | (53) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 42.04/10.94 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 42.04/10.94 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v1) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) % 42.04/10.94 | (56) ! [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)) % 42.04/10.94 | (57) ! [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)) % 42.04/10.95 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) % 42.04/10.95 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 = 0 | v6 = 0))) % 42.04/10.95 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) % 42.04/10.95 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 42.04/10.95 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 42.04/10.95 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 42.04/10.95 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 42.04/10.95 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 42.04/10.95 | (66) ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 42.04/10.95 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) % 42.04/10.95 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 42.04/10.95 | (69) ! [v0] : ! [v1] : ( ~ (line(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (point(v3) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) % 42.04/10.95 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 42.04/10.95 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 42.04/10.95 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 42.04/10.95 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 42.04/10.95 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) % 42.04/10.95 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 42.04/10.95 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 42.04/10.95 | (77) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v2, v3) = 0 & incident_point_and_line(v0, v4) = v5 & line_connecting(v2, v1) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0) % 42.04/10.95 | (78) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) % 42.04/10.95 | (79) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 42.04/10.95 | (80) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 42.04/10.95 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 42.04/10.95 | (82) ! [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) % 42.04/10.96 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 42.04/10.96 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) % 42.04/10.96 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 42.04/10.96 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 42.04/10.96 | (87) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 42.04/10.96 | (88) ! [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] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) % 42.04/10.96 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 42.04/10.96 | (90) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & orthogonal_through_point(v0, v1) = v2)) % 42.04/10.96 | (91) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) % 42.04/10.96 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 42.04/10.96 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) % 42.04/10.96 | (94) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 42.04/10.96 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 42.04/10.96 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 42.04/10.96 | (97) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 42.04/10.96 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 42.04/10.96 | (99) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) % 42.04/10.96 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 42.04/10.96 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) % 42.04/10.96 | (102) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) % 42.04/10.97 | (103) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 42.04/10.97 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 42.04/10.97 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 42.04/10.97 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 42.04/10.97 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 42.04/10.97 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 42.04/10.97 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 42.04/10.97 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) % 42.04/10.97 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 42.04/10.97 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 42.04/10.97 | (113) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) % 42.04/10.97 | (114) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 42.04/10.97 | (115) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) % 42.04/10.97 | (116) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 42.04/10.97 | (117) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 42.04/10.97 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 42.04/10.97 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) % 42.04/10.97 | (120) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & line_connecting(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) % 42.04/10.97 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 42.04/10.97 | (122) ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 42.04/10.97 | (123) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) % 42.04/10.97 | (124) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 42.04/10.97 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) % 42.04/10.97 | (126) ! [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] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 42.04/10.97 | (127) ! [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) % 42.04/10.97 | % 42.04/10.97 | Instantiating (77) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 yields: % 42.04/10.97 | (128) ~ (all_1_0_0 = 0) & incident_point_and_line(all_1_3_3, all_1_2_2) = 0 & incident_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0 & line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1 & line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2 & distinct_points(all_1_4_4, all_1_3_3) = 0 & distinct_points(all_1_5_5, all_1_3_3) = 0 & distinct_points(all_1_5_5, all_1_4_4) = 0 % 42.04/10.97 | % 42.04/10.97 | Applying alpha-rule on (128) yields: % 42.04/10.97 | (129) distinct_points(all_1_4_4, all_1_3_3) = 0 % 42.04/10.97 | (130) incident_point_and_line(all_1_3_3, all_1_2_2) = 0 % 42.04/10.97 | (131) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2 % 42.04/10.97 | (132) distinct_points(all_1_5_5, all_1_3_3) = 0 % 42.04/10.97 | (133) distinct_points(all_1_5_5, all_1_4_4) = 0 % 42.04/10.97 | (134) line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1 % 42.04/10.97 | (135) ~ (all_1_0_0 = 0) % 42.04/10.97 | (136) incident_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0 % 42.04/10.97 | % 42.04/10.97 | Instantiating formula (87) with all_1_4_4 yields: % 42.04/10.97 | (137) ~ (distinct_points(all_1_4_4, all_1_4_4) = 0) % 42.04/10.97 | % 42.04/10.97 | Instantiating formula (11) with all_1_2_2, all_1_3_3 and discharging atoms incident_point_and_line(all_1_3_3, all_1_2_2) = 0, yields: % 42.04/10.97 | (138) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_3_3, all_1_2_2) = v0) % 42.04/10.97 | % 42.04/10.97 | Instantiating formula (61) with all_1_0_0, all_1_1_1, all_1_5_5 and discharging atoms incident_point_and_line(all_1_5_5, all_1_1_1) = all_1_0_0, yields: % 42.27/10.97 | (139) all_1_0_0 = 0 | apart_point_and_line(all_1_5_5, all_1_1_1) = 0 % 42.27/10.97 | % 42.27/10.97 | Instantiating formula (96) with all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1, yields: % 42.27/10.97 | (140) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_3_3) = v0 & point(all_1_4_4) = v1 & line(all_1_1_1) = v3 & distinct_points(all_1_3_3, all_1_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (39) with all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1, yields: % 42.27/10.98 | (141) ? [v0] : ? [v1] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (15) with all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1, yields: % 42.27/10.98 | (142) ? [v0] : ? [v1] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (96) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields: % 42.27/10.98 | (143) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_4_4) = v1 & point(all_1_5_5) = v0 & line(all_1_2_2) = v3 & distinct_points(all_1_5_5, all_1_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (39) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields: % 42.27/10.98 | (144) ? [v0] : ? [v1] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (15) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields: % 42.27/10.98 | (145) ? [v0] : ? [v1] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (80) with all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 42.27/10.98 | (146) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_4_4, all_1_3_3) = v0 & apart_point_and_line(all_1_3_3, v0) = v1) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (97) with all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 42.27/10.98 | (147) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_4_4, all_1_3_3) = v0 & apart_point_and_line(all_1_4_4, v0) = v1) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (120) with all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 42.27/10.98 | (148) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_3_3) = v1 & point(all_1_5_5) = v0 & line(v2) = v3 & line_connecting(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (80) with all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 42.27/10.98 | (149) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_3_3, v0) = v1) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (97) with all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 42.27/10.98 | (150) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_5_5, v0) = v1) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (120) with all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 42.27/10.98 | (151) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_4_4) = v1 & point(all_1_5_5) = v0 & line(v2) = v3 & line_connecting(all_1_5_5, all_1_4_4) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (80) with all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 42.27/10.98 | (152) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1) % 42.27/10.98 | % 42.27/10.98 | Instantiating formula (97) with all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 42.27/10.98 | (153) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(all_1_5_5, v0) = v1) % 42.27/10.98 | % 42.27/10.98 | Instantiating (150) with all_18_0_7, all_18_1_8 yields: % 42.27/10.98 | (154) ~ (all_18_0_7 = 0) & line_connecting(all_1_5_5, all_1_3_3) = all_18_1_8 & apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7 % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (154) yields: % 42.27/10.98 | (155) ~ (all_18_0_7 = 0) % 42.27/10.98 | (156) line_connecting(all_1_5_5, all_1_3_3) = all_18_1_8 % 42.27/10.98 | (157) apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7 % 42.27/10.98 | % 42.27/10.98 | Instantiating (149) with all_20_0_9, all_20_1_10 yields: % 42.27/10.98 | (158) ~ (all_20_0_9 = 0) & line_connecting(all_1_5_5, all_1_3_3) = all_20_1_10 & apart_point_and_line(all_1_3_3, all_20_1_10) = all_20_0_9 % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (158) yields: % 42.27/10.98 | (159) ~ (all_20_0_9 = 0) % 42.27/10.98 | (160) line_connecting(all_1_5_5, all_1_3_3) = all_20_1_10 % 42.27/10.98 | (161) apart_point_and_line(all_1_3_3, all_20_1_10) = all_20_0_9 % 42.27/10.98 | % 42.27/10.98 | Instantiating (147) with all_22_0_11, all_22_1_12 yields: % 42.27/10.98 | (162) ~ (all_22_0_11 = 0) & line_connecting(all_1_4_4, all_1_3_3) = all_22_1_12 & apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11 % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (162) yields: % 42.27/10.98 | (163) ~ (all_22_0_11 = 0) % 42.27/10.98 | (164) line_connecting(all_1_4_4, all_1_3_3) = all_22_1_12 % 42.27/10.98 | (165) apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11 % 42.27/10.98 | % 42.27/10.98 | Instantiating (153) with all_26_0_17, all_26_1_18 yields: % 42.27/10.98 | (166) ~ (all_26_0_17 = 0) & line_connecting(all_1_5_5, all_1_4_4) = all_26_1_18 & apart_point_and_line(all_1_5_5, all_26_1_18) = all_26_0_17 % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (166) yields: % 42.27/10.98 | (167) ~ (all_26_0_17 = 0) % 42.27/10.98 | (168) line_connecting(all_1_5_5, all_1_4_4) = all_26_1_18 % 42.27/10.98 | (169) apart_point_and_line(all_1_5_5, all_26_1_18) = all_26_0_17 % 42.27/10.98 | % 42.27/10.98 | Instantiating (151) with all_28_0_19, all_28_1_20, all_28_2_21, all_28_3_22 yields: % 42.27/10.98 | (170) point(all_1_4_4) = all_28_2_21 & point(all_1_5_5) = all_28_3_22 & line(all_28_1_20) = all_28_0_19 & line_connecting(all_1_5_5, all_1_4_4) = all_28_1_20 & ( ~ (all_28_2_21 = 0) | ~ (all_28_3_22 = 0) | all_28_0_19 = 0) % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (170) yields: % 42.27/10.98 | (171) point(all_1_5_5) = all_28_3_22 % 42.27/10.98 | (172) point(all_1_4_4) = all_28_2_21 % 42.27/10.98 | (173) line_connecting(all_1_5_5, all_1_4_4) = all_28_1_20 % 42.27/10.98 | (174) ~ (all_28_2_21 = 0) | ~ (all_28_3_22 = 0) | all_28_0_19 = 0 % 42.27/10.98 | (175) line(all_28_1_20) = all_28_0_19 % 42.27/10.98 | % 42.27/10.98 | Instantiating (152) with all_32_0_24, all_32_1_25 yields: % 42.27/10.98 | (176) ~ (all_32_0_24 = 0) & line_connecting(all_1_5_5, all_1_4_4) = all_32_1_25 & apart_point_and_line(all_1_4_4, all_32_1_25) = all_32_0_24 % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (176) yields: % 42.27/10.98 | (177) ~ (all_32_0_24 = 0) % 42.27/10.98 | (178) line_connecting(all_1_5_5, all_1_4_4) = all_32_1_25 % 42.27/10.98 | (179) apart_point_and_line(all_1_4_4, all_32_1_25) = all_32_0_24 % 42.27/10.98 | % 42.27/10.98 | Instantiating (145) with all_34_0_26, all_34_1_27 yields: % 42.27/10.98 | (180) apart_point_and_line(all_1_5_5, all_1_2_2) = all_34_0_26 & distinct_points(all_1_5_5, all_1_4_4) = all_34_1_27 & ( ~ (all_34_0_26 = 0) | ~ (all_34_1_27 = 0)) % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (180) yields: % 42.27/10.98 | (181) apart_point_and_line(all_1_5_5, all_1_2_2) = all_34_0_26 % 42.27/10.98 | (182) distinct_points(all_1_5_5, all_1_4_4) = all_34_1_27 % 42.27/10.98 | (183) ~ (all_34_0_26 = 0) | ~ (all_34_1_27 = 0) % 42.27/10.98 | % 42.27/10.98 | Instantiating (146) with all_36_0_28, all_36_1_29 yields: % 42.27/10.98 | (184) ~ (all_36_0_28 = 0) & line_connecting(all_1_4_4, all_1_3_3) = all_36_1_29 & apart_point_and_line(all_1_3_3, all_36_1_29) = all_36_0_28 % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (184) yields: % 42.27/10.98 | (185) ~ (all_36_0_28 = 0) % 42.27/10.98 | (186) line_connecting(all_1_4_4, all_1_3_3) = all_36_1_29 % 42.27/10.98 | (187) apart_point_and_line(all_1_3_3, all_36_1_29) = all_36_0_28 % 42.27/10.98 | % 42.27/10.98 | Instantiating (148) with all_38_0_30, all_38_1_31, all_38_2_32, all_38_3_33 yields: % 42.27/10.98 | (188) point(all_1_3_3) = all_38_2_32 & point(all_1_5_5) = all_38_3_33 & line(all_38_1_31) = all_38_0_30 & line_connecting(all_1_5_5, all_1_3_3) = all_38_1_31 & ( ~ (all_38_2_32 = 0) | ~ (all_38_3_33 = 0) | all_38_0_30 = 0) % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (188) yields: % 42.27/10.98 | (189) line_connecting(all_1_5_5, all_1_3_3) = all_38_1_31 % 42.27/10.98 | (190) line(all_38_1_31) = all_38_0_30 % 42.27/10.98 | (191) point(all_1_3_3) = all_38_2_32 % 42.27/10.98 | (192) point(all_1_5_5) = all_38_3_33 % 42.27/10.98 | (193) ~ (all_38_2_32 = 0) | ~ (all_38_3_33 = 0) | all_38_0_30 = 0 % 42.27/10.98 | % 42.27/10.98 | Instantiating (144) with all_42_0_35, all_42_1_36 yields: % 42.27/10.98 | (194) apart_point_and_line(all_1_4_4, all_1_2_2) = all_42_0_35 & distinct_points(all_1_5_5, all_1_4_4) = all_42_1_36 & ( ~ (all_42_0_35 = 0) | ~ (all_42_1_36 = 0)) % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (194) yields: % 42.27/10.98 | (195) apart_point_and_line(all_1_4_4, all_1_2_2) = all_42_0_35 % 42.27/10.98 | (196) distinct_points(all_1_5_5, all_1_4_4) = all_42_1_36 % 42.27/10.98 | (197) ~ (all_42_0_35 = 0) | ~ (all_42_1_36 = 0) % 42.27/10.98 | % 42.27/10.98 | Instantiating (143) with all_44_0_37, all_44_1_38, all_44_2_39, all_44_3_40 yields: % 42.27/10.98 | (198) point(all_1_4_4) = all_44_2_39 & point(all_1_5_5) = all_44_3_40 & line(all_1_2_2) = all_44_0_37 & distinct_points(all_1_5_5, all_1_4_4) = all_44_1_38 & ( ~ (all_44_1_38 = 0) | ~ (all_44_2_39 = 0) | ~ (all_44_3_40 = 0) | all_44_0_37 = 0) % 42.27/10.98 | % 42.27/10.98 | Applying alpha-rule on (198) yields: % 42.27/10.98 | (199) line(all_1_2_2) = all_44_0_37 % 42.27/10.98 | (200) point(all_1_5_5) = all_44_3_40 % 42.27/10.98 | (201) distinct_points(all_1_5_5, all_1_4_4) = all_44_1_38 % 42.27/10.98 | (202) ~ (all_44_1_38 = 0) | ~ (all_44_2_39 = 0) | ~ (all_44_3_40 = 0) | all_44_0_37 = 0 % 42.27/10.98 | (203) point(all_1_4_4) = all_44_2_39 % 42.27/10.98 | % 42.27/10.98 | Instantiating (140) with all_46_0_41, all_46_1_42, all_46_2_43, all_46_3_44 yields: % 42.27/10.98 | (204) point(all_1_3_3) = all_46_3_44 & point(all_1_4_4) = all_46_2_43 & line(all_1_1_1) = all_46_0_41 & distinct_points(all_1_3_3, all_1_4_4) = all_46_1_42 & ( ~ (all_46_1_42 = 0) | ~ (all_46_2_43 = 0) | ~ (all_46_3_44 = 0) | all_46_0_41 = 0) % 42.27/10.99 | % 42.27/10.99 | Applying alpha-rule on (204) yields: % 42.27/10.99 | (205) ~ (all_46_1_42 = 0) | ~ (all_46_2_43 = 0) | ~ (all_46_3_44 = 0) | all_46_0_41 = 0 % 42.27/10.99 | (206) point(all_1_3_3) = all_46_3_44 % 42.27/10.99 | (207) distinct_points(all_1_3_3, all_1_4_4) = all_46_1_42 % 42.27/10.99 | (208) point(all_1_4_4) = all_46_2_43 % 42.27/10.99 | (209) line(all_1_1_1) = all_46_0_41 % 42.27/10.99 | % 42.27/10.99 | Instantiating (142) with all_48_0_45, all_48_1_46 yields: % 42.27/10.99 | (210) apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45 & distinct_points(all_1_3_3, all_1_4_4) = all_48_1_46 & ( ~ (all_48_0_45 = 0) | ~ (all_48_1_46 = 0)) % 42.27/10.99 | % 42.27/10.99 | Applying alpha-rule on (210) yields: % 42.27/10.99 | (211) apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45 % 42.27/10.99 | (212) distinct_points(all_1_3_3, all_1_4_4) = all_48_1_46 % 42.27/10.99 | (213) ~ (all_48_0_45 = 0) | ~ (all_48_1_46 = 0) % 42.27/10.99 | % 42.27/10.99 | Instantiating (141) with all_50_0_47, all_50_1_48 yields: % 42.27/10.99 | (214) apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47 & distinct_points(all_1_3_3, all_1_4_4) = all_50_1_48 & ( ~ (all_50_0_47 = 0) | ~ (all_50_1_48 = 0)) % 42.27/10.99 | % 42.27/10.99 | Applying alpha-rule on (214) yields: % 42.27/10.99 | (215) apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47 % 42.27/10.99 | (216) distinct_points(all_1_3_3, all_1_4_4) = all_50_1_48 % 42.27/10.99 | (217) ~ (all_50_0_47 = 0) | ~ (all_50_1_48 = 0) % 42.27/10.99 | % 42.27/10.99 | Instantiating (138) with all_52_0_49 yields: % 42.27/10.99 | (218) ~ (all_52_0_49 = 0) & apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49 % 42.27/10.99 | % 42.27/10.99 | Applying alpha-rule on (218) yields: % 42.27/10.99 | (219) ~ (all_52_0_49 = 0) % 42.27/10.99 | (220) apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49 % 42.27/10.99 | % 42.27/10.99 +-Applying beta-rule and splitting (139), into two cases. % 42.27/10.99 |-Branch one: % 42.27/10.99 | (221) apart_point_and_line(all_1_5_5, all_1_1_1) = 0 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (108) with all_1_4_4, all_1_3_3, all_22_1_12, all_36_1_29 and discharging atoms line_connecting(all_1_4_4, all_1_3_3) = all_36_1_29, line_connecting(all_1_4_4, all_1_3_3) = all_22_1_12, yields: % 42.27/10.99 | (222) all_36_1_29 = all_22_1_12 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (108) with all_1_5_5, all_1_3_3, all_20_1_10, all_38_1_31 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_38_1_31, line_connecting(all_1_5_5, all_1_3_3) = all_20_1_10, yields: % 42.27/10.99 | (223) all_38_1_31 = all_20_1_10 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (108) with all_1_5_5, all_1_3_3, all_18_1_8, all_38_1_31 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_38_1_31, line_connecting(all_1_5_5, all_1_3_3) = all_18_1_8, yields: % 42.27/10.99 | (224) all_38_1_31 = all_18_1_8 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (108) with all_1_5_5, all_1_4_4, all_28_1_20, all_1_2_2 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_28_1_20, line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields: % 42.27/10.99 | (225) all_28_1_20 = all_1_2_2 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (108) with all_1_5_5, all_1_4_4, all_28_1_20, all_32_1_25 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_32_1_25, line_connecting(all_1_5_5, all_1_4_4) = all_28_1_20, yields: % 42.27/10.99 | (226) all_32_1_25 = all_28_1_20 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (108) with all_1_5_5, all_1_4_4, all_26_1_18, all_32_1_25 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_32_1_25, line_connecting(all_1_5_5, all_1_4_4) = all_26_1_18, yields: % 42.27/10.99 | (227) all_32_1_25 = all_26_1_18 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_42_0_35, all_32_0_24 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_42_0_35, yields: % 42.27/10.99 | (228) all_42_0_35 = all_32_0_24 | ~ (apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24) % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (109) with all_1_5_5, all_1_2_2, all_34_0_26, all_26_0_17 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_34_0_26, yields: % 42.27/10.99 | (229) all_34_0_26 = all_26_0_17 | ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17) % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (104) with all_1_3_3, all_1_4_4, all_48_1_46, all_50_1_48 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_50_1_48, distinct_points(all_1_3_3, all_1_4_4) = all_48_1_46, yields: % 42.27/10.99 | (230) all_50_1_48 = all_48_1_46 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (104) with all_1_3_3, all_1_4_4, all_46_1_42, all_50_1_48 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_50_1_48, distinct_points(all_1_3_3, all_1_4_4) = all_46_1_42, yields: % 42.27/10.99 | (231) all_50_1_48 = all_46_1_42 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (104) with all_1_5_5, all_1_4_4, all_42_1_36, 0 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_42_1_36, distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 42.27/10.99 | (232) all_42_1_36 = 0 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (104) with all_1_5_5, all_1_4_4, all_42_1_36, all_44_1_38 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_44_1_38, distinct_points(all_1_5_5, all_1_4_4) = all_42_1_36, yields: % 42.27/10.99 | (233) all_44_1_38 = all_42_1_36 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (104) with all_1_5_5, all_1_4_4, all_34_1_27, all_44_1_38 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_44_1_38, distinct_points(all_1_5_5, all_1_4_4) = all_34_1_27, yields: % 42.27/10.99 | (234) all_44_1_38 = all_34_1_27 % 42.27/10.99 | % 42.27/10.99 | Combining equations (230,231) yields a new equation: % 42.27/10.99 | (235) all_48_1_46 = all_46_1_42 % 42.27/10.99 | % 42.27/10.99 | Simplifying 235 yields: % 42.27/10.99 | (236) all_48_1_46 = all_46_1_42 % 42.27/10.99 | % 42.27/10.99 | Combining equations (233,234) yields a new equation: % 42.27/10.99 | (237) all_42_1_36 = all_34_1_27 % 42.27/10.99 | % 42.27/10.99 | Simplifying 237 yields: % 42.27/10.99 | (238) all_42_1_36 = all_34_1_27 % 42.27/10.99 | % 42.27/10.99 | Combining equations (232,238) yields a new equation: % 42.27/10.99 | (239) all_34_1_27 = 0 % 42.27/10.99 | % 42.27/10.99 | Combining equations (224,223) yields a new equation: % 42.27/10.99 | (240) all_20_1_10 = all_18_1_8 % 42.27/10.99 | % 42.27/10.99 | Combining equations (226,227) yields a new equation: % 42.27/10.99 | (241) all_28_1_20 = all_26_1_18 % 42.27/10.99 | % 42.27/10.99 | Simplifying 241 yields: % 42.27/10.99 | (242) all_28_1_20 = all_26_1_18 % 42.27/10.99 | % 42.27/10.99 | Combining equations (225,242) yields a new equation: % 42.27/10.99 | (243) all_26_1_18 = all_1_2_2 % 42.27/10.99 | % 42.27/10.99 | Combining equations (243,227) yields a new equation: % 42.27/10.99 | (244) all_32_1_25 = all_1_2_2 % 42.27/10.99 | % 42.27/10.99 | Combining equations (239,238) yields a new equation: % 42.27/10.99 | (232) all_42_1_36 = 0 % 42.27/10.99 | % 42.27/10.99 | From (222) and (187) follows: % 42.27/10.99 | (246) apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28 % 42.27/10.99 | % 42.27/10.99 | From (240) and (161) follows: % 42.27/10.99 | (247) apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9 % 42.27/10.99 | % 42.27/10.99 | From (244) and (179) follows: % 42.27/10.99 | (248) apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24 % 42.27/10.99 | % 42.27/10.99 | From (243) and (169) follows: % 42.27/10.99 | (249) apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17 % 42.27/10.99 | % 42.27/10.99 | From (236) and (212) follows: % 42.27/10.99 | (207) distinct_points(all_1_3_3, all_1_4_4) = all_46_1_42 % 42.27/10.99 | % 42.27/10.99 | From (239) and (182) follows: % 42.27/10.99 | (133) distinct_points(all_1_5_5, all_1_4_4) = 0 % 42.27/10.99 | % 42.27/10.99 +-Applying beta-rule and splitting (197), into two cases. % 42.27/10.99 |-Branch one: % 42.27/10.99 | (252) ~ (all_42_0_35 = 0) % 42.27/10.99 | % 42.27/10.99 +-Applying beta-rule and splitting (183), into two cases. % 42.27/10.99 |-Branch one: % 42.27/10.99 | (253) ~ (all_34_0_26 = 0) % 42.27/10.99 | % 42.27/10.99 +-Applying beta-rule and splitting (228), into two cases. % 42.27/10.99 |-Branch one: % 42.27/10.99 | (254) ~ (apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24) % 42.27/10.99 | % 42.27/10.99 | Using (248) and (254) yields: % 42.27/10.99 | (255) $false % 42.27/10.99 | % 42.27/10.99 |-The branch is then unsatisfiable % 42.27/10.99 |-Branch two: % 42.27/10.99 | (248) apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24 % 42.27/10.99 | (257) all_42_0_35 = all_32_0_24 % 42.27/10.99 | % 42.27/10.99 | Equations (257) can reduce 252 to: % 42.27/10.99 | (177) ~ (all_32_0_24 = 0) % 42.27/10.99 | % 42.27/10.99 | From (257) and (195) follows: % 42.27/10.99 | (248) apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24 % 42.27/10.99 | % 42.27/10.99 +-Applying beta-rule and splitting (229), into two cases. % 42.27/10.99 |-Branch one: % 42.27/10.99 | (260) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17) % 42.27/10.99 | % 42.27/10.99 | Using (249) and (260) yields: % 42.27/10.99 | (255) $false % 42.27/10.99 | % 42.27/10.99 |-The branch is then unsatisfiable % 42.27/10.99 |-Branch two: % 42.27/10.99 | (249) apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17 % 42.27/10.99 | (263) all_34_0_26 = all_26_0_17 % 42.27/10.99 | % 42.27/10.99 | Equations (263) can reduce 253 to: % 42.27/10.99 | (167) ~ (all_26_0_17 = 0) % 42.27/10.99 | % 42.27/10.99 | From (263) and (181) follows: % 42.27/10.99 | (249) apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17 % 42.27/10.99 | % 42.27/10.99 | Instantiating formula (7) with all_36_0_28, all_36_0_28, all_22_1_12, all_22_1_12, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, yields: % 42.27/10.99 | (266) all_36_0_28 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_22_1_12) = v1 & distinct_lines(all_22_1_12, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (3) with all_36_0_28, all_36_0_28, all_22_1_12, all_22_1_12, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, yields: % 42.27/11.00 | (267) all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & distinct_lines(all_22_1_12, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_20_0_9, all_36_0_28, all_18_1_8, all_22_1_12, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 42.27/11.00 | (268) all_36_0_28 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v1 & apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & distinct_lines(all_22_1_12, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_20_0_9, all_36_0_28, all_18_1_8, all_22_1_12, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, yields: % 42.27/11.00 | (269) all_36_0_28 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_18_1_8) = v1 & distinct_lines(all_22_1_12, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_36_0_28, all_20_0_9, all_22_1_12, all_18_1_8, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, yields: % 42.27/11.00 | (270) all_36_0_28 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_22_1_12) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_20_0_9, all_20_0_9, all_18_1_8, all_18_1_8, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 42.27/11.00 | (271) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & apart_point_and_line(all_1_4_4, all_18_1_8) = v1 & distinct_lines(all_18_1_8, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_20_0_9, all_20_0_9, all_18_1_8, all_18_1_8, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, yields: % 42.27/11.00 | (272) all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_18_1_8) = v1 & distinct_lines(all_18_1_8, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_48_0_45, all_36_0_28, all_1_1_1, all_22_1_12, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 42.27/11.00 | (273) all_48_0_45 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_22_1_12) = v1 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_36_0_28, all_48_0_45, all_22_1_12, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 42.27/11.00 | (274) all_48_0_45 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_22_1_12) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_48_0_45, all_36_0_28, all_1_1_1, all_22_1_12, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (275) all_48_0_45 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_1_1_1) = v1 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_36_0_28, all_48_0_45, all_22_1_12, all_1_1_1, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (276) all_48_0_45 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_22_1_12) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (3) with all_48_0_45, all_36_0_28, all_1_1_1, all_22_1_12, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (277) all_48_0_45 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (3) with all_36_0_28, all_48_0_45, all_22_1_12, all_1_1_1, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (278) all_48_0_45 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (88) with all_48_0_45, all_36_0_28, all_22_1_12, all_1_1_1, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (279) all_48_0_45 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (88) with all_36_0_28, all_48_0_45, all_1_1_1, all_22_1_12, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (280) all_48_0_45 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_48_0_45, all_20_0_9, all_1_1_1, all_18_1_8, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 42.27/11.00 | (281) all_48_0_45 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v1 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_18_1_8, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_20_0_9, all_48_0_45, all_18_1_8, all_1_1_1, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 42.27/11.00 | (282) all_48_0_45 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_48_0_45, all_20_0_9, all_1_1_1, all_18_1_8, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 42.27/11.00 | (283) all_48_0_45 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_18_1_8) = v1 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_18_1_8, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_20_0_9, all_48_0_45, all_18_1_8, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 42.27/11.00 | (284) all_48_0_45 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_18_1_8) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_48_0_45, all_20_0_9, all_1_1_1, all_18_1_8, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (285) all_48_0_45 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_1_1_1) = v1 & distinct_lines(all_18_1_8, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_20_0_9, all_48_0_45, all_18_1_8, all_1_1_1, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (286) all_48_0_45 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_18_1_8) = v1 & distinct_lines(all_1_1_1, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (3) with all_48_0_45, all_20_0_9, all_1_1_1, all_18_1_8, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (287) all_48_0_45 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v3 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_18_1_8, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (3) with all_20_0_9, all_48_0_45, all_18_1_8, all_1_1_1, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.00 | (288) all_48_0_45 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_18_1_8) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_52_0_49, all_20_0_9, all_1_2_2, all_18_1_8, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, yields: % 42.27/11.00 | (289) all_52_0_49 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_1_2_2) = v1 & distinct_lines(all_18_1_8, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (7) with all_20_0_9, all_52_0_49, all_18_1_8, all_1_2_2, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, yields: % 42.27/11.00 | (290) all_52_0_49 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_18_1_8) = v1 & distinct_lines(all_1_2_2, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.00 | % 42.27/11.00 | Instantiating formula (66) with all_52_0_49, all_48_0_45, all_1_2_2, all_1_1_1, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 42.27/11.00 | (291) all_52_0_49 = 0 | all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (66) with all_48_0_45, all_52_0_49, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 42.27/11.01 | (292) all_52_0_49 = 0 | all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (7) with all_52_0_49, all_48_0_45, all_1_2_2, all_1_1_1, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, yields: % 42.27/11.01 | (293) all_52_0_49 = 0 | all_48_0_45 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_1_2_2) = v1 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (7) with all_48_0_45, all_52_0_49, all_1_1_1, all_1_2_2, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, yields: % 42.27/11.01 | (294) all_52_0_49 = 0 | all_48_0_45 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_1_1_1) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_52_0_49, all_22_0_11, all_1_2_2, all_22_1_12, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, yields: % 42.27/11.01 | (295) all_52_0_49 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_22_1_12, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (88) with all_22_0_11, all_52_0_49, all_1_2_2, all_22_1_12, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, yields: % 42.27/11.01 | (296) all_52_0_49 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_22_1_12, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_50_0_47, all_48_0_45, all_1_1_1, all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (297) all_50_0_47 = 0 | all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_48_0_45, all_50_0_47, all_1_1_1, all_1_1_1, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (298) all_50_0_47 = 0 | all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_50_0_47, all_52_0_49, all_1_1_1, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (299) all_52_0_49 = 0 | all_50_0_47 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (88) with all_52_0_49, all_50_0_47, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (300) all_52_0_49 = 0 | all_50_0_47 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (7) with all_50_0_47, all_22_0_11, all_1_1_1, all_22_1_12, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (301) all_50_0_47 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_1_1_1) = v1 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (7) with all_22_0_11, all_50_0_47, all_22_1_12, all_1_1_1, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (302) all_50_0_47 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_22_1_12) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_50_0_47, all_22_0_11, all_1_1_1, all_22_1_12, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (303) all_50_0_47 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_22_0_11, all_50_0_47, all_22_1_12, all_1_1_1, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (304) all_50_0_47 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (88) with all_50_0_47, all_22_0_11, all_22_1_12, all_1_1_1, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (305) all_50_0_47 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (7) with all_50_0_47, all_50_0_47, all_1_1_1, all_1_1_1, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.01 | (306) all_50_0_47 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (7) with all_32_0_24, all_50_0_47, all_1_2_2, all_1_1_1, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 42.27/11.01 | (307) all_50_0_47 = 0 | all_32_0_24 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_1_2_2) = v1 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_18_0_7, all_20_0_9, all_18_1_8, all_18_1_8, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, yields: % 42.27/11.01 | (308) all_20_0_9 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v2 & apart_point_and_line(all_1_5_5, all_18_1_8) = v3 & distinct_lines(all_18_1_8, all_18_1_8) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_18_0_7, all_48_0_45, all_18_1_8, all_1_1_1, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, yields: % 42.27/11.01 | (309) all_48_0_45 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_18_1_8) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_48_0_45, all_18_0_7, all_1_1_1, all_18_1_8, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, yields: % 42.27/11.01 | (310) all_48_0_45 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_18_1_8, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (88) with all_18_0_7, all_48_0_45, all_1_1_1, all_18_1_8, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, yields: % 42.27/11.01 | (311) all_48_0_45 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_18_1_8, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (88) with all_48_0_45, all_18_0_7, all_18_1_8, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, yields: % 42.27/11.01 | (312) all_48_0_45 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_18_1_8) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (3) with all_26_0_17, all_32_0_24, all_1_2_2, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 42.27/11.01 | (313) all_32_0_24 = 0 | all_26_0_17 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (127) with all_26_0_17, all_1_2_2, all_1_1_1, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = 0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 42.27/11.01 | (314) all_26_0_17 = 0 | distinct_lines(all_1_1_1, all_1_2_2) = 0 % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (126) with all_26_0_17, all_26_0_17, all_1_2_2, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 42.27/11.01 | (315) all_26_0_17 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (7) with all_26_0_17, all_26_0_17, all_1_2_2, all_1_2_2, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 42.27/11.01 | (316) all_26_0_17 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (40) with all_46_1_42, all_1_4_4, all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_46_1_42, distinct_points(all_1_4_4, all_1_3_3) = 0, ~ (distinct_points(all_1_4_4, all_1_4_4) = 0), yields: % 42.27/11.01 | (317) all_46_1_42 = 0 % 42.27/11.01 | % 42.27/11.01 | Instantiating formula (126) with all_36_0_28, all_20_0_9, all_22_1_12, all_18_1_8, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9, yields: % 42.27/11.02 | (318) all_36_0_28 = 0 | all_20_0_9 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_18_1_8) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (126) with all_48_0_45, all_48_0_45, all_1_1_1, all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, yields: % 42.27/11.02 | (319) all_48_0_45 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (126) with all_52_0_49, all_48_0_45, all_1_2_2, all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_48_0_45, apart_point_and_line(all_1_3_3, all_1_2_2) = all_52_0_49, yields: % 42.27/11.02 | (320) all_52_0_49 = 0 | all_48_0_45 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (66) with all_22_0_11, all_32_0_24, all_22_1_12, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 42.27/11.02 | (321) all_32_0_24 = 0 | all_22_0_11 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (66) with all_50_0_47, all_22_0_11, all_1_1_1, all_22_1_12, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.27/11.02 | (322) all_50_0_47 = 0 | all_22_0_11 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v1 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (66) with all_50_0_47, all_32_0_24, all_1_1_1, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 42.27/11.02 | (323) all_50_0_47 = 0 | all_32_0_24 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (66) with all_32_0_24, all_22_0_11, all_1_2_2, all_22_1_12, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 42.27/11.02 | (324) all_32_0_24 = 0 | all_22_0_11 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_22_1_12, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (66) with all_32_0_24, all_50_0_47, all_1_2_2, all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 42.27/11.02 | (325) all_50_0_47 = 0 | all_32_0_24 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (66) with all_32_0_24, all_32_0_24, all_1_2_2, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 42.27/11.02 | (326) all_32_0_24 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (120) with all_1_4_4, all_1_3_3 yields: % 42.27/11.02 | (327) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_3_3) = v0 & point(all_1_4_4) = v1 & line(v2) = v3 & line_connecting(all_1_3_3, all_1_4_4) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (80) with all_1_4_4, all_1_3_3 yields: % 42.27/11.02 | (328) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (97) with all_1_4_4, all_1_3_3 yields: % 42.27/11.02 | (329) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_3_3, v0) = v1) % 42.27/11.02 | % 42.27/11.02 | Instantiating formula (52) with all_1_4_4, all_1_3_3 yields: % 42.27/11.02 | (330) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & equal_points(all_1_3_3, all_1_4_4) = v0) % 42.27/11.02 | % 42.27/11.02 | Combining equations (317,236) yields a new equation: % 42.27/11.02 | (331) all_48_1_46 = 0 % 42.27/11.02 | % 42.27/11.02 | Combining equations (317,231) yields a new equation: % 42.27/11.02 | (332) all_50_1_48 = 0 % 42.27/11.02 | % 42.27/11.02 | From (317) and (207) follows: % 42.27/11.02 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (329), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.02 | % 42.27/11.02 | Using (333) and (334) yields: % 42.27/11.02 | (255) $false % 42.27/11.02 | % 42.27/11.02 |-The branch is then unsatisfiable % 42.27/11.02 |-Branch two: % 42.27/11.02 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.02 | (337) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_3_3, v0) = v1) % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (314), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (338) distinct_lines(all_1_1_1, all_1_2_2) = 0 % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (316), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (339) all_26_0_17 = 0 % 42.27/11.02 | % 42.27/11.02 | Equations (339) can reduce 167 to: % 42.27/11.02 | (340) $false % 42.27/11.02 | % 42.27/11.02 |-The branch is then unsatisfiable % 42.27/11.02 |-Branch two: % 42.27/11.02 | (167) ~ (all_26_0_17 = 0) % 42.27/11.02 | (342) ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (327), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.02 | % 42.27/11.02 | Using (333) and (334) yields: % 42.27/11.02 | (255) $false % 42.27/11.02 | % 42.27/11.02 |-The branch is then unsatisfiable % 42.27/11.02 |-Branch two: % 42.27/11.02 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.02 | (346) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_3_3) = v0 & point(all_1_4_4) = v1 & line(v2) = v3 & line_connecting(all_1_3_3, all_1_4_4) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (328), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.02 | % 42.27/11.02 | Using (333) and (334) yields: % 42.27/11.02 | (255) $false % 42.27/11.02 | % 42.27/11.02 |-The branch is then unsatisfiable % 42.27/11.02 |-Branch two: % 42.27/11.02 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.02 | (350) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1) % 42.27/11.02 | % 42.27/11.02 | Instantiating (350) with all_115_0_66, all_115_1_67 yields: % 42.27/11.02 | (351) ~ (all_115_0_66 = 0) & line_connecting(all_1_3_3, all_1_4_4) = all_115_1_67 & apart_point_and_line(all_1_4_4, all_115_1_67) = all_115_0_66 % 42.27/11.02 | % 42.27/11.02 | Applying alpha-rule on (351) yields: % 42.27/11.02 | (352) ~ (all_115_0_66 = 0) % 42.27/11.02 | (353) line_connecting(all_1_3_3, all_1_4_4) = all_115_1_67 % 42.27/11.02 | (354) apart_point_and_line(all_1_4_4, all_115_1_67) = all_115_0_66 % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (326), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.02 | % 42.27/11.02 | Using (333) and (334) yields: % 42.27/11.02 | (255) $false % 42.27/11.02 | % 42.27/11.02 |-The branch is then unsatisfiable % 42.27/11.02 |-Branch two: % 42.27/11.02 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.02 | (358) all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (324), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.02 | % 42.27/11.02 | Using (333) and (334) yields: % 42.27/11.02 | (255) $false % 42.27/11.02 | % 42.27/11.02 |-The branch is then unsatisfiable % 42.27/11.02 |-Branch two: % 42.27/11.02 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.02 | (362) all_32_0_24 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_22_1_12, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (321), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.02 | % 42.27/11.02 | Using (333) and (334) yields: % 42.27/11.02 | (255) $false % 42.27/11.02 | % 42.27/11.02 |-The branch is then unsatisfiable % 42.27/11.02 |-Branch two: % 42.27/11.02 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.02 | (366) all_32_0_24 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (213), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (367) ~ (all_48_0_45 = 0) % 42.27/11.02 | % 42.27/11.02 +-Applying beta-rule and splitting (366), into two cases. % 42.27/11.02 |-Branch one: % 42.27/11.02 | (368) all_32_0_24 = 0 % 42.27/11.02 | % 42.27/11.02 | Equations (368) can reduce 177 to: % 42.27/11.02 | (340) $false % 42.27/11.02 | % 42.27/11.02 |-The branch is then unsatisfiable % 42.27/11.02 |-Branch two: % 42.27/11.02 | (177) ~ (all_32_0_24 = 0) % 42.27/11.03 | (371) all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (358), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (368) all_32_0_24 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (368) can reduce 177 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (177) ~ (all_32_0_24 = 0) % 42.27/11.03 | (375) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (266), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (376) all_36_0_28 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (376) can reduce 185 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (185) ~ (all_36_0_28 = 0) % 42.27/11.03 | (379) ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_22_1_12) = v1 & distinct_lines(all_22_1_12, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (267), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (376) all_36_0_28 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (376) can reduce 185 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (185) ~ (all_36_0_28 = 0) % 42.27/11.03 | (383) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & distinct_lines(all_22_1_12, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (217), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (384) ~ (all_50_0_47 = 0) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (268), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (376) all_36_0_28 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (376) can reduce 185 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (185) ~ (all_36_0_28 = 0) % 42.27/11.03 | (388) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v1 & apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & distinct_lines(all_22_1_12, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (371), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (389) all_22_0_11 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (389) can reduce 163 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (163) ~ (all_22_0_11 = 0) % 42.27/11.03 | (392) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (315), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (339) all_26_0_17 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (339) can reduce 167 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (167) ~ (all_26_0_17 = 0) % 42.27/11.03 | (396) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 | Instantiating (396) with all_169_0_80, all_169_1_81, all_169_2_82 yields: % 42.27/11.03 | (397) apart_point_and_line(all_1_4_4, all_1_2_2) = all_169_0_80 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_169_1_81 & distinct_lines(all_1_2_2, all_1_2_2) = all_169_2_82 & ( ~ (all_169_2_82 = 0) | all_169_0_80 = 0 | all_169_1_81 = 0) % 42.27/11.03 | % 42.27/11.03 | Applying alpha-rule on (397) yields: % 42.27/11.03 | (398) apart_point_and_line(all_1_4_4, all_1_2_2) = all_169_0_80 % 42.27/11.03 | (399) apart_point_and_line(all_1_4_4, all_1_2_2) = all_169_1_81 % 42.27/11.03 | (400) distinct_lines(all_1_2_2, all_1_2_2) = all_169_2_82 % 42.27/11.03 | (401) ~ (all_169_2_82 = 0) | all_169_0_80 = 0 | all_169_1_81 = 0 % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (322), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.03 | % 42.27/11.03 | Using (333) and (334) yields: % 42.27/11.03 | (255) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.03 | (405) all_50_0_47 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v1 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (388), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (406) all_20_0_9 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (406) can reduce 159 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (159) ~ (all_20_0_9 = 0) % 42.27/11.03 | (409) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v1 & apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & distinct_lines(all_22_1_12, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (272), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (406) all_20_0_9 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (406) can reduce 159 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (159) ~ (all_20_0_9 = 0) % 42.27/11.03 | (413) ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_18_1_8) = v1 & distinct_lines(all_18_1_8, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (330), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.03 | % 42.27/11.03 | Using (333) and (334) yields: % 42.27/11.03 | (255) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.03 | (417) ? [v0] : ( ~ (v0 = 0) & equal_points(all_1_3_3, all_1_4_4) = v0) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (271), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (406) all_20_0_9 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (406) can reduce 159 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (159) ~ (all_20_0_9 = 0) % 42.27/11.03 | (421) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & apart_point_and_line(all_1_4_4, all_18_1_8) = v1 & distinct_lines(all_18_1_8, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (276), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (422) all_48_0_45 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (422) can reduce 367 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (367) ~ (all_48_0_45 = 0) % 42.27/11.03 | (425) all_36_0_28 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_22_1_12) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (275), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (422) all_48_0_45 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (422) can reduce 367 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (367) ~ (all_48_0_45 = 0) % 42.27/11.03 | (429) all_36_0_28 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_1_1_1) = v1 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (279), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (422) all_48_0_45 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (422) can reduce 367 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (367) ~ (all_48_0_45 = 0) % 42.27/11.03 | (433) all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (280), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (422) all_48_0_45 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (422) can reduce 367 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (367) ~ (all_48_0_45 = 0) % 42.27/11.03 | (437) all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (277), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (422) all_48_0_45 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (422) can reduce 367 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (367) ~ (all_48_0_45 = 0) % 42.27/11.03 | (441) all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.03 | % 42.27/11.03 +-Applying beta-rule and splitting (278), into two cases. % 42.27/11.03 |-Branch one: % 42.27/11.03 | (422) all_48_0_45 = 0 % 42.27/11.03 | % 42.27/11.03 | Equations (422) can reduce 367 to: % 42.27/11.03 | (340) $false % 42.27/11.03 | % 42.27/11.03 |-The branch is then unsatisfiable % 42.27/11.03 |-Branch two: % 42.27/11.03 | (367) ~ (all_48_0_45 = 0) % 42.27/11.03 | (445) all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.03 | % 42.27/11.04 +-Applying beta-rule and splitting (273), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (422) all_48_0_45 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (422) can reduce 367 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (367) ~ (all_48_0_45 = 0) % 42.27/11.04 | (449) all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_22_1_12) = v1 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (274), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (422) all_48_0_45 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (422) can reduce 367 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (367) ~ (all_48_0_45 = 0) % 42.27/11.04 | (453) all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_22_1_12) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (405), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (454) all_50_0_47 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (454) can reduce 384 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (384) ~ (all_50_0_47 = 0) % 42.27/11.04 | (457) all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v1 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (325), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.04 | % 42.27/11.04 | Using (333) and (334) yields: % 42.27/11.04 | (255) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.04 | (461) all_50_0_47 = 0 | all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (453), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (376) all_36_0_28 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (376) can reduce 185 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (185) ~ (all_36_0_28 = 0) % 42.27/11.04 | (465) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_22_1_12) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (323), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.27/11.04 | % 42.27/11.04 | Using (333) and (334) yields: % 42.27/11.04 | (255) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.27/11.04 | (469) all_50_0_47 = 0 | all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (437), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (376) all_36_0_28 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (376) can reduce 185 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (185) ~ (all_36_0_28 = 0) % 42.27/11.04 | (473) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (441), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (376) all_36_0_28 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (376) can reduce 185 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (185) ~ (all_36_0_28 = 0) % 42.27/11.04 | (477) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (291), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (478) all_52_0_49 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (478) can reduce 219 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (219) ~ (all_52_0_49 = 0) % 42.27/11.04 | (481) all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (289), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (478) all_52_0_49 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (478) can reduce 219 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (219) ~ (all_52_0_49 = 0) % 42.27/11.04 | (485) all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_1_2_2) = v1 & distinct_lines(all_18_1_8, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (290), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (478) all_52_0_49 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (478) can reduce 219 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (219) ~ (all_52_0_49 = 0) % 42.27/11.04 | (489) all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_18_1_8) = v1 & distinct_lines(all_1_2_2, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (301), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (454) all_50_0_47 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (454) can reduce 384 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (384) ~ (all_50_0_47 = 0) % 42.27/11.04 | (493) all_22_0_11 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_1_1_1) = v1 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (302), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (454) all_50_0_47 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (454) can reduce 384 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (384) ~ (all_50_0_47 = 0) % 42.27/11.04 | (497) all_22_0_11 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_22_1_12) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (292), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (478) all_52_0_49 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (478) can reduce 219 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (219) ~ (all_52_0_49 = 0) % 42.27/11.04 | (501) all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (297), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (454) all_50_0_47 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (454) can reduce 384 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (384) ~ (all_50_0_47 = 0) % 42.27/11.04 | (505) all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (305), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (454) all_50_0_47 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (454) can reduce 384 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.27/11.04 |-The branch is then unsatisfiable % 42.27/11.04 |-Branch two: % 42.27/11.04 | (384) ~ (all_50_0_47 = 0) % 42.27/11.04 | (509) all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.27/11.04 | % 42.27/11.04 +-Applying beta-rule and splitting (300), into two cases. % 42.27/11.04 |-Branch one: % 42.27/11.04 | (478) all_52_0_49 = 0 % 42.27/11.04 | % 42.27/11.04 | Equations (478) can reduce 219 to: % 42.27/11.04 | (340) $false % 42.27/11.04 | % 42.60/11.04 |-The branch is then unsatisfiable % 42.60/11.04 |-Branch two: % 42.60/11.04 | (219) ~ (all_52_0_49 = 0) % 42.60/11.04 | (513) all_50_0_47 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.04 | % 42.60/11.04 +-Applying beta-rule and splitting (295), into two cases. % 42.60/11.04 |-Branch one: % 42.60/11.04 | (478) all_52_0_49 = 0 % 42.60/11.04 | % 42.60/11.04 | Equations (478) can reduce 219 to: % 42.60/11.04 | (340) $false % 42.60/11.04 | % 42.60/11.04 |-The branch is then unsatisfiable % 42.60/11.04 |-Branch two: % 42.60/11.04 | (219) ~ (all_52_0_49 = 0) % 42.60/11.04 | (517) all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_22_1_12, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.04 | % 42.60/11.04 +-Applying beta-rule and splitting (296), into two cases. % 42.60/11.04 |-Branch one: % 42.60/11.04 | (478) all_52_0_49 = 0 % 42.60/11.04 | % 42.60/11.04 | Equations (478) can reduce 219 to: % 42.60/11.04 | (340) $false % 42.60/11.04 | % 42.60/11.04 |-The branch is then unsatisfiable % 42.60/11.04 |-Branch two: % 42.60/11.04 | (219) ~ (all_52_0_49 = 0) % 42.60/11.04 | (521) all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_22_1_12, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.04 | % 42.60/11.04 +-Applying beta-rule and splitting (298), into two cases. % 42.60/11.04 |-Branch one: % 42.60/11.04 | (454) all_50_0_47 = 0 % 42.60/11.04 | % 42.60/11.04 | Equations (454) can reduce 384 to: % 42.60/11.04 | (340) $false % 42.60/11.04 | % 42.60/11.04 |-The branch is then unsatisfiable % 42.60/11.04 |-Branch two: % 42.60/11.04 | (384) ~ (all_50_0_47 = 0) % 42.60/11.04 | (525) all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.04 | % 42.60/11.04 +-Applying beta-rule and splitting (299), into two cases. % 42.60/11.04 |-Branch one: % 42.60/11.04 | (478) all_52_0_49 = 0 % 42.60/11.04 | % 42.60/11.04 | Equations (478) can reduce 219 to: % 42.60/11.04 | (340) $false % 42.60/11.04 | % 42.60/11.04 |-The branch is then unsatisfiable % 42.60/11.04 |-Branch two: % 42.60/11.04 | (219) ~ (all_52_0_49 = 0) % 42.60/11.04 | (529) all_50_0_47 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (318), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.60/11.05 | % 42.60/11.05 | Using (333) and (334) yields: % 42.60/11.05 | (255) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.60/11.05 | (533) all_36_0_28 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_18_1_8) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (304), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (454) all_50_0_47 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (454) can reduce 384 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (384) ~ (all_50_0_47 = 0) % 42.60/11.05 | (537) all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (303), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (454) all_50_0_47 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (454) can reduce 384 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (384) ~ (all_50_0_47 = 0) % 42.60/11.05 | (541) all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (469), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (454) all_50_0_47 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (454) can reduce 384 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (384) ~ (all_50_0_47 = 0) % 42.60/11.05 | (545) all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (320), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.60/11.05 | % 42.60/11.05 | Using (333) and (334) yields: % 42.60/11.05 | (255) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.60/11.05 | (291) all_52_0_49 = 0 | all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (319), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (334) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) % 42.60/11.05 | % 42.60/11.05 | Using (333) and (334) yields: % 42.60/11.05 | (255) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (333) distinct_points(all_1_3_3, all_1_4_4) = 0 % 42.60/11.05 | (553) all_48_0_45 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (362), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (368) all_32_0_24 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (368) can reduce 177 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (177) ~ (all_32_0_24 = 0) % 42.60/11.05 | (557) all_22_0_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_22_1_12, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (425), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (376) all_36_0_28 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (376) can reduce 185 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (185) ~ (all_36_0_28 = 0) % 42.60/11.05 | (561) ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_22_1_12) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (493), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (389) all_22_0_11 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (389) can reduce 163 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (163) ~ (all_22_0_11 = 0) % 42.60/11.05 | (565) ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_1_1_1) = v1 & distinct_lines(all_22_1_12, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (509), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (389) all_22_0_11 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (389) can reduce 163 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (163) ~ (all_22_0_11 = 0) % 42.60/11.05 | (569) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.05 | % 42.60/11.05 | Instantiating (569) with all_346_0_111, all_346_1_112, all_346_2_113, all_346_3_114 yields: % 42.60/11.05 | (570) apart_point_and_line(all_1_4_4, all_22_1_12) = all_346_0_111 & apart_point_and_line(all_1_4_4, all_1_1_1) = all_346_1_112 & distinct_lines(all_1_1_1, all_22_1_12) = all_346_2_113 & distinct_points(all_1_4_4, all_1_4_4) = all_346_3_114 & ( ~ (all_346_2_113 = 0) | ~ (all_346_3_114 = 0) | all_346_0_111 = 0 | all_346_1_112 = 0) % 42.60/11.05 | % 42.60/11.05 | Applying alpha-rule on (570) yields: % 42.60/11.05 | (571) ~ (all_346_2_113 = 0) | ~ (all_346_3_114 = 0) | all_346_0_111 = 0 | all_346_1_112 = 0 % 42.60/11.05 | (572) distinct_lines(all_1_1_1, all_22_1_12) = all_346_2_113 % 42.60/11.05 | (573) apart_point_and_line(all_1_4_4, all_22_1_12) = all_346_0_111 % 42.60/11.05 | (574) distinct_points(all_1_4_4, all_1_4_4) = all_346_3_114 % 42.60/11.05 | (575) apart_point_and_line(all_1_4_4, all_1_1_1) = all_346_1_112 % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (517), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (389) all_22_0_11 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (389) can reduce 163 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (163) ~ (all_22_0_11 = 0) % 42.60/11.05 | (579) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_22_1_12) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_22_1_12, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.05 | % 42.60/11.05 | Instantiating (579) with all_351_0_115, all_351_1_116, all_351_2_117, all_351_3_118 yields: % 42.60/11.05 | (580) apart_point_and_line(all_1_3_3, all_22_1_12) = all_351_0_115 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_351_1_116 & distinct_lines(all_22_1_12, all_1_2_2) = all_351_2_117 & distinct_points(all_1_4_4, all_1_3_3) = all_351_3_118 & ( ~ (all_351_2_117 = 0) | ~ (all_351_3_118 = 0) | all_351_0_115 = 0 | all_351_1_116 = 0) % 42.60/11.05 | % 42.60/11.05 | Applying alpha-rule on (580) yields: % 42.60/11.05 | (581) distinct_lines(all_22_1_12, all_1_2_2) = all_351_2_117 % 42.60/11.05 | (582) apart_point_and_line(all_1_4_4, all_1_2_2) = all_351_1_116 % 42.60/11.05 | (583) apart_point_and_line(all_1_3_3, all_22_1_12) = all_351_0_115 % 42.60/11.05 | (584) distinct_points(all_1_4_4, all_1_3_3) = all_351_3_118 % 42.60/11.05 | (585) ~ (all_351_2_117 = 0) | ~ (all_351_3_118 = 0) | all_351_0_115 = 0 | all_351_1_116 = 0 % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (529), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (454) all_50_0_47 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (454) can reduce 384 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (384) ~ (all_50_0_47 = 0) % 42.60/11.05 | (589) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.05 | % 42.60/11.05 | Instantiating (589) with all_356_0_119, all_356_1_120, all_356_2_121, all_356_3_122 yields: % 42.60/11.05 | (590) apart_point_and_line(all_1_3_3, all_1_1_1) = all_356_1_120 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_356_0_119 & distinct_lines(all_1_2_2, all_1_1_1) = all_356_2_121 & distinct_points(all_1_3_3, all_1_4_4) = all_356_3_122 & ( ~ (all_356_2_121 = 0) | ~ (all_356_3_122 = 0) | all_356_0_119 = 0 | all_356_1_120 = 0) % 42.60/11.05 | % 42.60/11.05 | Applying alpha-rule on (590) yields: % 42.60/11.05 | (591) distinct_points(all_1_3_3, all_1_4_4) = all_356_3_122 % 42.60/11.05 | (592) apart_point_and_line(all_1_4_4, all_1_2_2) = all_356_0_119 % 42.60/11.05 | (593) ~ (all_356_2_121 = 0) | ~ (all_356_3_122 = 0) | all_356_0_119 = 0 | all_356_1_120 = 0 % 42.60/11.05 | (594) apart_point_and_line(all_1_3_3, all_1_1_1) = all_356_1_120 % 42.60/11.05 | (595) distinct_lines(all_1_2_2, all_1_1_1) = all_356_2_121 % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (537), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (389) all_22_0_11 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (389) can reduce 163 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (163) ~ (all_22_0_11 = 0) % 42.60/11.05 | (599) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.05 | % 42.60/11.05 | Instantiating (599) with all_366_0_127, all_366_1_128, all_366_2_129, all_366_3_130 yields: % 42.60/11.05 | (600) apart_point_and_line(all_1_4_4, all_22_1_12) = all_366_1_128 & apart_point_and_line(all_1_4_4, all_1_1_1) = all_366_0_127 & distinct_lines(all_1_1_1, all_22_1_12) = all_366_2_129 & distinct_points(all_1_4_4, all_1_4_4) = all_366_3_130 & ( ~ (all_366_2_129 = 0) | ~ (all_366_3_130 = 0) | all_366_0_127 = 0 | all_366_1_128 = 0) % 42.60/11.05 | % 42.60/11.05 | Applying alpha-rule on (600) yields: % 42.60/11.05 | (601) apart_point_and_line(all_1_4_4, all_1_1_1) = all_366_0_127 % 42.60/11.05 | (602) distinct_lines(all_1_1_1, all_22_1_12) = all_366_2_129 % 42.60/11.05 | (603) ~ (all_366_2_129 = 0) | ~ (all_366_3_130 = 0) | all_366_0_127 = 0 | all_366_1_128 = 0 % 42.60/11.05 | (604) apart_point_and_line(all_1_4_4, all_22_1_12) = all_366_1_128 % 42.60/11.05 | (605) distinct_points(all_1_4_4, all_1_4_4) = all_366_3_130 % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (533), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (376) all_36_0_28 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (376) can reduce 185 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (185) ~ (all_36_0_28 = 0) % 42.60/11.05 | (609) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_18_1_8) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.05 | % 42.60/11.05 +-Applying beta-rule and splitting (609), into two cases. % 42.60/11.05 |-Branch one: % 42.60/11.05 | (406) all_20_0_9 = 0 % 42.60/11.05 | % 42.60/11.05 | Equations (406) can reduce 159 to: % 42.60/11.05 | (340) $false % 42.60/11.05 | % 42.60/11.05 |-The branch is then unsatisfiable % 42.60/11.05 |-Branch two: % 42.60/11.05 | (159) ~ (all_20_0_9 = 0) % 42.60/11.05 | (613) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & apart_point_and_line(all_1_4_4, all_18_1_8) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (553), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (617) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 | Instantiating (617) with all_387_0_134, all_387_1_135, all_387_2_136 yields: % 42.60/11.06 | (618) apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_0_134 & apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_1_135 & distinct_lines(all_1_1_1, all_1_1_1) = all_387_2_136 & ( ~ (all_387_2_136 = 0) | all_387_0_134 = 0 | all_387_1_135 = 0) % 42.60/11.06 | % 42.60/11.06 | Applying alpha-rule on (618) yields: % 42.60/11.06 | (619) apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_0_134 % 42.60/11.06 | (620) apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_1_135 % 42.60/11.06 | (621) distinct_lines(all_1_1_1, all_1_1_1) = all_387_2_136 % 42.60/11.06 | (622) ~ (all_387_2_136 = 0) | all_387_0_134 = 0 | all_387_1_135 = 0 % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (306), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (454) all_50_0_47 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (454) can reduce 384 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (384) ~ (all_50_0_47 = 0) % 42.60/11.06 | (626) ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (293), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (478) all_52_0_49 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (478) can reduce 219 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (219) ~ (all_52_0_49 = 0) % 42.60/11.06 | (630) all_48_0_45 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_1_2_2) = v1 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (294), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (478) all_52_0_49 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (478) can reduce 219 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (219) ~ (all_52_0_49 = 0) % 42.60/11.06 | (634) all_48_0_45 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_1_1_1) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (269), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (376) all_36_0_28 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (376) can reduce 185 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (185) ~ (all_36_0_28 = 0) % 42.60/11.06 | (638) all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_18_1_8) = v1 & distinct_lines(all_22_1_12, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (270), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (376) all_36_0_28 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (376) can reduce 185 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (185) ~ (all_36_0_28 = 0) % 42.60/11.06 | (642) all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_22_1_12) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (285), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (646) all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_1_1_1) = v1 & distinct_lines(all_18_1_8, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (286), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (650) all_20_0_9 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_18_1_8) = v1 & distinct_lines(all_1_1_1, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (287), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (654) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v3 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_18_1_8, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (288), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (658) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_18_1_8) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (281), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (662) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v1 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_18_1_8, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (282), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (666) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (283), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (670) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_18_1_8) = v1 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_18_1_8, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (284), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (674) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_18_1_8) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (309), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (678) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_18_1_8) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (308), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (406) all_20_0_9 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (406) can reduce 159 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (159) ~ (all_20_0_9 = 0) % 42.60/11.06 | (682) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v2 & apart_point_and_line(all_1_5_5, all_18_1_8) = v3 & distinct_lines(all_18_1_8, all_18_1_8) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (310), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (686) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_18_1_8, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (311), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (690) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_18_1_8, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (312), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (694) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_18_1_8) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_18_1_8) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (485), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (406) all_20_0_9 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (406) can reduce 159 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (159) ~ (all_20_0_9 = 0) % 42.60/11.06 | (698) ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_1_2_2) = v1 & distinct_lines(all_18_1_8, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (634), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (422) all_48_0_45 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (422) can reduce 367 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (367) ~ (all_48_0_45 = 0) % 42.60/11.06 | (702) ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_1_1_1) = v1 & distinct_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (642), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.06 | (406) all_20_0_9 = 0 % 42.60/11.06 | % 42.60/11.06 | Equations (406) can reduce 159 to: % 42.60/11.06 | (340) $false % 42.60/11.06 | % 42.60/11.06 |-The branch is then unsatisfiable % 42.60/11.06 |-Branch two: % 42.60/11.06 | (159) ~ (all_20_0_9 = 0) % 42.60/11.06 | (706) ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_22_1_12) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.60/11.06 | % 42.60/11.06 +-Applying beta-rule and splitting (646), into two cases. % 42.60/11.06 |-Branch one: % 42.60/11.07 | (406) all_20_0_9 = 0 % 42.60/11.07 | % 42.60/11.07 | Equations (406) can reduce 159 to: % 42.60/11.07 | (340) $false % 42.60/11.07 | % 42.60/11.07 |-The branch is then unsatisfiable % 42.60/11.07 |-Branch two: % 42.60/11.07 | (159) ~ (all_20_0_9 = 0) % 42.60/11.07 | (710) ? [v0] : ? [v1] : (convergent_lines(all_18_1_8, all_1_1_1) = v1 & distinct_lines(all_18_1_8, all_1_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.69/11.07 | % 42.69/11.07 +-Applying beta-rule and splitting (650), into two cases. % 42.69/11.07 |-Branch one: % 42.69/11.07 | (406) all_20_0_9 = 0 % 42.69/11.07 | % 42.69/11.07 | Equations (406) can reduce 159 to: % 42.69/11.07 | (340) $false % 42.69/11.07 | % 42.69/11.07 |-The branch is then unsatisfiable % 42.69/11.07 |-Branch two: % 42.69/11.07 | (159) ~ (all_20_0_9 = 0) % 42.69/11.07 | (714) ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_18_1_8) = v1 & distinct_lines(all_1_1_1, all_18_1_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.69/11.07 | % 42.69/11.07 +-Applying beta-rule and splitting (666), into two cases. % 42.69/11.07 |-Branch one: % 42.69/11.07 | (406) all_20_0_9 = 0 % 42.69/11.07 | % 42.69/11.07 | Equations (406) can reduce 159 to: % 42.69/11.07 | (340) $false % 42.69/11.07 | % 42.69/11.07 |-The branch is then unsatisfiable % 42.69/11.07 |-Branch two: % 42.69/11.07 | (159) ~ (all_20_0_9 = 0) % 42.69/11.07 | (718) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.69/11.07 | % 42.69/11.07 | Instantiating (718) with all_505_0_149, all_505_1_150, all_505_2_151 yields: % 42.69/11.07 | (719) apart_point_and_line(all_1_4_4, all_18_1_8) = all_505_0_149 & apart_point_and_line(all_1_4_4, all_1_1_1) = all_505_1_150 & distinct_lines(all_1_1_1, all_18_1_8) = all_505_2_151 & ( ~ (all_505_2_151 = 0) | all_505_0_149 = 0 | all_505_1_150 = 0) % 42.69/11.07 | % 42.69/11.07 | Applying alpha-rule on (719) yields: % 42.69/11.07 | (720) apart_point_and_line(all_1_4_4, all_18_1_8) = all_505_0_149 % 42.69/11.07 | (721) apart_point_and_line(all_1_4_4, all_1_1_1) = all_505_1_150 % 42.69/11.07 | (722) distinct_lines(all_1_1_1, all_18_1_8) = all_505_2_151 % 42.69/11.07 | (723) ~ (all_505_2_151 = 0) | all_505_0_149 = 0 | all_505_1_150 = 0 % 42.69/11.07 | % 42.69/11.07 +-Applying beta-rule and splitting (307), into two cases. % 42.69/11.07 |-Branch one: % 42.69/11.07 | (454) all_50_0_47 = 0 % 42.69/11.07 | % 42.69/11.07 | Equations (454) can reduce 384 to: % 42.69/11.07 | (340) $false % 42.69/11.07 | % 42.69/11.07 |-The branch is then unsatisfiable % 42.69/11.07 |-Branch two: % 42.69/11.07 | (384) ~ (all_50_0_47 = 0) % 42.69/11.07 | (727) all_32_0_24 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_1_2_2) = v1 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.69/11.07 | % 42.69/11.07 +-Applying beta-rule and splitting (313), into two cases. % 42.69/11.07 |-Branch one: % 42.69/11.07 | (368) all_32_0_24 = 0 % 42.69/11.07 | % 42.69/11.07 | Equations (368) can reduce 177 to: % 42.69/11.07 | (340) $false % 42.69/11.07 | % 42.69/11.07 |-The branch is then unsatisfiable % 42.69/11.07 |-Branch two: % 42.69/11.07 | (177) ~ (all_32_0_24 = 0) % 42.69/11.07 | (731) all_26_0_17 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 42.69/11.07 | % 42.69/11.07 +-Applying beta-rule and splitting (727), into two cases. % 42.69/11.07 |-Branch one: % 42.69/11.07 | (368) all_32_0_24 = 0 % 42.69/11.07 | % 42.69/11.07 | Equations (368) can reduce 177 to: % 42.69/11.07 | (340) $false % 42.69/11.07 | % 42.69/11.07 |-The branch is then unsatisfiable % 42.69/11.07 |-Branch two: % 42.69/11.07 | (177) ~ (all_32_0_24 = 0) % 42.69/11.07 | (735) ? [v0] : ? [v1] : (convergent_lines(all_1_1_1, all_1_2_2) = v1 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 42.69/11.07 | % 42.69/11.07 | Instantiating (735) with all_586_0_188, all_586_1_189 yields: % 42.69/11.07 | (736) convergent_lines(all_1_1_1, all_1_2_2) = all_586_0_188 & distinct_lines(all_1_1_1, all_1_2_2) = all_586_1_189 & ( ~ (all_586_1_189 = 0) | all_586_0_188 = 0) % 42.69/11.07 | % 42.69/11.07 | Applying alpha-rule on (736) yields: % 42.69/11.07 | (737) convergent_lines(all_1_1_1, all_1_2_2) = all_586_0_188 % 42.69/11.07 | (738) distinct_lines(all_1_1_1, all_1_2_2) = all_586_1_189 % 42.69/11.07 | (739) ~ (all_586_1_189 = 0) | all_586_0_188 = 0 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (108) with all_1_3_3, all_1_4_4, all_115_1_67, all_1_1_1 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_115_1_67, line_connecting(all_1_3_3, all_1_4_4) = all_1_1_1, yields: % 42.69/11.07 | (740) all_115_1_67 = all_1_1_1 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_1_1, all_387_0_134, all_505_1_150 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_505_1_150, apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_0_134, yields: % 42.69/11.07 | (741) all_505_1_150 = all_387_0_134 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_1_1, all_387_1_135, all_50_0_47 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_1_135, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.69/11.07 | (742) all_387_1_135 = all_50_0_47 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_1_1, all_387_1_135, all_387_0_134 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_0_134, apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_1_135, yields: % 42.69/11.07 | (743) all_387_0_134 = all_387_1_135 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_1_1, all_366_0_127, all_505_1_150 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_505_1_150, apart_point_and_line(all_1_4_4, all_1_1_1) = all_366_0_127, yields: % 42.69/11.07 | (744) all_505_1_150 = all_366_0_127 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_1_1, all_346_1_112, all_115_0_66 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_346_1_112, yields: % 42.69/11.07 | (745) all_346_1_112 = all_115_0_66 | ~ (apart_point_and_line(all_1_4_4, all_1_1_1) = all_115_0_66) % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_1_1, all_346_1_112, all_387_1_135 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_387_1_135, apart_point_and_line(all_1_4_4, all_1_1_1) = all_346_1_112, yields: % 42.69/11.07 | (746) all_387_1_135 = all_346_1_112 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_351_1_116, all_32_0_24 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_351_1_116, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 42.69/11.07 | (747) all_351_1_116 = all_32_0_24 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_351_1_116, all_356_0_119 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_356_0_119, apart_point_and_line(all_1_4_4, all_1_2_2) = all_351_1_116, yields: % 42.69/11.07 | (748) all_356_0_119 = all_351_1_116 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_169_0_80, all_356_0_119 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_356_0_119, apart_point_and_line(all_1_4_4, all_1_2_2) = all_169_0_80, yields: % 42.69/11.07 | (749) all_356_0_119 = all_169_0_80 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_169_1_81, all_351_1_116 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_351_1_116, apart_point_and_line(all_1_4_4, all_1_2_2) = all_169_1_81, yields: % 42.69/11.07 | (750) all_351_1_116 = all_169_1_81 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (105) with all_1_1_1, all_1_2_2, all_586_1_189, 0 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_586_1_189, distinct_lines(all_1_1_1, all_1_2_2) = 0, yields: % 42.69/11.07 | (751) all_586_1_189 = 0 % 42.69/11.07 | % 42.69/11.07 | Combining equations (741,744) yields a new equation: % 42.69/11.07 | (752) all_387_0_134 = all_366_0_127 % 42.69/11.07 | % 42.69/11.07 | Simplifying 752 yields: % 42.69/11.07 | (753) all_387_0_134 = all_366_0_127 % 42.69/11.07 | % 42.69/11.07 | Combining equations (743,753) yields a new equation: % 42.69/11.07 | (754) all_387_1_135 = all_366_0_127 % 42.69/11.07 | % 42.69/11.07 | Simplifying 754 yields: % 42.69/11.07 | (755) all_387_1_135 = all_366_0_127 % 42.69/11.07 | % 42.69/11.07 | Combining equations (742,755) yields a new equation: % 42.69/11.07 | (756) all_366_0_127 = all_50_0_47 % 42.69/11.07 | % 42.69/11.07 | Combining equations (746,755) yields a new equation: % 42.69/11.07 | (757) all_366_0_127 = all_346_1_112 % 42.69/11.07 | % 42.69/11.07 | Combining equations (757,756) yields a new equation: % 42.69/11.07 | (758) all_346_1_112 = all_50_0_47 % 42.69/11.07 | % 42.69/11.07 | Simplifying 758 yields: % 42.69/11.07 | (759) all_346_1_112 = all_50_0_47 % 42.69/11.07 | % 42.69/11.07 | Combining equations (748,749) yields a new equation: % 42.69/11.07 | (760) all_351_1_116 = all_169_0_80 % 42.69/11.07 | % 42.69/11.07 | Simplifying 760 yields: % 42.69/11.07 | (761) all_351_1_116 = all_169_0_80 % 42.69/11.07 | % 42.69/11.07 | Combining equations (750,761) yields a new equation: % 42.69/11.07 | (762) all_169_0_80 = all_169_1_81 % 42.69/11.07 | % 42.69/11.07 | Combining equations (747,761) yields a new equation: % 42.69/11.07 | (763) all_169_0_80 = all_32_0_24 % 42.69/11.07 | % 42.69/11.07 | Combining equations (762,763) yields a new equation: % 42.69/11.07 | (764) all_169_1_81 = all_32_0_24 % 42.69/11.07 | % 42.69/11.07 | Simplifying 764 yields: % 42.69/11.07 | (765) all_169_1_81 = all_32_0_24 % 42.69/11.07 | % 42.69/11.07 | From (740) and (354) follows: % 42.69/11.07 | (766) apart_point_and_line(all_1_4_4, all_1_1_1) = all_115_0_66 % 42.69/11.07 | % 42.69/11.07 | From (765) and (399) follows: % 42.69/11.07 | (248) apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24 % 42.69/11.07 | % 42.69/11.07 | From (751) and (738) follows: % 42.69/11.07 | (338) distinct_lines(all_1_1_1, all_1_2_2) = 0 % 42.69/11.07 | % 42.69/11.07 +-Applying beta-rule and splitting (481), into two cases. % 42.69/11.07 |-Branch one: % 42.69/11.07 | (422) all_48_0_45 = 0 % 42.69/11.07 | % 42.69/11.07 | Equations (422) can reduce 367 to: % 42.69/11.07 | (340) $false % 42.69/11.07 | % 42.69/11.07 |-The branch is then unsatisfiable % 42.69/11.07 |-Branch two: % 42.69/11.07 | (367) ~ (all_48_0_45 = 0) % 42.69/11.07 | (772) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.69/11.07 | % 42.69/11.07 | Instantiating (772) with all_624_0_198, all_624_1_199, all_624_2_200 yields: % 42.69/11.07 | (773) apart_point_and_line(all_1_4_4, all_1_1_1) = all_624_1_199 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_624_0_198 & distinct_lines(all_1_1_1, all_1_2_2) = all_624_2_200 & ( ~ (all_624_2_200 = 0) | all_624_0_198 = 0 | all_624_1_199 = 0) % 42.69/11.07 | % 42.69/11.07 | Applying alpha-rule on (773) yields: % 42.69/11.07 | (774) apart_point_and_line(all_1_4_4, all_1_1_1) = all_624_1_199 % 42.69/11.07 | (775) apart_point_and_line(all_1_4_4, all_1_2_2) = all_624_0_198 % 42.69/11.07 | (776) distinct_lines(all_1_1_1, all_1_2_2) = all_624_2_200 % 42.69/11.07 | (777) ~ (all_624_2_200 = 0) | all_624_0_198 = 0 | all_624_1_199 = 0 % 42.69/11.07 | % 42.69/11.07 +-Applying beta-rule and splitting (745), into two cases. % 42.69/11.07 |-Branch one: % 42.69/11.07 | (778) ~ (apart_point_and_line(all_1_4_4, all_1_1_1) = all_115_0_66) % 42.69/11.07 | % 42.69/11.07 | Using (766) and (778) yields: % 42.69/11.07 | (255) $false % 42.69/11.07 | % 42.69/11.07 |-The branch is then unsatisfiable % 42.69/11.07 |-Branch two: % 42.69/11.07 | (766) apart_point_and_line(all_1_4_4, all_1_1_1) = all_115_0_66 % 42.69/11.07 | (781) all_346_1_112 = all_115_0_66 % 42.69/11.07 | % 42.69/11.07 | Combining equations (759,781) yields a new equation: % 42.69/11.07 | (782) all_115_0_66 = all_50_0_47 % 42.69/11.07 | % 42.69/11.07 | Equations (782) can reduce 352 to: % 42.69/11.07 | (384) ~ (all_50_0_47 = 0) % 42.69/11.07 | % 42.69/11.07 | From (782) and (766) follows: % 42.69/11.07 | (215) apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_1_1, all_624_1_199, all_50_0_47 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_624_1_199, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_47, yields: % 42.69/11.07 | (785) all_624_1_199 = all_50_0_47 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_624_0_198, all_32_0_24 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_624_0_198, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 42.69/11.07 | (786) all_624_0_198 = all_32_0_24 % 42.69/11.07 | % 42.69/11.07 | Instantiating formula (105) with all_1_1_1, all_1_2_2, all_624_2_200, 0 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_624_2_200, distinct_lines(all_1_1_1, all_1_2_2) = 0, yields: % 42.69/11.07 | (787) all_624_2_200 = 0 % 42.69/11.07 | % 42.69/11.07 +-Applying beta-rule and splitting (461), into two cases. % 42.69/11.07 |-Branch one: % 42.69/11.07 | (454) all_50_0_47 = 0 % 42.69/11.07 | % 42.69/11.07 | Equations (454) can reduce 384 to: % 42.69/11.07 | (340) $false % 42.69/11.07 | % 42.69/11.07 |-The branch is then unsatisfiable % 42.69/11.07 |-Branch two: % 42.69/11.07 | (384) ~ (all_50_0_47 = 0) % 42.69/11.07 | (791) all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.69/11.07 | % 42.69/11.08 +-Applying beta-rule and splitting (791), into two cases. % 42.69/11.08 |-Branch one: % 42.69/11.08 | (368) all_32_0_24 = 0 % 42.69/11.08 | % 42.69/11.08 | Equations (368) can reduce 177 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (177) ~ (all_32_0_24 = 0) % 42.69/11.08 | (795) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 42.69/11.08 | % 42.69/11.08 +-Applying beta-rule and splitting (777), into two cases. % 42.69/11.08 |-Branch one: % 42.69/11.08 | (796) ~ (all_624_2_200 = 0) % 42.69/11.08 | % 42.69/11.08 | Equations (787) can reduce 796 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (787) all_624_2_200 = 0 % 42.69/11.08 | (799) all_624_0_198 = 0 | all_624_1_199 = 0 % 42.69/11.08 | % 42.69/11.08 +-Applying beta-rule and splitting (799), into two cases. % 42.69/11.08 |-Branch one: % 42.69/11.08 | (800) all_624_0_198 = 0 % 42.69/11.08 | % 42.69/11.08 | Combining equations (786,800) yields a new equation: % 42.69/11.08 | (801) all_32_0_24 = 0 % 42.69/11.08 | % 42.69/11.08 | Simplifying 801 yields: % 42.69/11.08 | (368) all_32_0_24 = 0 % 42.69/11.08 | % 42.69/11.08 | Equations (368) can reduce 177 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (804) ~ (all_624_0_198 = 0) % 42.69/11.08 | (805) all_624_1_199 = 0 % 42.69/11.08 | % 42.69/11.08 | Combining equations (785,805) yields a new equation: % 42.69/11.08 | (806) all_50_0_47 = 0 % 42.69/11.08 | % 42.69/11.08 | Simplifying 806 yields: % 42.69/11.08 | (454) all_50_0_47 = 0 % 42.69/11.08 | % 42.69/11.08 | Equations (454) can reduce 384 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (454) all_50_0_47 = 0 % 42.69/11.08 | (810) ~ (all_50_1_48 = 0) % 42.69/11.08 | % 42.69/11.08 | Equations (332) can reduce 810 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (422) all_48_0_45 = 0 % 42.69/11.08 | (813) ~ (all_48_1_46 = 0) % 42.69/11.08 | % 42.69/11.08 | Equations (331) can reduce 813 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (815) ~ (distinct_lines(all_1_1_1, all_1_2_2) = 0) % 42.69/11.08 | (339) all_26_0_17 = 0 % 42.69/11.08 | % 42.69/11.08 | Equations (339) can reduce 167 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (818) all_34_0_26 = 0 % 42.69/11.08 | (819) ~ (all_34_1_27 = 0) % 42.69/11.08 | % 42.69/11.08 | Equations (239) can reduce 819 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (821) all_42_0_35 = 0 % 42.69/11.08 | (822) ~ (all_42_1_36 = 0) % 42.69/11.08 | % 42.69/11.08 | Equations (232) can reduce 822 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 |-Branch two: % 42.69/11.08 | (824) ~ (apart_point_and_line(all_1_5_5, all_1_1_1) = 0) % 42.69/11.08 | (825) all_1_0_0 = 0 % 42.69/11.08 | % 42.69/11.08 | Equations (825) can reduce 135 to: % 42.69/11.08 | (340) $false % 42.69/11.08 | % 42.69/11.08 |-The branch is then unsatisfiable % 42.69/11.08 % SZS output end Proof for theBenchmark % 42.69/11.08 % 42.69/11.08 10496ms %------------------------------------------------------------------------------