%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO190+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 03:48:27 EDT 2022 % Result : Theorem 31.11s 8.13s % Output : Proof 38.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : GEO190+3 : TPTP v8.1.0. Released v4.0.0. % 0.00/0.10 % Command : ePrincess-casc -timeout=%d %s % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 600 % 0.10/0.29 % DateTime : Fri Jun 17 20:44:46 EDT 2022 % 0.10/0.29 % CPUTime : % 0.14/0.48 ____ _ % 0.14/0.48 ___ / __ \_____(_)___ ________ __________ % 0.14/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.14/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.14/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.14/0.48 % 0.14/0.48 A Theorem Prover for First-Order Logic % 0.14/0.48 (ePrincess v.1.0) % 0.14/0.48 % 0.14/0.48 (c) Philipp Rümmer, 2009-2015 % 0.14/0.48 (c) Peter Backeman, 2014-2015 % 0.14/0.48 (contributions by Angelo Brillout, Peter Baumgartner) % 0.14/0.48 Free software under GNU Lesser General Public License (LGPL). % 0.14/0.48 Bug reports to peter@backeman.se % 0.14/0.48 % 0.14/0.48 For more information, visit http://user.uu.se/~petba168/breu/ % 0.14/0.48 % 0.14/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.14/0.52 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.44/0.81 Prover 0: Preprocessing ... % 2.17/1.02 Prover 0: Warning: ignoring some quantifiers % 2.17/1.05 Prover 0: Constructing countermodel ... % 11.77/3.34 Prover 0: gave up % 11.77/3.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 11.77/3.38 Prover 1: Preprocessing ... % 12.71/3.50 Prover 1: Constructing countermodel ... % 12.79/3.54 Prover 1: gave up % 12.79/3.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 12.79/3.58 Prover 2: Preprocessing ... % 13.62/3.75 Prover 2: Warning: ignoring some quantifiers % 13.62/3.76 Prover 2: Constructing countermodel ... % 21.05/5.50 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 21.21/5.53 Prover 3: Preprocessing ... % 21.21/5.55 Prover 3: Warning: ignoring some quantifiers % 21.21/5.55 Prover 3: Constructing countermodel ... % 26.23/6.90 Prover 3: gave up % 26.23/6.90 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 26.23/6.93 Prover 4: Preprocessing ... % 26.68/7.03 Prover 4: Warning: ignoring some quantifiers % 26.68/7.03 Prover 4: Constructing countermodel ... % 29.46/7.81 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 29.83/7.85 Prover 5: Preprocessing ... % 30.14/7.94 Prover 5: Constructing countermodel ... % 31.11/8.13 Prover 5: proved (315ms) % 31.11/8.13 Prover 2: stopped % 31.11/8.13 Prover 4: stopped % 31.11/8.13 % 31.11/8.13 No countermodel exists, formula is valid % 31.11/8.13 % SZS status Theorem for theBenchmark % 31.11/8.13 % 31.11/8.13 Generating proof ... found it (size 506) % 37.17/9.61 % 37.17/9.61 % SZS output start Proof for theBenchmark % 37.17/9.61 Assumed formulas after preprocessing and simplification: % 37.17/9.61 | (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, v4) = v5 & incident_point_and_line(v2, v3) = 0 & line_connecting(v1, v0) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0) % 37.17/9.69 | Applying alpha-rule on (0) yields: % 37.17/9.69 | (1) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) % 37.17/9.69 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 37.17/9.69 | (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))) % 37.17/9.69 | (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))) % 37.17/9.69 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 37.17/9.69 | (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)) % 37.17/9.69 | (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))) % 37.64/9.69 | (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)))) % 37.64/9.69 | (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))) % 37.64/9.69 | (10) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 37.64/9.69 | (11) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 37.64/9.69 | (12) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 37.64/9.69 | (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)))) % 37.64/9.70 | (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)))) % 37.64/9.70 | (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)))) % 37.64/9.70 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 37.64/9.70 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 37.64/9.70 | (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)))) % 37.64/9.70 | (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))) % 37.64/9.70 | (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)))) % 37.64/9.70 | (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))) % 37.64/9.70 | (22) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & parallel_through_point(v0, v1) = v2)) % 37.64/9.70 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 37.64/9.70 | (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) % 37.64/9.70 | (25) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 37.64/9.70 | (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)))) % 37.64/9.70 | (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)) % 37.64/9.70 | (28) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 37.64/9.70 | (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)) % 37.64/9.70 | (30) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) % 37.64/9.70 | (31) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 37.64/9.70 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 37.64/9.70 | (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)))) % 37.64/9.70 | (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))) % 37.64/9.70 | (35) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 37.64/9.70 | (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)) % 37.64/9.70 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) % 37.64/9.71 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 37.64/9.71 | (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)))) % 37.64/9.71 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 37.64/9.71 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 37.64/9.71 | (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) % 37.64/9.71 | (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))) % 37.64/9.71 | (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)))) % 37.64/9.71 | (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))) % 37.64/9.71 | (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))) % 37.64/9.71 | (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)))) % 37.64/9.71 | (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)))) % 37.64/9.71 | (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)))) % 37.64/9.71 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 37.64/9.71 | (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)) % 37.64/9.71 | (52) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) % 37.64/9.71 | (53) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 37.64/9.71 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 37.64/9.71 | (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))) % 37.64/9.71 | (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)) % 37.64/9.71 | (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)) % 37.64/9.71 | (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)))) % 37.64/9.71 | (59) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v2, v4) = v5 & incident_point_and_line(v2, v3) = 0 & line_connecting(v1, v0) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0) % 37.64/9.71 | (60) ! [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))) % 37.64/9.71 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) % 37.64/9.71 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 37.64/9.71 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 37.64/9.71 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 37.64/9.71 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 37.64/9.71 | (66) ! [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))) % 37.64/9.72 | (67) ! [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))) % 37.64/9.72 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) % 37.64/9.72 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 37.64/9.72 | (70) ! [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))) % 37.64/9.72 | (71) ! [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)))) % 37.64/9.72 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 37.64/9.72 | (73) ! [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))) % 37.64/9.72 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 37.64/9.72 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) % 37.64/9.72 | (76) ! [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)))) % 37.64/9.72 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 37.64/9.72 | (78) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) % 37.64/9.72 | (79) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 37.64/9.72 | (80) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 37.64/9.72 | (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))) % 37.64/9.72 | (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) % 37.64/9.72 | (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)))) % 37.64/9.72 | (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)))) % 37.64/9.72 | (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)))) % 37.64/9.72 | (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)))) % 37.64/9.72 | (87) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 37.64/9.72 | (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))) % 37.64/9.72 | (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)))) % 37.64/9.72 | (90) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (line(v2) = 0 & orthogonal_through_point(v0, v1) = v2)) % 37.64/9.72 | (91) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) % 37.64/9.72 | (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)))) % 37.64/9.72 | (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)))) % 37.64/9.72 | (94) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 37.64/9.72 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 37.64/9.72 | (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))) % 37.64/9.72 | (97) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 37.64/9.72 | (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)))) % 37.64/9.72 | (99) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) % 37.64/9.72 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 37.64/9.72 | (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)))) % 37.64/9.73 | (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))) % 37.64/9.73 | (103) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 37.64/9.73 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 37.64/9.73 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 37.64/9.73 | (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))) % 37.64/9.73 | (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)))) % 37.64/9.73 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 37.64/9.73 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 37.64/9.73 | (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)))) % 37.64/9.73 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 37.64/9.73 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 37.64/9.73 | (113) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) % 37.64/9.73 | (114) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 37.64/9.73 | (115) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) % 37.64/9.73 | (116) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 37.64/9.73 | (117) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 37.64/9.73 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 37.64/9.73 | (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)))) % 37.64/9.73 | (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))) % 37.64/9.73 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 37.64/9.73 | (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))) % 37.64/9.73 | (123) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) % 37.64/9.73 | (124) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 37.64/9.73 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) % 37.64/9.73 | (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))) % 37.64/9.73 | (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) % 37.64/9.73 | % 37.64/9.73 | Instantiating (59) 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: % 37.64/9.73 | (128) ~ (all_1_0_0 = 0) & incident_point_and_line(all_1_3_3, all_1_1_1) = all_1_0_0 & incident_point_and_line(all_1_3_3, all_1_2_2) = 0 & line_connecting(all_1_4_4, all_1_5_5) = 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 % 37.64/9.73 | % 37.64/9.73 | Applying alpha-rule on (128) yields: % 37.64/9.73 | (129) distinct_points(all_1_4_4, all_1_3_3) = 0 % 37.64/9.73 | (130) incident_point_and_line(all_1_3_3, all_1_2_2) = 0 % 37.64/9.73 | (131) incident_point_and_line(all_1_3_3, all_1_1_1) = all_1_0_0 % 37.64/9.73 | (132) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2 % 37.64/9.73 | (133) distinct_points(all_1_5_5, all_1_3_3) = 0 % 37.64/9.73 | (134) distinct_points(all_1_5_5, all_1_4_4) = 0 % 37.64/9.73 | (135) ~ (all_1_0_0 = 0) % 37.64/9.73 | (136) line_connecting(all_1_4_4, all_1_5_5) = all_1_1_1 % 37.64/9.73 | % 37.64/9.73 | Instantiating formula (87) with all_1_5_5 yields: % 37.64/9.73 | (137) ~ (distinct_points(all_1_5_5, all_1_5_5) = 0) % 37.64/9.73 | % 37.64/9.73 | Instantiating formula (62) with all_1_0_0, all_1_1_1, all_1_3_3 and discharging atoms incident_point_and_line(all_1_3_3, all_1_1_1) = all_1_0_0, yields: % 37.64/9.73 | (138) all_1_0_0 = 0 | apart_point_and_line(all_1_3_3, all_1_1_1) = 0 % 37.64/9.73 | % 37.64/9.73 | 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: % 37.64/9.73 | (139) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_3_3, all_1_2_2) = v0) % 37.64/9.73 | % 37.64/9.73 | Instantiating formula (96) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms line_connecting(all_1_4_4, all_1_5_5) = all_1_1_1, yields: % 37.64/9.73 | (140) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_4_4) = v0 & point(all_1_5_5) = v1 & line(all_1_1_1) = v3 & distinct_points(all_1_4_4, all_1_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 37.64/9.73 | % 37.64/9.73 | Instantiating formula (39) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms line_connecting(all_1_4_4, all_1_5_5) = all_1_1_1, yields: % 37.64/9.73 | (141) ? [v0] : ? [v1] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 37.64/9.73 | % 37.64/9.73 | Instantiating formula (15) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms line_connecting(all_1_4_4, all_1_5_5) = all_1_1_1, yields: % 37.64/9.73 | (142) ? [v0] : ? [v1] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 37.64/9.73 | % 37.64/9.73 | 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: % 37.64/9.73 | (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)) % 37.64/9.73 | % 37.64/9.73 | 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: % 37.64/9.73 | (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))) % 37.64/9.73 | % 37.64/9.73 | 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: % 37.64/9.73 | (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))) % 37.64/9.73 | % 37.64/9.73 | Instantiating formula (120) with all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 37.64/9.74 | (146) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_3_3) = v1 & point(all_1_4_4) = v0 & line(v2) = v3 & line_connecting(all_1_4_4, all_1_3_3) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 37.64/9.74 | % 37.64/9.74 | 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: % 37.64/9.74 | (147) ? [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) % 37.64/9.74 | % 37.64/9.74 | 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: % 37.64/9.74 | (148) ? [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) % 37.64/9.74 | % 37.64/9.74 | 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: % 37.64/9.74 | (149) ? [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)) % 37.64/9.74 | % 37.64/9.74 | 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: % 37.64/9.74 | (150) ? [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) % 37.64/9.74 | % 37.64/9.74 | 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: % 37.64/9.74 | (151) ? [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) % 37.64/9.74 | % 37.64/9.74 | 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: % 37.64/9.74 | (152) ? [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)) % 37.64/9.74 | % 37.64/9.74 | 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: % 37.64/9.74 | (153) ? [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) % 37.64/9.74 | % 37.64/9.74 | 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: % 37.64/9.74 | (154) ? [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) % 37.64/9.74 | % 37.64/9.74 | Instantiating (151) with all_18_0_7, all_18_1_8 yields: % 37.64/9.74 | (155) ~ (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 % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (155) yields: % 37.64/9.74 | (156) ~ (all_18_0_7 = 0) % 37.64/9.74 | (157) line_connecting(all_1_5_5, all_1_3_3) = all_18_1_8 % 37.64/9.74 | (158) apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7 % 37.64/9.74 | % 37.64/9.74 | Instantiating (150) with all_20_0_9, all_20_1_10 yields: % 37.64/9.74 | (159) ~ (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 % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (159) yields: % 37.64/9.74 | (160) ~ (all_20_0_9 = 0) % 37.64/9.74 | (161) line_connecting(all_1_5_5, all_1_3_3) = all_20_1_10 % 37.64/9.74 | (162) apart_point_and_line(all_1_3_3, all_20_1_10) = all_20_0_9 % 37.64/9.74 | % 37.64/9.74 | Instantiating (148) with all_22_0_11, all_22_1_12 yields: % 37.64/9.74 | (163) ~ (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 % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (163) yields: % 37.64/9.74 | (164) ~ (all_22_0_11 = 0) % 37.64/9.74 | (165) line_connecting(all_1_4_4, all_1_3_3) = all_22_1_12 % 37.64/9.74 | (166) apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11 % 37.64/9.74 | % 37.64/9.74 | Instantiating (146) with all_24_0_13, all_24_1_14, all_24_2_15, all_24_3_16 yields: % 37.64/9.74 | (167) point(all_1_3_3) = all_24_2_15 & point(all_1_4_4) = all_24_3_16 & line(all_24_1_14) = all_24_0_13 & line_connecting(all_1_4_4, all_1_3_3) = all_24_1_14 & ( ~ (all_24_2_15 = 0) | ~ (all_24_3_16 = 0) | all_24_0_13 = 0) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (167) yields: % 37.64/9.74 | (168) line_connecting(all_1_4_4, all_1_3_3) = all_24_1_14 % 37.64/9.74 | (169) point(all_1_3_3) = all_24_2_15 % 37.64/9.74 | (170) point(all_1_4_4) = all_24_3_16 % 37.64/9.74 | (171) ~ (all_24_2_15 = 0) | ~ (all_24_3_16 = 0) | all_24_0_13 = 0 % 37.64/9.74 | (172) line(all_24_1_14) = all_24_0_13 % 37.64/9.74 | % 37.64/9.74 | Instantiating (154) with all_26_0_17, all_26_1_18 yields: % 37.64/9.74 | (173) ~ (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 % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (173) yields: % 37.64/9.74 | (174) ~ (all_26_0_17 = 0) % 37.64/9.74 | (175) line_connecting(all_1_5_5, all_1_4_4) = all_26_1_18 % 37.64/9.74 | (176) apart_point_and_line(all_1_5_5, all_26_1_18) = all_26_0_17 % 37.64/9.74 | % 37.64/9.74 | Instantiating (152) with all_28_0_19, all_28_1_20, all_28_2_21, all_28_3_22 yields: % 37.64/9.74 | (177) 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) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (177) yields: % 37.64/9.74 | (178) point(all_1_5_5) = all_28_3_22 % 37.64/9.74 | (179) point(all_1_4_4) = all_28_2_21 % 37.64/9.74 | (180) line_connecting(all_1_5_5, all_1_4_4) = all_28_1_20 % 37.64/9.74 | (181) ~ (all_28_2_21 = 0) | ~ (all_28_3_22 = 0) | all_28_0_19 = 0 % 37.64/9.74 | (182) line(all_28_1_20) = all_28_0_19 % 37.64/9.74 | % 37.64/9.74 | Instantiating (153) with all_32_0_24, all_32_1_25 yields: % 37.64/9.74 | (183) ~ (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 % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (183) yields: % 37.64/9.74 | (184) ~ (all_32_0_24 = 0) % 37.64/9.74 | (185) line_connecting(all_1_5_5, all_1_4_4) = all_32_1_25 % 37.64/9.74 | (186) apart_point_and_line(all_1_4_4, all_32_1_25) = all_32_0_24 % 37.64/9.74 | % 37.64/9.74 | Instantiating (145) with all_34_0_26, all_34_1_27 yields: % 37.64/9.74 | (187) 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)) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (187) yields: % 37.64/9.74 | (188) apart_point_and_line(all_1_5_5, all_1_2_2) = all_34_0_26 % 37.64/9.74 | (189) distinct_points(all_1_5_5, all_1_4_4) = all_34_1_27 % 37.64/9.74 | (190) ~ (all_34_0_26 = 0) | ~ (all_34_1_27 = 0) % 37.64/9.74 | % 37.64/9.74 | Instantiating (147) with all_36_0_28, all_36_1_29 yields: % 37.64/9.74 | (191) ~ (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 % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (191) yields: % 37.64/9.74 | (192) ~ (all_36_0_28 = 0) % 37.64/9.74 | (193) line_connecting(all_1_4_4, all_1_3_3) = all_36_1_29 % 37.64/9.74 | (194) apart_point_and_line(all_1_3_3, all_36_1_29) = all_36_0_28 % 37.64/9.74 | % 37.64/9.74 | Instantiating (149) with all_38_0_30, all_38_1_31, all_38_2_32, all_38_3_33 yields: % 37.64/9.74 | (195) 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) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (195) yields: % 37.64/9.74 | (196) line_connecting(all_1_5_5, all_1_3_3) = all_38_1_31 % 37.64/9.74 | (197) line(all_38_1_31) = all_38_0_30 % 37.64/9.74 | (198) point(all_1_3_3) = all_38_2_32 % 37.64/9.74 | (199) point(all_1_5_5) = all_38_3_33 % 37.64/9.74 | (200) ~ (all_38_2_32 = 0) | ~ (all_38_3_33 = 0) | all_38_0_30 = 0 % 37.64/9.74 | % 37.64/9.74 | Instantiating (144) with all_42_0_35, all_42_1_36 yields: % 37.64/9.74 | (201) 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)) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (201) yields: % 37.64/9.74 | (202) apart_point_and_line(all_1_4_4, all_1_2_2) = all_42_0_35 % 37.64/9.74 | (203) distinct_points(all_1_5_5, all_1_4_4) = all_42_1_36 % 37.64/9.74 | (204) ~ (all_42_0_35 = 0) | ~ (all_42_1_36 = 0) % 37.64/9.74 | % 37.64/9.74 | Instantiating (143) with all_44_0_37, all_44_1_38, all_44_2_39, all_44_3_40 yields: % 37.64/9.74 | (205) 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) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (205) yields: % 37.64/9.74 | (206) line(all_1_2_2) = all_44_0_37 % 37.64/9.74 | (207) point(all_1_5_5) = all_44_3_40 % 37.64/9.74 | (208) distinct_points(all_1_5_5, all_1_4_4) = all_44_1_38 % 37.64/9.74 | (209) ~ (all_44_1_38 = 0) | ~ (all_44_2_39 = 0) | ~ (all_44_3_40 = 0) | all_44_0_37 = 0 % 37.64/9.74 | (210) point(all_1_4_4) = all_44_2_39 % 37.64/9.74 | % 37.64/9.74 | Instantiating (140) with all_46_0_41, all_46_1_42, all_46_2_43, all_46_3_44 yields: % 37.64/9.74 | (211) point(all_1_4_4) = all_46_3_44 & point(all_1_5_5) = all_46_2_43 & line(all_1_1_1) = all_46_0_41 & distinct_points(all_1_4_4, all_1_5_5) = all_46_1_42 & ( ~ (all_46_1_42 = 0) | ~ (all_46_2_43 = 0) | ~ (all_46_3_44 = 0) | all_46_0_41 = 0) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (211) yields: % 37.64/9.74 | (212) ~ (all_46_1_42 = 0) | ~ (all_46_2_43 = 0) | ~ (all_46_3_44 = 0) | all_46_0_41 = 0 % 37.64/9.74 | (213) distinct_points(all_1_4_4, all_1_5_5) = all_46_1_42 % 37.64/9.74 | (214) point(all_1_5_5) = all_46_2_43 % 37.64/9.74 | (215) line(all_1_1_1) = all_46_0_41 % 37.64/9.74 | (216) point(all_1_4_4) = all_46_3_44 % 37.64/9.74 | % 37.64/9.74 | Instantiating (139) with all_48_0_45 yields: % 37.64/9.74 | (217) ~ (all_48_0_45 = 0) & apart_point_and_line(all_1_3_3, all_1_2_2) = all_48_0_45 % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (217) yields: % 37.64/9.74 | (218) ~ (all_48_0_45 = 0) % 37.64/9.74 | (219) apart_point_and_line(all_1_3_3, all_1_2_2) = all_48_0_45 % 37.64/9.74 | % 37.64/9.74 | Instantiating (142) with all_50_0_46, all_50_1_47 yields: % 37.64/9.74 | (220) apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46 & distinct_points(all_1_4_4, all_1_5_5) = all_50_1_47 & ( ~ (all_50_0_46 = 0) | ~ (all_50_1_47 = 0)) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (220) yields: % 37.64/9.74 | (221) apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46 % 37.64/9.74 | (222) distinct_points(all_1_4_4, all_1_5_5) = all_50_1_47 % 37.64/9.74 | (223) ~ (all_50_0_46 = 0) | ~ (all_50_1_47 = 0) % 37.64/9.74 | % 37.64/9.74 | Instantiating (141) with all_52_0_48, all_52_1_49 yields: % 37.64/9.74 | (224) apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48 & distinct_points(all_1_4_4, all_1_5_5) = all_52_1_49 & ( ~ (all_52_0_48 = 0) | ~ (all_52_1_49 = 0)) % 37.64/9.74 | % 37.64/9.74 | Applying alpha-rule on (224) yields: % 37.64/9.74 | (225) apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48 % 37.64/9.75 | (226) distinct_points(all_1_4_4, all_1_5_5) = all_52_1_49 % 37.64/9.75 | (227) ~ (all_52_0_48 = 0) | ~ (all_52_1_49 = 0) % 37.64/9.75 | % 37.64/9.75 +-Applying beta-rule and splitting (138), into two cases. % 37.64/9.75 |-Branch one: % 37.64/9.75 | (228) apart_point_and_line(all_1_3_3, all_1_1_1) = 0 % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (108) with all_1_4_4, all_1_3_3, all_24_1_14, 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_24_1_14, yields: % 37.64/9.75 | (229) all_36_1_29 = all_24_1_14 % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (230) all_36_1_29 = all_22_1_12 % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (231) all_38_1_31 = all_20_1_10 % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (232) all_38_1_31 = all_18_1_8 % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (108) with all_1_5_5, all_1_4_4, all_32_1_25, all_1_2_2 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_1_2_2, yields: % 37.64/9.75 | (233) all_32_1_25 = all_1_2_2 % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (234) all_32_1_25 = all_28_1_20 % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (108) with all_1_5_5, all_1_4_4, all_26_1_18, all_28_1_20 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_26_1_18, yields: % 37.64/9.75 | (235) all_28_1_20 = all_26_1_18 % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (236) all_42_0_35 = all_32_0_24 | ~ (apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24) % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (237) all_34_0_26 = all_26_0_17 | ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17) % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (104) with all_1_4_4, all_1_5_5, all_50_1_47, all_52_1_49 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_52_1_49, distinct_points(all_1_4_4, all_1_5_5) = all_50_1_47, yields: % 37.64/9.75 | (238) all_52_1_49 = all_50_1_47 % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (104) with all_1_4_4, all_1_5_5, all_46_1_42, all_52_1_49 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_52_1_49, distinct_points(all_1_4_4, all_1_5_5) = all_46_1_42, yields: % 37.64/9.75 | (239) all_52_1_49 = all_46_1_42 % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (104) with all_1_5_5, all_1_4_4, all_44_1_38, 0 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) = 0, yields: % 37.64/9.75 | (240) all_44_1_38 = 0 % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (241) all_44_1_38 = all_42_1_36 % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (104) with all_1_5_5, all_1_4_4, all_34_1_27, all_42_1_36 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) = all_34_1_27, yields: % 37.64/9.75 | (242) all_42_1_36 = all_34_1_27 % 37.64/9.75 | % 37.64/9.75 | Combining equations (238,239) yields a new equation: % 37.64/9.75 | (243) all_50_1_47 = all_46_1_42 % 37.64/9.75 | % 37.64/9.75 | Simplifying 243 yields: % 37.64/9.75 | (244) all_50_1_47 = all_46_1_42 % 37.64/9.75 | % 37.64/9.75 | Combining equations (241,240) yields a new equation: % 37.64/9.75 | (245) all_42_1_36 = 0 % 37.64/9.75 | % 37.64/9.75 | Simplifying 245 yields: % 37.64/9.75 | (246) all_42_1_36 = 0 % 37.64/9.75 | % 37.64/9.75 | Combining equations (242,246) yields a new equation: % 37.64/9.75 | (247) all_34_1_27 = 0 % 37.64/9.75 | % 37.64/9.75 | Simplifying 247 yields: % 37.64/9.75 | (248) all_34_1_27 = 0 % 37.64/9.75 | % 37.64/9.75 | Combining equations (232,231) yields a new equation: % 37.64/9.75 | (249) all_20_1_10 = all_18_1_8 % 37.64/9.75 | % 37.64/9.75 | Combining equations (230,229) yields a new equation: % 37.64/9.75 | (250) all_24_1_14 = all_22_1_12 % 37.64/9.75 | % 37.64/9.75 | Combining equations (234,233) yields a new equation: % 37.64/9.75 | (251) all_28_1_20 = all_1_2_2 % 37.64/9.75 | % 37.64/9.75 | Simplifying 251 yields: % 37.64/9.75 | (252) all_28_1_20 = all_1_2_2 % 37.64/9.75 | % 37.64/9.75 | Combining equations (252,235) yields a new equation: % 37.64/9.75 | (253) all_26_1_18 = all_1_2_2 % 37.64/9.75 | % 37.64/9.75 | Combining equations (250,229) yields a new equation: % 37.64/9.75 | (230) all_36_1_29 = all_22_1_12 % 37.64/9.75 | % 37.64/9.75 | From (230) and (194) follows: % 37.64/9.75 | (255) apart_point_and_line(all_1_3_3, all_22_1_12) = all_36_0_28 % 37.64/9.75 | % 37.64/9.75 | From (249) and (162) follows: % 37.64/9.75 | (256) apart_point_and_line(all_1_3_3, all_18_1_8) = all_20_0_9 % 37.64/9.75 | % 37.64/9.75 | From (233) and (186) follows: % 37.64/9.75 | (257) apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24 % 37.64/9.75 | % 37.64/9.75 | From (253) and (176) follows: % 37.64/9.75 | (258) apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17 % 37.64/9.75 | % 37.64/9.75 | From (244) and (222) follows: % 37.64/9.75 | (213) distinct_points(all_1_4_4, all_1_5_5) = all_46_1_42 % 37.64/9.75 | % 37.64/9.75 | From (248) and (189) follows: % 37.64/9.75 | (134) distinct_points(all_1_5_5, all_1_4_4) = 0 % 37.64/9.75 | % 37.64/9.75 +-Applying beta-rule and splitting (237), into two cases. % 37.64/9.75 |-Branch one: % 37.64/9.75 | (261) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17) % 37.64/9.75 | % 37.64/9.75 | Using (258) and (261) yields: % 37.64/9.75 | (262) $false % 37.64/9.75 | % 37.64/9.75 |-The branch is then unsatisfiable % 37.64/9.75 |-Branch two: % 37.64/9.75 | (258) apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17 % 37.64/9.75 | (264) all_34_0_26 = all_26_0_17 % 37.64/9.75 | % 37.64/9.75 | From (264) and (188) follows: % 37.64/9.75 | (258) apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17 % 37.64/9.75 | % 37.64/9.75 +-Applying beta-rule and splitting (236), into two cases. % 37.64/9.75 |-Branch one: % 37.64/9.75 | (266) ~ (apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24) % 37.64/9.75 | % 37.64/9.75 | Using (257) and (266) yields: % 37.64/9.75 | (262) $false % 37.64/9.75 | % 37.64/9.75 |-The branch is then unsatisfiable % 37.64/9.75 |-Branch two: % 37.64/9.75 | (257) apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24 % 37.64/9.75 | (269) all_42_0_35 = all_32_0_24 % 37.64/9.75 | % 37.64/9.75 | From (269) and (202) follows: % 37.64/9.75 | (257) apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24 % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (67) with all_36_0_28, all_36_0_28, all_22_1_12, 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, distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 37.64/9.75 | (271) 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_22_1_12) = v1 & distinct_lines(all_22_1_12, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (272) 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)) % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (273) 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)) % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (67) 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: % 37.64/9.75 | (274) 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)) % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (67) with all_36_0_28, all_20_0_9, all_22_1_12, all_18_1_8, 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: % 37.64/9.75 | (275) 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)) % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (67) with all_20_0_9, all_36_0_28, all_18_1_8, 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_18_1_8) = all_20_0_9, distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 37.64/9.75 | (276) all_36_0_28 = 0 | all_20_0_9 = 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_18_1_8) = v2 & distinct_lines(all_22_1_12, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.75 | % 37.64/9.75 | Instantiating formula (67) with all_36_0_28, all_20_0_9, all_22_1_12, all_18_1_8, 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_18_1_8) = all_20_0_9, distinct_points(all_1_5_5, all_1_3_3) = 0, yields: % 37.64/9.75 | (277) all_36_0_28 = 0 | all_20_0_9 = 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_18_1_8) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.75 | % 37.64/9.75 | 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: % 37.64/9.75 | (278) 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)) % 37.64/9.76 | % 37.64/9.76 | 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: % 37.64/9.76 | (279) 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (3) with all_36_0_28, all_20_0_9, all_22_1_12, all_18_1_8, 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_18_1_8) = all_20_0_9, yields: % 37.64/9.76 | (280) all_36_0_28 = 0 | all_20_0_9 = 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_18_1_8) = v3 & distinct_lines(all_18_1_8, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (88) with all_20_0_9, all_36_0_28, all_22_1_12, all_18_1_8, 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_18_1_8) = all_20_0_9, yields: % 37.64/9.76 | (281) all_36_0_28 = 0 | all_20_0_9 = 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_18_1_8) = v2 & distinct_lines(all_18_1_8, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (127) with 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) = 0, apart_point_and_line(all_1_3_3, all_1_2_2) = all_48_0_45, yields: % 37.64/9.76 | (282) all_48_0_45 = 0 | distinct_lines(all_1_1_1, all_1_2_2) = 0 % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (3) with all_22_0_11, all_48_0_45, 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_3_3, all_1_2_2) = all_48_0_45, apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, yields: % 37.64/9.76 | (283) all_48_0_45 = 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_1_2_2, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (3) with all_48_0_45, 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_48_0_45, apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, yields: % 37.64/9.76 | (284) all_48_0_45 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (88) with all_22_0_11, all_48_0_45, 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_48_0_45, apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, yields: % 37.64/9.76 | (285) all_48_0_45 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (88) with all_48_0_45, all_22_0_11, all_22_1_12, 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_48_0_45, apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, yields: % 37.64/9.76 | (286) all_48_0_45 = 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_1_2_2, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (67) with all_22_0_11, all_22_0_11, all_22_1_12, all_22_1_12, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_22_1_12) = all_22_0_11, distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 37.64/9.76 | (287) all_22_0_11 = 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_22_1_12) = v1 & distinct_lines(all_22_1_12, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (3) with all_50_0_46, all_36_0_28, 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_3_3, all_22_1_12) = all_36_0_28, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46, yields: % 37.64/9.76 | (288) all_50_0_46 = 0 | all_36_0_28 = 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_22_1_12) = v3 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (3) with all_36_0_28, all_50_0_46, all_22_1_12, all_1_1_1, 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_4_4, all_1_1_1) = all_50_0_46, yields: % 37.64/9.76 | (289) all_50_0_46 = 0 | all_36_0_28 = 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_22_1_12) = v2 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (88) with all_50_0_46, all_36_0_28, all_22_1_12, all_1_1_1, 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_4_4, all_1_1_1) = all_50_0_46, yields: % 37.64/9.76 | (290) all_50_0_46 = 0 | all_36_0_28 = 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_22_1_12) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (88) with all_36_0_28, all_50_0_46, all_1_1_1, 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_4_4, all_1_1_1) = all_50_0_46, yields: % 37.64/9.76 | (291) all_50_0_46 = 0 | all_36_0_28 = 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_22_1_12) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (88) with all_48_0_45, all_50_0_46, 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_48_0_45, apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46, yields: % 37.64/9.76 | (292) all_50_0_46 = 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_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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (126) with all_50_0_46, all_22_0_11, all_1_1_1, all_22_1_12, all_1_3_3, 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_46, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 37.64/9.76 | (293) all_50_0_46 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (126) with all_22_0_11, all_50_0_46, all_22_1_12, all_1_1_1, all_1_3_3, 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_46, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 37.64/9.76 | (294) all_50_0_46 = 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_1_1) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (67) with all_50_0_46, all_22_0_11, all_1_1_1, all_22_1_12, all_1_4_4, all_1_5_5 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_46, distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 37.64/9.76 | (295) all_50_0_46 = 0 | all_22_0_11 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (67) with all_22_0_11, all_50_0_46, all_22_1_12, all_1_1_1, all_1_4_4, all_1_5_5 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_46, distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 37.64/9.76 | (296) all_50_0_46 = 0 | all_22_0_11 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (7) with all_50_0_46, 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_46, yields: % 37.64/9.76 | (297) all_50_0_46 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (7) with all_22_0_11, all_50_0_46, 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_46, yields: % 37.64/9.76 | (298) all_50_0_46 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (3) with all_50_0_46, 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_46, yields: % 37.64/9.76 | (299) all_50_0_46 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (3) with all_22_0_11, all_50_0_46, 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_46, yields: % 37.64/9.76 | (300) all_50_0_46 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (88) with all_50_0_46, 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_46, yields: % 37.64/9.76 | (301) all_50_0_46 = 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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (88) with all_22_0_11, all_50_0_46, 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_46, yields: % 37.64/9.76 | (302) all_50_0_46 = 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_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)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (126) with all_50_0_46, all_50_0_46, 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_4_4, all_1_1_1) = all_50_0_46, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 37.64/9.76 | (303) all_50_0_46 = 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_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.76 | % 37.64/9.76 | Instantiating formula (67) with all_50_0_46, all_50_0_46, all_1_1_1, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46, distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 37.64/9.76 | (304) all_50_0_46 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_50_0_46, all_50_0_46, 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_46, yields: % 37.64/9.77 | (305) all_50_0_46 = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_50_0_46, all_50_0_46, all_1_1_1, all_1_1_1, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46, yields: % 37.64/9.77 | (306) all_50_0_46 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, 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_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_32_0_24, all_36_0_28, 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_22_1_12) = all_36_0_28, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 37.64/9.77 | (307) all_36_0_28 = 0 | all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_22_1_12) = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_36_0_28, all_32_0_24, all_22_1_12, all_1_2_2, 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_4_4, all_1_2_2) = all_32_0_24, yields: % 37.64/9.77 | (308) all_36_0_28 = 0 | all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & distinct_lines(all_1_2_2, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (88) with all_32_0_24, all_20_0_9, all_18_1_8, all_1_2_2, all_1_4_4, 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_4_4, all_1_2_2) = all_32_0_24, yields: % 37.64/9.77 | (309) all_32_0_24 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_18_1_8) = v3 & distinct_lines(all_1_2_2, all_18_1_8) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (88) with all_20_0_9, all_32_0_24, all_1_2_2, 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_4_4, all_1_2_2) = all_32_0_24, yields: % 37.64/9.77 | (310) all_32_0_24 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & distinct_lines(all_18_1_8, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_32_0_24, all_48_0_45, 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_3_3, all_1_2_2) = all_48_0_45, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 37.64/9.77 | (311) all_48_0_45 = 0 | all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (126) with all_32_0_24, 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_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, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 37.64/9.77 | (312) 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (126) with all_22_0_11, all_32_0_24, all_22_1_12, all_1_2_2, all_1_3_3, 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_2_2) = all_32_0_24, distinct_points(all_1_4_4, all_1_3_3) = 0, yields: % 37.64/9.77 | (313) 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (67) with all_32_0_24, all_22_0_11, all_1_2_2, all_22_1_12, all_1_4_4, all_1_5_5 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, distinct_points(all_1_5_5, all_1_4_4) = 0, yields: % 37.64/9.77 | (314) all_32_0_24 = 0 | all_22_0_11 = 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_2_2) = v2 & distinct_lines(all_22_1_12, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_32_0_24, all_22_0_11, all_1_2_2, 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_2_2) = all_32_0_24, yields: % 37.64/9.77 | (315) all_32_0_24 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_1_2_2) = v1 & distinct_lines(all_22_1_12, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_22_0_11, all_32_0_24, all_22_1_12, all_1_2_2, 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_2_2) = all_32_0_24, yields: % 37.64/9.77 | (316) all_32_0_24 = 0 | all_22_0_11 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_22_1_12) = v1 & distinct_lines(all_1_2_2, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_50_0_46, all_32_0_24, all_1_1_1, all_1_2_2, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 37.64/9.77 | (317) all_50_0_46 = 0 | all_32_0_24 = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_32_0_24, all_32_0_24, all_1_2_2, all_1_2_2, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 37.64/9.77 | (318) all_32_0_24 = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (88) with all_32_0_24, all_18_0_7, all_18_1_8, all_1_2_2, all_1_4_4, all_1_5_5 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_18_1_8) = all_18_0_7, yields: % 37.64/9.77 | (319) all_32_0_24 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_18_1_8) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (88) with all_52_0_48, all_36_0_28, all_22_1_12, all_1_1_1, all_1_5_5, 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_5_5, all_1_1_1) = all_52_0_48, yields: % 37.64/9.77 | (320) all_52_0_48 = 0 | all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_22_1_12) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_52_0_48, all_20_0_9, 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_18_1_8) = all_20_0_9, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 37.64/9.77 | (321) all_52_0_48 = 0 | all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_18_1_8) = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (88) with all_32_0_24, all_52_0_48, all_1_1_1, all_1_2_2, all_1_4_4, all_1_5_5 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_1_1) = all_52_0_48, yields: % 37.64/9.77 | (322) all_52_0_48 = 0 | all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_52_0_48, all_18_0_7, all_1_1_1, all_18_1_8, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 37.64/9.77 | (323) all_52_0_48 = 0 | all_18_0_7 = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_18_0_7, all_52_0_48, all_18_1_8, all_1_1_1, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 37.64/9.77 | (324) all_52_0_48 = 0 | all_18_0_7 = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_52_0_48, all_18_0_7, all_1_1_1, all_18_1_8, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 37.64/9.77 | (325) all_52_0_48 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, 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_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_18_0_7, all_52_0_48, all_18_1_8, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 37.64/9.77 | (326) all_52_0_48 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (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) = v3 & distinct_lines(all_1_1_1, all_18_1_8) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (88) with all_52_0_48, all_18_0_7, all_18_1_8, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 37.64/9.77 | (327) all_52_0_48 = 0 | all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, 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_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_26_0_17, all_50_0_46, all_1_2_2, all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 37.64/9.77 | (328) all_50_0_46 = 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_1_1) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (3) with all_50_0_46, all_26_0_17, all_1_1_1, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 37.64/9.77 | (329) all_50_0_46 = 0 | all_26_0_17 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (88) with all_26_0_17, all_50_0_46, all_1_1_1, 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_1_1) = all_50_0_46, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 37.64/9.77 | (330) all_50_0_46 = 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_1_1) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_26_0_17, all_18_0_7, all_1_2_2, all_18_1_8, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 37.64/9.77 | (331) all_26_0_17 = 0 | all_18_0_7 = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_18_0_7, all_26_0_17, all_18_1_8, all_1_2_2, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 37.64/9.77 | (332) all_26_0_17 = 0 | all_18_0_7 = 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)) % 37.64/9.77 | % 37.64/9.77 | Instantiating formula (7) with all_26_0_17, all_52_0_48, 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) = all_52_0_48, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 37.64/9.78 | (333) all_52_0_48 = 0 | all_26_0_17 = 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)) % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (7) with all_52_0_48, all_26_0_17, all_1_1_1, all_1_2_2, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 37.64/9.78 | (334) all_52_0_48 = 0 | all_26_0_17 = 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)) % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (40) with all_46_1_42, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_46_1_42, distinct_points(all_1_5_5, all_1_4_4) = 0, ~ (distinct_points(all_1_5_5, all_1_5_5) = 0), yields: % 37.64/9.78 | (335) all_46_1_42 = 0 % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (126) with all_32_0_24, all_50_0_46, all_1_2_2, all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_50_0_46, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 37.64/9.78 | (336) all_50_0_46 = 0 | all_32_0_24 = 0 | ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (67) with all_18_0_7, all_52_0_48, all_18_1_8, all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_18_1_8) = all_18_0_7, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 37.64/9.78 | (337) all_52_0_48 = 0 | all_18_0_7 = 0 | ~ (distinct_points(all_1_4_4, all_1_5_5) = 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)) % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (67) with all_26_0_17, all_52_0_48, all_1_2_2, all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, apart_point_and_line(all_1_5_5, all_1_2_2) = all_26_0_17, yields: % 37.64/9.78 | (338) all_52_0_48 = 0 | all_26_0_17 = 0 | ~ (distinct_points(all_1_4_4, all_1_5_5) = 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)) % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (120) with all_1_5_5, all_1_4_4 yields: % 37.64/9.78 | (339) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_4_4) = v0 & point(all_1_5_5) = v1 & line(v2) = v3 & line_connecting(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (80) with all_1_5_5, all_1_4_4 yields: % 37.64/9.78 | (340) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1) % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (97) with all_1_5_5, all_1_4_4 yields: % 37.64/9.78 | (341) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_4_4, v0) = v1) % 37.64/9.78 | % 37.64/9.78 | Instantiating formula (52) with all_1_5_5, all_1_4_4 yields: % 37.64/9.78 | (342) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & equal_points(all_1_4_4, all_1_5_5) = v0) % 37.64/9.78 | % 37.64/9.78 | Combining equations (335,244) yields a new equation: % 37.64/9.78 | (343) all_50_1_47 = 0 % 37.64/9.78 | % 37.64/9.78 | Combining equations (335,239) yields a new equation: % 37.64/9.78 | (344) all_52_1_49 = 0 % 37.64/9.78 | % 37.64/9.78 | From (335) and (213) follows: % 37.64/9.78 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (272), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (346) all_36_0_28 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (346) can reduce 192 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (192) ~ (all_36_0_28 = 0) % 37.64/9.78 | (349) ? [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)) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (273), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (346) all_36_0_28 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (346) can reduce 192 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (192) ~ (all_36_0_28 = 0) % 37.64/9.78 | (353) ? [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)) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (318), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (354) all_32_0_24 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (354) can reduce 184 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (184) ~ (all_32_0_24 = 0) % 37.64/9.78 | (357) ? [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)) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (274), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (346) all_36_0_28 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (346) can reduce 192 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (192) ~ (all_36_0_28 = 0) % 37.64/9.78 | (361) 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)) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (341), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (362) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) % 37.64/9.78 | % 37.64/9.78 | Using (345) and (362) yields: % 37.64/9.78 | (262) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 37.64/9.78 | (365) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_4_4, v0) = v1) % 37.64/9.78 | % 37.64/9.78 | Instantiating (365) with all_119_0_68, all_119_1_69 yields: % 37.64/9.78 | (366) ~ (all_119_0_68 = 0) & line_connecting(all_1_4_4, all_1_5_5) = all_119_1_69 & apart_point_and_line(all_1_4_4, all_119_1_69) = all_119_0_68 % 37.64/9.78 | % 37.64/9.78 | Applying alpha-rule on (366) yields: % 37.64/9.78 | (367) ~ (all_119_0_68 = 0) % 37.64/9.78 | (368) line_connecting(all_1_4_4, all_1_5_5) = all_119_1_69 % 37.64/9.78 | (369) apart_point_and_line(all_1_4_4, all_119_1_69) = all_119_0_68 % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (223), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (370) ~ (all_50_0_46 = 0) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (282), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (371) distinct_lines(all_1_1_1, all_1_2_2) = 0 % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (305), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (372) all_50_0_46 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (372) can reduce 370 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (370) ~ (all_50_0_46 = 0) % 37.64/9.78 | (375) ? [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)) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (303), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (372) all_50_0_46 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (372) can reduce 370 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (370) ~ (all_50_0_46 = 0) % 37.64/9.78 | (379) ? [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_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (287), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (380) all_22_0_11 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (380) can reduce 164 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (164) ~ (all_22_0_11 = 0) % 37.64/9.78 | (383) ? [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_22_1_12) = v1 & distinct_lines(all_22_1_12, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (304), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (372) all_50_0_46 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (372) can reduce 370 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (370) ~ (all_50_0_46 = 0) % 37.64/9.78 | (387) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.78 | % 37.64/9.78 | Instantiating (387) with all_162_0_84, all_162_1_85, all_162_2_86 yields: % 37.64/9.78 | (388) apart_point_and_line(all_1_5_5, all_1_1_1) = all_162_0_84 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_162_1_85 & distinct_lines(all_1_1_1, all_1_1_1) = all_162_2_86 & ( ~ (all_162_2_86 = 0) | all_162_0_84 = 0 | all_162_1_85 = 0) % 37.64/9.78 | % 37.64/9.78 | Applying alpha-rule on (388) yields: % 37.64/9.78 | (389) apart_point_and_line(all_1_5_5, all_1_1_1) = all_162_0_84 % 37.64/9.78 | (390) apart_point_and_line(all_1_5_5, all_1_1_1) = all_162_1_85 % 37.64/9.78 | (391) distinct_lines(all_1_1_1, all_1_1_1) = all_162_2_86 % 37.64/9.78 | (392) ~ (all_162_2_86 = 0) | all_162_0_84 = 0 | all_162_1_85 = 0 % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (278), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (346) all_36_0_28 = 0 % 37.64/9.78 | % 37.64/9.78 | Equations (346) can reduce 192 to: % 37.64/9.78 | (347) $false % 37.64/9.78 | % 37.64/9.78 |-The branch is then unsatisfiable % 37.64/9.78 |-Branch two: % 37.64/9.78 | (192) ~ (all_36_0_28 = 0) % 37.64/9.78 | (396) 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)) % 37.64/9.78 | % 37.64/9.78 +-Applying beta-rule and splitting (279), into two cases. % 37.64/9.78 |-Branch one: % 37.64/9.78 | (346) all_36_0_28 = 0 % 37.64/9.78 | % 37.64/9.79 | Equations (346) can reduce 192 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (192) ~ (all_36_0_28 = 0) % 37.64/9.79 | (400) 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)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (271), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (346) all_36_0_28 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (346) can reduce 192 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (192) ~ (all_36_0_28 = 0) % 37.64/9.79 | (383) ? [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_22_1_12) = v1 & distinct_lines(all_22_1_12, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (297), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (372) all_50_0_46 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (372) can reduce 370 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (370) ~ (all_50_0_46 = 0) % 37.64/9.79 | (408) 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)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (298), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (372) all_50_0_46 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (372) can reduce 370 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (370) ~ (all_50_0_46 = 0) % 37.64/9.79 | (412) 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)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (306), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (372) all_50_0_46 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (372) can reduce 370 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (370) ~ (all_50_0_46 = 0) % 37.64/9.79 | (416) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, 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_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (311), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (417) all_48_0_45 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (417) can reduce 218 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (218) ~ (all_48_0_45 = 0) % 37.64/9.79 | (420) all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (312), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (354) all_32_0_24 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (354) can reduce 184 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (184) ~ (all_32_0_24 = 0) % 37.64/9.79 | (424) 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)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (292), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (372) all_50_0_46 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (372) can reduce 370 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (370) ~ (all_50_0_46 = 0) % 37.64/9.79 | (428) 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_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)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (299), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (372) all_50_0_46 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (372) can reduce 370 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (370) ~ (all_50_0_46 = 0) % 37.64/9.79 | (432) 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)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (277), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (346) all_36_0_28 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (346) can reduce 192 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (192) ~ (all_36_0_28 = 0) % 37.64/9.79 | (436) all_20_0_9 = 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_18_1_8) = v1 & distinct_lines(all_18_1_8, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (300), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (372) all_50_0_46 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (372) can reduce 370 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (370) ~ (all_50_0_46 = 0) % 37.64/9.79 | (440) 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)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (301), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (372) all_50_0_46 = 0 % 37.64/9.79 | % 37.64/9.79 | Equations (372) can reduce 370 to: % 37.64/9.79 | (347) $false % 37.64/9.79 | % 37.64/9.79 |-The branch is then unsatisfiable % 37.64/9.79 |-Branch two: % 37.64/9.79 | (370) ~ (all_50_0_46 = 0) % 37.64/9.79 | (444) 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)) % 37.64/9.79 | % 37.64/9.79 +-Applying beta-rule and splitting (302), into two cases. % 37.64/9.79 |-Branch one: % 37.64/9.79 | (372) all_50_0_46 = 0 % 37.64/9.79 | % 38.09/9.79 | Equations (372) can reduce 370 to: % 38.09/9.79 | (347) $false % 38.09/9.79 | % 38.09/9.79 |-The branch is then unsatisfiable % 38.09/9.79 |-Branch two: % 38.09/9.79 | (370) ~ (all_50_0_46 = 0) % 38.09/9.79 | (448) 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_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)) % 38.09/9.79 | % 38.09/9.79 +-Applying beta-rule and splitting (314), into two cases. % 38.09/9.79 |-Branch one: % 38.09/9.79 | (354) all_32_0_24 = 0 % 38.09/9.79 | % 38.09/9.79 | Equations (354) can reduce 184 to: % 38.09/9.79 | (347) $false % 38.09/9.79 | % 38.09/9.79 |-The branch is then unsatisfiable % 38.09/9.79 |-Branch two: % 38.09/9.79 | (184) ~ (all_32_0_24 = 0) % 38.09/9.79 | (452) all_22_0_11 = 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_2_2) = v2 & distinct_lines(all_22_1_12, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 38.09/9.79 | % 38.09/9.79 +-Applying beta-rule and splitting (283), into two cases. % 38.09/9.79 |-Branch one: % 38.09/9.79 | (417) all_48_0_45 = 0 % 38.09/9.79 | % 38.09/9.79 | Equations (417) can reduce 218 to: % 38.09/9.79 | (347) $false % 38.09/9.79 | % 38.09/9.79 |-The branch is then unsatisfiable % 38.09/9.79 |-Branch two: % 38.09/9.79 | (218) ~ (all_48_0_45 = 0) % 38.09/9.79 | (456) 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_1_2_2, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.09/9.79 | % 38.09/9.79 +-Applying beta-rule and splitting (284), into two cases. % 38.09/9.79 |-Branch one: % 38.09/9.79 | (417) all_48_0_45 = 0 % 38.09/9.79 | % 38.09/9.79 | Equations (417) can reduce 218 to: % 38.09/9.79 | (347) $false % 38.09/9.79 | % 38.09/9.79 |-The branch is then unsatisfiable % 38.09/9.79 |-Branch two: % 38.09/9.79 | (218) ~ (all_48_0_45 = 0) % 38.09/9.79 | (460) 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)) % 38.09/9.79 | % 38.09/9.79 +-Applying beta-rule and splitting (294), into two cases. % 38.09/9.79 |-Branch one: % 38.09/9.79 | (372) all_50_0_46 = 0 % 38.09/9.79 | % 38.09/9.79 | Equations (372) can reduce 370 to: % 38.09/9.79 | (347) $false % 38.09/9.79 | % 38.09/9.79 |-The branch is then unsatisfiable % 38.09/9.79 |-Branch two: % 38.09/9.79 | (370) ~ (all_50_0_46 = 0) % 38.09/9.79 | (464) 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_1_1) = v1 & distinct_lines(all_1_1_1, all_22_1_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 38.09/9.79 | % 38.09/9.79 +-Applying beta-rule and splitting (293), into two cases. % 38.09/9.79 |-Branch one: % 38.09/9.79 | (372) all_50_0_46 = 0 % 38.09/9.79 | % 38.09/9.79 | Equations (372) can reduce 370 to: % 38.09/9.79 | (347) $false % 38.09/9.79 | % 38.09/9.79 |-The branch is then unsatisfiable % 38.09/9.79 |-Branch two: % 38.09/9.79 | (370) ~ (all_50_0_46 = 0) % 38.09/9.79 | (468) 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)) % 38.09/9.79 | % 38.09/9.79 +-Applying beta-rule and splitting (296), into two cases. % 38.09/9.79 |-Branch one: % 38.09/9.79 | (372) all_50_0_46 = 0 % 38.09/9.79 | % 38.09/9.79 | Equations (372) can reduce 370 to: % 38.09/9.79 | (347) $false % 38.09/9.79 | % 38.09/9.79 |-The branch is then unsatisfiable % 38.09/9.79 |-Branch two: % 38.09/9.79 | (370) ~ (all_50_0_46 = 0) % 38.09/9.79 | (472) all_22_0_11 = 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)) % 38.09/9.80 | % 38.09/9.80 +-Applying beta-rule and splitting (280), into two cases. % 38.09/9.80 |-Branch one: % 38.09/9.80 | (346) all_36_0_28 = 0 % 38.09/9.80 | % 38.09/9.80 | Equations (346) can reduce 192 to: % 38.09/9.80 | (347) $false % 38.09/9.80 | % 38.09/9.80 |-The branch is then unsatisfiable % 38.09/9.80 |-Branch two: % 38.09/9.80 | (192) ~ (all_36_0_28 = 0) % 38.09/9.80 | (476) all_20_0_9 = 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_18_1_8) = v3 & distinct_lines(all_18_1_8, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.09/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (286), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (417) all_48_0_45 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (417) can reduce 218 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (218) ~ (all_48_0_45 = 0) % 38.11/9.80 | (480) 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_1_2_2, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (288), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (372) all_50_0_46 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (372) can reduce 370 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (370) ~ (all_50_0_46 = 0) % 38.11/9.80 | (484) all_36_0_28 = 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_22_1_12) = v3 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (289), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (372) all_50_0_46 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (372) can reduce 370 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (370) ~ (all_50_0_46 = 0) % 38.11/9.80 | (488) all_36_0_28 = 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_22_1_12) = v2 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (291), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (372) all_50_0_46 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (372) can reduce 370 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (370) ~ (all_50_0_46 = 0) % 38.11/9.80 | (492) all_36_0_28 = 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_22_1_12) = v2 & distinct_lines(all_22_1_12, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (281), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (346) all_36_0_28 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (346) can reduce 192 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (192) ~ (all_36_0_28 = 0) % 38.11/9.80 | (496) all_20_0_9 = 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_18_1_8) = v2 & distinct_lines(all_18_1_8, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (295), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (372) all_50_0_46 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (372) can reduce 370 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (370) ~ (all_50_0_46 = 0) % 38.11/9.80 | (500) all_22_0_11 = 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)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (313), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (354) all_32_0_24 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (354) can reduce 184 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (184) ~ (all_32_0_24 = 0) % 38.11/9.80 | (504) 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)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (290), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (372) all_50_0_46 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (372) can reduce 370 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (370) ~ (all_50_0_46 = 0) % 38.11/9.80 | (508) all_36_0_28 = 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_22_1_12) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (275), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (346) all_36_0_28 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (346) can reduce 192 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (192) ~ (all_36_0_28 = 0) % 38.11/9.80 | (512) 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)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (276), into two cases. % 38.11/9.80 |-Branch one: % 38.11/9.80 | (346) all_36_0_28 = 0 % 38.11/9.80 | % 38.11/9.80 | Equations (346) can reduce 192 to: % 38.11/9.80 | (347) $false % 38.11/9.80 | % 38.11/9.80 |-The branch is then unsatisfiable % 38.11/9.80 |-Branch two: % 38.11/9.80 | (192) ~ (all_36_0_28 = 0) % 38.11/9.80 | (516) all_20_0_9 = 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_18_1_8) = v2 & distinct_lines(all_22_1_12, all_18_1_8) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 38.11/9.80 | % 38.11/9.80 +-Applying beta-rule and splitting (307), into two cases. % 38.11/9.80 |-Branch one: % 38.13/9.80 | (346) all_36_0_28 = 0 % 38.13/9.80 | % 38.13/9.80 | Equations (346) can reduce 192 to: % 38.13/9.80 | (347) $false % 38.13/9.80 | % 38.13/9.80 |-The branch is then unsatisfiable % 38.13/9.80 |-Branch two: % 38.13/9.80 | (192) ~ (all_36_0_28 = 0) % 38.13/9.80 | (520) all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_22_1_12) = 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)) % 38.13/9.80 | % 38.13/9.80 +-Applying beta-rule and splitting (285), into two cases. % 38.13/9.80 |-Branch one: % 38.13/9.80 | (417) all_48_0_45 = 0 % 38.13/9.80 | % 38.13/9.80 | Equations (417) can reduce 218 to: % 38.13/9.80 | (347) $false % 38.13/9.80 | % 38.13/9.80 |-The branch is then unsatisfiable % 38.13/9.80 |-Branch two: % 38.13/9.80 | (218) ~ (all_48_0_45 = 0) % 38.13/9.80 | (524) 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)) % 38.13/9.80 | % 38.14/9.80 +-Applying beta-rule and splitting (308), into two cases. % 38.14/9.80 |-Branch one: % 38.14/9.80 | (346) all_36_0_28 = 0 % 38.14/9.80 | % 38.14/9.80 | Equations (346) can reduce 192 to: % 38.14/9.80 | (347) $false % 38.14/9.80 | % 38.14/9.80 |-The branch is then unsatisfiable % 38.14/9.80 |-Branch two: % 38.14/9.80 | (192) ~ (all_36_0_28 = 0) % 38.14/9.80 | (528) all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & distinct_lines(all_1_2_2, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.80 | % 38.14/9.80 +-Applying beta-rule and splitting (309), into two cases. % 38.14/9.80 |-Branch one: % 38.14/9.80 | (354) all_32_0_24 = 0 % 38.14/9.80 | % 38.14/9.80 | Equations (354) can reduce 184 to: % 38.14/9.80 | (347) $false % 38.14/9.80 | % 38.14/9.80 |-The branch is then unsatisfiable % 38.14/9.80 |-Branch two: % 38.14/9.80 | (184) ~ (all_32_0_24 = 0) % 38.14/9.80 | (532) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_18_1_8) = v3 & distinct_lines(all_1_2_2, all_18_1_8) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.80 | % 38.14/9.80 +-Applying beta-rule and splitting (310), into two cases. % 38.14/9.80 |-Branch one: % 38.14/9.80 | (354) all_32_0_24 = 0 % 38.14/9.80 | % 38.14/9.80 | Equations (354) can reduce 184 to: % 38.14/9.80 | (347) $false % 38.14/9.80 | % 38.14/9.80 |-The branch is then unsatisfiable % 38.14/9.80 |-Branch two: % 38.14/9.80 | (184) ~ (all_32_0_24 = 0) % 38.14/9.80 | (536) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_4_4, all_18_1_8) = v2 & distinct_lines(all_18_1_8, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.80 | % 38.14/9.80 +-Applying beta-rule and splitting (227), into two cases. % 38.14/9.80 |-Branch one: % 38.14/9.80 | (537) ~ (all_52_0_48 = 0) % 38.14/9.80 | % 38.14/9.80 +-Applying beta-rule and splitting (448), into two cases. % 38.14/9.80 |-Branch one: % 38.14/9.80 | (380) all_22_0_11 = 0 % 38.14/9.80 | % 38.14/9.80 | Equations (380) can reduce 164 to: % 38.14/9.80 | (347) $false % 38.14/9.80 | % 38.14/9.80 |-The branch is then unsatisfiable % 38.14/9.80 |-Branch two: % 38.14/9.80 | (164) ~ (all_22_0_11 = 0) % 38.14/9.80 | (541) ? [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_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)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (460), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (380) all_22_0_11 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (380) can reduce 164 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (164) ~ (all_22_0_11 = 0) % 38.14/9.81 | (545) ? [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)) % 38.14/9.81 | % 38.14/9.81 | Instantiating (545) with all_288_0_98, all_288_1_99, all_288_2_100, all_288_3_101 yields: % 38.14/9.81 | (546) apart_point_and_line(all_1_3_3, all_22_1_12) = all_288_0_98 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_288_1_99 & distinct_lines(all_22_1_12, all_1_2_2) = all_288_2_100 & distinct_points(all_1_4_4, all_1_3_3) = all_288_3_101 & ( ~ (all_288_2_100 = 0) | ~ (all_288_3_101 = 0) | all_288_0_98 = 0 | all_288_1_99 = 0) % 38.14/9.81 | % 38.14/9.81 | Applying alpha-rule on (546) yields: % 38.14/9.81 | (547) apart_point_and_line(all_1_4_4, all_1_2_2) = all_288_1_99 % 38.14/9.81 | (548) distinct_points(all_1_4_4, all_1_3_3) = all_288_3_101 % 38.14/9.81 | (549) apart_point_and_line(all_1_3_3, all_22_1_12) = all_288_0_98 % 38.14/9.81 | (550) ~ (all_288_2_100 = 0) | ~ (all_288_3_101 = 0) | all_288_0_98 = 0 | all_288_1_99 = 0 % 38.14/9.81 | (551) distinct_lines(all_22_1_12, all_1_2_2) = all_288_2_100 % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (500), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (380) all_22_0_11 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (380) can reduce 164 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (164) ~ (all_22_0_11 = 0) % 38.14/9.81 | (555) ? [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)) % 38.14/9.81 | % 38.14/9.81 | Instantiating (555) with all_293_0_102, all_293_1_103, all_293_2_104 yields: % 38.14/9.81 | (556) apart_point_and_line(all_1_5_5, all_22_1_12) = all_293_1_103 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_293_0_102 & distinct_lines(all_22_1_12, all_1_1_1) = all_293_2_104 & ( ~ (all_293_2_104 = 0) | all_293_0_102 = 0 | all_293_1_103 = 0) % 38.14/9.81 | % 38.14/9.81 | Applying alpha-rule on (556) yields: % 38.14/9.81 | (557) apart_point_and_line(all_1_5_5, all_22_1_12) = all_293_1_103 % 38.14/9.81 | (558) apart_point_and_line(all_1_5_5, all_1_1_1) = all_293_0_102 % 38.14/9.81 | (559) distinct_lines(all_22_1_12, all_1_1_1) = all_293_2_104 % 38.14/9.81 | (560) ~ (all_293_2_104 = 0) | all_293_0_102 = 0 | all_293_1_103 = 0 % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (520), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (354) all_32_0_24 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (354) can reduce 184 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (184) ~ (all_32_0_24 = 0) % 38.14/9.81 | (564) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_22_1_12) = 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)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (524), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (380) all_22_0_11 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (380) can reduce 164 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (164) ~ (all_22_0_11 = 0) % 38.14/9.81 | (568) ? [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)) % 38.14/9.81 | % 38.14/9.81 | Instantiating (568) with all_308_0_113, all_308_1_114, all_308_2_115, all_308_3_116 yields: % 38.14/9.81 | (569) apart_point_and_line(all_1_3_3, all_22_1_12) = all_308_1_114 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_308_0_113 & distinct_lines(all_22_1_12, all_1_2_2) = all_308_2_115 & distinct_points(all_1_3_3, all_1_4_4) = all_308_3_116 & ( ~ (all_308_2_115 = 0) | ~ (all_308_3_116 = 0) | all_308_0_113 = 0 | all_308_1_114 = 0) % 38.14/9.81 | % 38.14/9.81 | Applying alpha-rule on (569) yields: % 38.14/9.81 | (570) distinct_lines(all_22_1_12, all_1_2_2) = all_308_2_115 % 38.14/9.81 | (571) apart_point_and_line(all_1_3_3, all_22_1_12) = all_308_1_114 % 38.14/9.81 | (572) apart_point_and_line(all_1_4_4, all_1_2_2) = all_308_0_113 % 38.14/9.81 | (573) ~ (all_308_2_115 = 0) | ~ (all_308_3_116 = 0) | all_308_0_113 = 0 | all_308_1_114 = 0 % 38.14/9.81 | (574) distinct_points(all_1_3_3, all_1_4_4) = all_308_3_116 % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (528), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (354) all_32_0_24 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (354) can reduce 184 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (184) ~ (all_32_0_24 = 0) % 38.14/9.81 | (578) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_4_4, all_22_1_12) = v2 & distinct_lines(all_1_2_2, all_22_1_12) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (319), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (354) all_32_0_24 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (354) can reduce 184 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (184) ~ (all_32_0_24 = 0) % 38.14/9.81 | (582) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_18_1_8) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_18_1_8) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (342), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (362) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) % 38.14/9.81 | % 38.14/9.81 | Using (345) and (362) yields: % 38.14/9.81 | (262) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 38.14/9.81 | (586) ? [v0] : ( ~ (v0 = 0) & equal_points(all_1_4_4, all_1_5_5) = v0) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (333), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (587) all_52_0_48 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (587) can reduce 537 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (537) ~ (all_52_0_48 = 0) % 38.14/9.81 | (590) all_26_0_17 = 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)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (334), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (587) all_52_0_48 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (587) can reduce 537 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (537) ~ (all_52_0_48 = 0) % 38.14/9.81 | (594) all_26_0_17 = 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)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (324), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (587) all_52_0_48 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (587) can reduce 537 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (537) ~ (all_52_0_48 = 0) % 38.14/9.81 | (598) all_18_0_7 = 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)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (326), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (587) all_52_0_48 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (587) can reduce 537 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (537) ~ (all_52_0_48 = 0) % 38.14/9.81 | (602) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (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) = v3 & distinct_lines(all_1_1_1, all_18_1_8) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (327), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (587) all_52_0_48 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (587) can reduce 537 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.81 |-Branch two: % 38.14/9.81 | (537) ~ (all_52_0_48 = 0) % 38.14/9.81 | (606) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, 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_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.81 | % 38.14/9.81 +-Applying beta-rule and splitting (325), into two cases. % 38.14/9.81 |-Branch one: % 38.14/9.81 | (587) all_52_0_48 = 0 % 38.14/9.81 | % 38.14/9.81 | Equations (587) can reduce 537 to: % 38.14/9.81 | (347) $false % 38.14/9.81 | % 38.14/9.81 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (537) ~ (all_52_0_48 = 0) % 38.14/9.82 | (610) all_18_0_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, 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_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (329), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (372) all_50_0_46 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (372) can reduce 370 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (370) ~ (all_50_0_46 = 0) % 38.14/9.82 | (614) all_26_0_17 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (320), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (587) all_52_0_48 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (587) can reduce 537 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (537) ~ (all_52_0_48 = 0) % 38.14/9.82 | (618) all_36_0_28 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_22_1_12) = v3 & distinct_lines(all_1_1_1, all_22_1_12) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (321), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (587) all_52_0_48 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (587) can reduce 537 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (537) ~ (all_52_0_48 = 0) % 38.14/9.82 | (622) all_20_0_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_18_1_8) = 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)) % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (330), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (372) all_50_0_46 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (372) can reduce 370 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (370) ~ (all_50_0_46 = 0) % 38.14/9.82 | (626) 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_1_1) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (626), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (627) all_26_0_17 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (627) can reduce 174 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (174) ~ (all_26_0_17 = 0) % 38.14/9.82 | (630) ? [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_1_1) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.82 | % 38.14/9.82 | Instantiating (630) with all_432_0_152, all_432_1_153, all_432_2_154, all_432_3_155 yields: % 38.14/9.82 | (631) apart_point_and_line(all_1_4_4, all_1_2_2) = all_432_1_153 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_432_0_152 & distinct_lines(all_1_2_2, all_1_1_1) = all_432_2_154 & distinct_points(all_1_4_4, all_1_5_5) = all_432_3_155 & ( ~ (all_432_2_154 = 0) | ~ (all_432_3_155 = 0) | all_432_0_152 = 0 | all_432_1_153 = 0) % 38.14/9.82 | % 38.14/9.82 | Applying alpha-rule on (631) yields: % 38.14/9.82 | (632) apart_point_and_line(all_1_4_4, all_1_2_2) = all_432_1_153 % 38.14/9.82 | (633) distinct_lines(all_1_2_2, all_1_1_1) = all_432_2_154 % 38.14/9.82 | (634) distinct_points(all_1_4_4, all_1_5_5) = all_432_3_155 % 38.14/9.82 | (635) apart_point_and_line(all_1_5_5, all_1_1_1) = all_432_0_152 % 38.14/9.82 | (636) ~ (all_432_2_154 = 0) | ~ (all_432_3_155 = 0) | all_432_0_152 = 0 | all_432_1_153 = 0 % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (339), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (362) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) % 38.14/9.82 | % 38.14/9.82 | Using (345) and (362) yields: % 38.14/9.82 | (262) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 38.14/9.82 | (640) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_1_4_4) = v0 & point(all_1_5_5) = v1 & line(v2) = v3 & line_connecting(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 38.14/9.82 | % 38.14/9.82 | Instantiating (640) with all_441_0_156, all_441_1_157, all_441_2_158, all_441_3_159 yields: % 38.14/9.82 | (641) point(all_1_4_4) = all_441_3_159 & point(all_1_5_5) = all_441_2_158 & line(all_441_1_157) = all_441_0_156 & line_connecting(all_1_4_4, all_1_5_5) = all_441_1_157 & ( ~ (all_441_2_158 = 0) | ~ (all_441_3_159 = 0) | all_441_0_156 = 0) % 38.14/9.82 | % 38.14/9.82 | Applying alpha-rule on (641) yields: % 38.14/9.82 | (642) point(all_1_5_5) = all_441_2_158 % 38.14/9.82 | (643) line_connecting(all_1_4_4, all_1_5_5) = all_441_1_157 % 38.14/9.82 | (644) ~ (all_441_2_158 = 0) | ~ (all_441_3_159 = 0) | all_441_0_156 = 0 % 38.14/9.82 | (645) line(all_441_1_157) = all_441_0_156 % 38.14/9.82 | (646) point(all_1_4_4) = all_441_3_159 % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (340), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (362) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) % 38.14/9.82 | % 38.14/9.82 | Using (345) and (362) yields: % 38.14/9.82 | (262) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 38.14/9.82 | (650) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1) % 38.14/9.82 | % 38.14/9.82 | Instantiating (650) with all_446_0_160, all_446_1_161 yields: % 38.14/9.82 | (651) ~ (all_446_0_160 = 0) & line_connecting(all_1_4_4, all_1_5_5) = all_446_1_161 & apart_point_and_line(all_1_5_5, all_446_1_161) = all_446_0_160 % 38.14/9.82 | % 38.14/9.82 | Applying alpha-rule on (651) yields: % 38.14/9.82 | (652) ~ (all_446_0_160 = 0) % 38.14/9.82 | (653) line_connecting(all_1_4_4, all_1_5_5) = all_446_1_161 % 38.14/9.82 | (654) apart_point_and_line(all_1_5_5, all_446_1_161) = all_446_0_160 % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (590), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (627) all_26_0_17 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (627) can reduce 174 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (174) ~ (all_26_0_17 = 0) % 38.14/9.82 | (658) ? [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)) % 38.14/9.82 | % 38.14/9.82 | Instantiating (658) with all_460_0_162, all_460_1_163 yields: % 38.14/9.82 | (659) convergent_lines(all_1_1_1, all_1_2_2) = all_460_0_162 & distinct_lines(all_1_1_1, all_1_2_2) = all_460_1_163 & ( ~ (all_460_1_163 = 0) | all_460_0_162 = 0) % 38.14/9.82 | % 38.14/9.82 | Applying alpha-rule on (659) yields: % 38.14/9.82 | (660) convergent_lines(all_1_1_1, all_1_2_2) = all_460_0_162 % 38.14/9.82 | (661) distinct_lines(all_1_1_1, all_1_2_2) = all_460_1_163 % 38.14/9.82 | (662) ~ (all_460_1_163 = 0) | all_460_0_162 = 0 % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (315), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (354) all_32_0_24 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (354) can reduce 184 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (184) ~ (all_32_0_24 = 0) % 38.14/9.82 | (666) all_22_0_11 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_22_1_12, all_1_2_2) = v1 & distinct_lines(all_22_1_12, all_1_2_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (316), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (354) all_32_0_24 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (354) can reduce 184 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (184) ~ (all_32_0_24 = 0) % 38.14/9.82 | (670) all_22_0_11 = 0 | ? [v0] : ? [v1] : (convergent_lines(all_1_2_2, all_22_1_12) = v1 & distinct_lines(all_1_2_2, all_22_1_12) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 38.14/9.82 | % 38.14/9.82 +-Applying beta-rule and splitting (323), into two cases. % 38.14/9.82 |-Branch one: % 38.14/9.82 | (587) all_52_0_48 = 0 % 38.14/9.82 | % 38.14/9.82 | Equations (587) can reduce 537 to: % 38.14/9.82 | (347) $false % 38.14/9.82 | % 38.14/9.82 |-The branch is then unsatisfiable % 38.14/9.82 |-Branch two: % 38.14/9.82 | (537) ~ (all_52_0_48 = 0) % 38.14/9.82 | (674) all_18_0_7 = 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)) % 38.14/9.83 | % 38.14/9.83 +-Applying beta-rule and splitting (331), into two cases. % 38.14/9.83 |-Branch one: % 38.14/9.83 | (627) all_26_0_17 = 0 % 38.14/9.83 | % 38.14/9.83 | Equations (627) can reduce 174 to: % 38.14/9.83 | (347) $false % 38.14/9.83 | % 38.14/9.83 |-The branch is then unsatisfiable % 38.14/9.83 |-Branch two: % 38.14/9.83 | (174) ~ (all_26_0_17 = 0) % 38.14/9.83 | (678) all_18_0_7 = 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)) % 38.14/9.83 | % 38.14/9.83 +-Applying beta-rule and splitting (332), into two cases. % 38.14/9.83 |-Branch one: % 38.14/9.83 | (627) all_26_0_17 = 0 % 38.14/9.83 | % 38.14/9.83 | Equations (627) can reduce 174 to: % 38.14/9.83 | (347) $false % 38.14/9.83 | % 38.14/9.83 |-The branch is then unsatisfiable % 38.14/9.83 |-Branch two: % 38.14/9.83 | (174) ~ (all_26_0_17 = 0) % 38.14/9.83 | (682) all_18_0_7 = 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)) % 38.14/9.83 | % 38.14/9.83 +-Applying beta-rule and splitting (317), into two cases. % 38.14/9.83 |-Branch one: % 38.14/9.83 | (372) all_50_0_46 = 0 % 38.14/9.83 | % 38.14/9.83 | Equations (372) can reduce 370 to: % 38.14/9.83 | (347) $false % 38.14/9.83 | % 38.14/9.83 |-The branch is then unsatisfiable % 38.14/9.83 |-Branch two: % 38.14/9.83 | (370) ~ (all_50_0_46 = 0) % 38.14/9.83 | (686) all_32_0_24 = 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)) % 38.14/9.83 | % 38.14/9.83 +-Applying beta-rule and splitting (594), into two cases. % 38.14/9.83 |-Branch one: % 38.14/9.83 | (627) all_26_0_17 = 0 % 38.14/9.83 | % 38.14/9.83 | Equations (627) can reduce 174 to: % 38.14/9.83 | (347) $false % 38.14/9.83 | % 38.14/9.83 |-The branch is then unsatisfiable % 38.14/9.83 |-Branch two: % 38.14/9.83 | (174) ~ (all_26_0_17 = 0) % 38.14/9.83 | (690) ? [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)) % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (108) with all_1_4_4, all_1_5_5, all_441_1_157, all_1_1_1 and discharging atoms line_connecting(all_1_4_4, all_1_5_5) = all_441_1_157, line_connecting(all_1_4_4, all_1_5_5) = all_1_1_1, yields: % 38.14/9.83 | (691) all_441_1_157 = all_1_1_1 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (108) with all_1_4_4, all_1_5_5, all_441_1_157, all_446_1_161 and discharging atoms line_connecting(all_1_4_4, all_1_5_5) = all_446_1_161, line_connecting(all_1_4_4, all_1_5_5) = all_441_1_157, yields: % 38.14/9.83 | (692) all_446_1_161 = all_441_1_157 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (108) with all_1_4_4, all_1_5_5, all_119_1_69, all_446_1_161 and discharging atoms line_connecting(all_1_4_4, all_1_5_5) = all_446_1_161, line_connecting(all_1_4_4, all_1_5_5) = all_119_1_69, yields: % 38.14/9.83 | (693) all_446_1_161 = all_119_1_69 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_432_1_153, all_32_0_24 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_432_1_153, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 38.14/9.83 | (694) all_432_1_153 = all_32_0_24 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_308_0_113, all_432_1_153 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_432_1_153, apart_point_and_line(all_1_4_4, all_1_2_2) = all_308_0_113, yields: % 38.14/9.83 | (695) all_432_1_153 = all_308_0_113 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_288_1_99, all_432_1_153 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_432_1_153, apart_point_and_line(all_1_4_4, all_1_2_2) = all_288_1_99, yields: % 38.14/9.83 | (696) all_432_1_153 = all_288_1_99 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (109) with all_1_5_5, all_1_1_1, all_432_0_152, all_52_0_48 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_432_0_152, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 38.14/9.83 | (697) all_432_0_152 = all_52_0_48 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (109) with all_1_5_5, all_1_1_1, all_293_0_102, all_432_0_152 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_432_0_152, apart_point_and_line(all_1_5_5, all_1_1_1) = all_293_0_102, yields: % 38.14/9.83 | (698) all_432_0_152 = all_293_0_102 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (109) with all_1_5_5, all_1_1_1, all_162_0_84, all_446_0_160 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_162_0_84, yields: % 38.14/9.83 | (699) all_446_0_160 = all_162_0_84 | ~ (apart_point_and_line(all_1_5_5, all_1_1_1) = all_446_0_160) % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (109) with all_1_5_5, all_1_1_1, all_162_0_84, all_432_0_152 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_432_0_152, apart_point_and_line(all_1_5_5, all_1_1_1) = all_162_0_84, yields: % 38.14/9.83 | (700) all_432_0_152 = all_162_0_84 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (109) with all_1_5_5, all_1_1_1, all_162_1_85, all_293_0_102 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_293_0_102, apart_point_and_line(all_1_5_5, all_1_1_1) = all_162_1_85, yields: % 38.14/9.83 | (701) all_293_0_102 = all_162_1_85 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (105) with all_1_1_1, all_1_2_2, all_460_1_163, 0 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_460_1_163, distinct_lines(all_1_1_1, all_1_2_2) = 0, yields: % 38.14/9.83 | (702) all_460_1_163 = 0 % 38.14/9.83 | % 38.14/9.83 | Instantiating formula (104) with all_1_4_4, all_1_5_5, 0, all_432_3_155 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_432_3_155, distinct_points(all_1_4_4, all_1_5_5) = 0, yields: % 38.14/9.83 | (703) all_432_3_155 = 0 % 38.14/9.83 | % 38.14/9.83 | Combining equations (692,693) yields a new equation: % 38.14/9.83 | (704) all_441_1_157 = all_119_1_69 % 38.14/9.83 | % 38.14/9.83 | Simplifying 704 yields: % 38.14/9.83 | (705) all_441_1_157 = all_119_1_69 % 38.14/9.83 | % 38.14/9.83 | Combining equations (691,705) yields a new equation: % 38.14/9.83 | (706) all_119_1_69 = all_1_1_1 % 38.14/9.83 | % 38.14/9.83 | Combining equations (698,700) yields a new equation: % 38.14/9.83 | (707) all_293_0_102 = all_162_0_84 % 38.14/9.83 | % 38.14/9.83 | Simplifying 707 yields: % 38.14/9.83 | (708) all_293_0_102 = all_162_0_84 % 38.14/9.83 | % 38.14/9.83 | Combining equations (697,700) yields a new equation: % 38.14/9.83 | (709) all_162_0_84 = all_52_0_48 % 38.14/9.83 | % 38.14/9.83 | Combining equations (694,695) yields a new equation: % 38.14/9.83 | (710) all_308_0_113 = all_32_0_24 % 38.14/9.83 | % 38.14/9.83 | Combining equations (696,695) yields a new equation: % 38.14/9.83 | (711) all_308_0_113 = all_288_1_99 % 38.14/9.83 | % 38.14/9.83 | Combining equations (711,710) yields a new equation: % 38.14/9.83 | (712) all_288_1_99 = all_32_0_24 % 38.14/9.83 | % 38.14/9.83 | Simplifying 712 yields: % 38.14/9.83 | (713) all_288_1_99 = all_32_0_24 % 38.14/9.83 | % 38.14/9.83 | Combining equations (708,701) yields a new equation: % 38.14/9.83 | (714) all_162_0_84 = all_162_1_85 % 38.14/9.83 | % 38.14/9.83 | Simplifying 714 yields: % 38.14/9.83 | (715) all_162_0_84 = all_162_1_85 % 38.14/9.83 | % 38.14/9.83 | Combining equations (709,715) yields a new equation: % 38.14/9.83 | (716) all_162_1_85 = all_52_0_48 % 38.14/9.83 | % 38.14/9.83 | Combining equations (716,715) yields a new equation: % 38.14/9.83 | (709) all_162_0_84 = all_52_0_48 % 38.14/9.83 | % 38.14/9.83 | Combining equations (706,693) yields a new equation: % 38.14/9.83 | (718) all_446_1_161 = all_1_1_1 % 38.14/9.83 | % 38.14/9.83 | From (713) and (547) follows: % 38.14/9.83 | (257) apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24 % 38.14/9.83 | % 38.14/9.83 | From (718) and (654) follows: % 38.14/9.83 | (720) apart_point_and_line(all_1_5_5, all_1_1_1) = all_446_0_160 % 38.14/9.83 | % 38.14/9.83 | From (702) and (661) follows: % 38.14/9.83 | (371) distinct_lines(all_1_1_1, all_1_2_2) = 0 % 38.14/9.83 | % 38.14/9.83 | From (703) and (634) follows: % 38.14/9.83 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 38.14/9.83 | % 38.14/9.83 +-Applying beta-rule and splitting (328), into two cases. % 38.14/9.83 |-Branch one: % 38.14/9.83 | (372) all_50_0_46 = 0 % 38.14/9.83 | % 38.14/9.83 | Equations (372) can reduce 370 to: % 38.14/9.83 | (347) $false % 38.14/9.83 | % 38.14/9.83 |-The branch is then unsatisfiable % 38.14/9.83 |-Branch two: % 38.14/9.83 | (370) ~ (all_50_0_46 = 0) % 38.14/9.83 | (726) 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_1_1) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.83 | % 38.14/9.83 +-Applying beta-rule and splitting (726), into two cases. % 38.14/9.83 |-Branch one: % 38.14/9.83 | (627) all_26_0_17 = 0 % 38.14/9.83 | % 38.14/9.83 | Equations (627) can reduce 174 to: % 38.14/9.83 | (347) $false % 38.14/9.83 | % 38.14/9.83 |-The branch is then unsatisfiable % 38.14/9.83 |-Branch two: % 38.14/9.83 | (174) ~ (all_26_0_17 = 0) % 38.14/9.83 | (730) ? [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_1_1) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.83 | % 38.14/9.83 | Instantiating (730) with all_560_0_182, all_560_1_183, all_560_2_184, all_560_3_185 yields: % 38.14/9.83 | (731) apart_point_and_line(all_1_4_4, all_1_2_2) = all_560_1_183 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_560_0_182 & distinct_lines(all_1_1_1, all_1_2_2) = all_560_2_184 & distinct_points(all_1_4_4, all_1_5_5) = all_560_3_185 & ( ~ (all_560_2_184 = 0) | ~ (all_560_3_185 = 0) | all_560_0_182 = 0 | all_560_1_183 = 0) % 38.14/9.83 | % 38.14/9.83 | Applying alpha-rule on (731) yields: % 38.14/9.84 | (732) apart_point_and_line(all_1_4_4, all_1_2_2) = all_560_1_183 % 38.14/9.84 | (733) distinct_lines(all_1_1_1, all_1_2_2) = all_560_2_184 % 38.14/9.84 | (734) ~ (all_560_2_184 = 0) | ~ (all_560_3_185 = 0) | all_560_0_182 = 0 | all_560_1_183 = 0 % 38.14/9.84 | (735) apart_point_and_line(all_1_5_5, all_1_1_1) = all_560_0_182 % 38.14/9.84 | (736) distinct_points(all_1_4_4, all_1_5_5) = all_560_3_185 % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (322), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (587) all_52_0_48 = 0 % 38.14/9.84 | % 38.14/9.84 | Equations (587) can reduce 537 to: % 38.14/9.84 | (347) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (537) ~ (all_52_0_48 = 0) % 38.14/9.84 | (740) all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (740), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (354) all_32_0_24 = 0 % 38.14/9.84 | % 38.14/9.84 | Equations (354) can reduce 184 to: % 38.14/9.84 | (347) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (184) ~ (all_32_0_24 = 0) % 38.14/9.84 | (744) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (699), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (745) ~ (apart_point_and_line(all_1_5_5, all_1_1_1) = all_446_0_160) % 38.14/9.84 | % 38.14/9.84 | Using (720) and (745) yields: % 38.14/9.84 | (262) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (720) apart_point_and_line(all_1_5_5, all_1_1_1) = all_446_0_160 % 38.14/9.84 | (748) all_446_0_160 = all_162_0_84 % 38.14/9.84 | % 38.14/9.84 | Combining equations (709,748) yields a new equation: % 38.14/9.84 | (749) all_446_0_160 = all_52_0_48 % 38.14/9.84 | % 38.14/9.84 | Equations (749) can reduce 652 to: % 38.14/9.84 | (537) ~ (all_52_0_48 = 0) % 38.14/9.84 | % 38.14/9.84 | From (749) and (720) follows: % 38.14/9.84 | (225) apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48 % 38.14/9.84 | % 38.14/9.84 | Instantiating formula (109) with all_1_4_4, all_1_2_2, all_560_1_183, all_32_0_24 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_560_1_183, apart_point_and_line(all_1_4_4, all_1_2_2) = all_32_0_24, yields: % 38.14/9.84 | (752) all_560_1_183 = all_32_0_24 % 38.14/9.84 | % 38.14/9.84 | Instantiating formula (109) with all_1_5_5, all_1_1_1, all_560_0_182, all_52_0_48 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_560_0_182, apart_point_and_line(all_1_5_5, all_1_1_1) = all_52_0_48, yields: % 38.14/9.84 | (753) all_560_0_182 = all_52_0_48 % 38.14/9.84 | % 38.14/9.84 | Instantiating formula (105) with all_1_1_1, all_1_2_2, all_560_2_184, 0 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_560_2_184, distinct_lines(all_1_1_1, all_1_2_2) = 0, yields: % 38.14/9.84 | (754) all_560_2_184 = 0 % 38.14/9.84 | % 38.14/9.84 | Instantiating formula (104) with all_1_4_4, all_1_5_5, all_560_3_185, 0 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_560_3_185, distinct_points(all_1_4_4, all_1_5_5) = 0, yields: % 38.14/9.84 | (755) all_560_3_185 = 0 % 38.14/9.84 | % 38.14/9.84 | From (755) and (736) follows: % 38.14/9.84 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (337), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (362) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) % 38.14/9.84 | % 38.14/9.84 | Using (345) and (362) yields: % 38.14/9.84 | (262) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 38.14/9.84 | (760) all_52_0_48 = 0 | all_18_0_7 = 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)) % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (734), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (761) ~ (all_560_2_184 = 0) % 38.14/9.84 | % 38.14/9.84 | Equations (754) can reduce 761 to: % 38.14/9.84 | (347) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (754) all_560_2_184 = 0 % 38.14/9.84 | (764) ~ (all_560_3_185 = 0) | all_560_0_182 = 0 | all_560_1_183 = 0 % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (760), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (587) all_52_0_48 = 0 % 38.14/9.84 | % 38.14/9.84 | Equations (587) can reduce 537 to: % 38.14/9.84 | (347) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (537) ~ (all_52_0_48 = 0) % 38.14/9.84 | (768) all_18_0_7 = 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)) % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (336), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (362) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) % 38.14/9.84 | % 38.14/9.84 | Using (345) and (362) yields: % 38.14/9.84 | (262) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 38.14/9.84 | (772) all_50_0_46 = 0 | all_32_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (764), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (773) ~ (all_560_3_185 = 0) % 38.14/9.84 | % 38.14/9.84 | Equations (755) can reduce 773 to: % 38.14/9.84 | (347) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (755) all_560_3_185 = 0 % 38.14/9.84 | (776) all_560_0_182 = 0 | all_560_1_183 = 0 % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (338), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (362) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) % 38.14/9.84 | % 38.14/9.84 | Using (345) and (362) yields: % 38.14/9.84 | (262) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (345) distinct_points(all_1_4_4, all_1_5_5) = 0 % 38.14/9.84 | (780) all_52_0_48 = 0 | all_26_0_17 = 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)) % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (780), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (587) all_52_0_48 = 0 % 38.14/9.84 | % 38.14/9.84 | Equations (587) can reduce 537 to: % 38.14/9.84 | (347) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (537) ~ (all_52_0_48 = 0) % 38.14/9.84 | (784) all_26_0_17 = 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)) % 38.14/9.84 | % 38.14/9.84 +-Applying beta-rule and splitting (776), into two cases. % 38.14/9.84 |-Branch one: % 38.14/9.84 | (785) all_560_0_182 = 0 % 38.14/9.84 | % 38.14/9.84 | Combining equations (785,753) yields a new equation: % 38.14/9.84 | (587) all_52_0_48 = 0 % 38.14/9.84 | % 38.14/9.84 | Equations (587) can reduce 537 to: % 38.14/9.84 | (347) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.84 |-Branch two: % 38.14/9.84 | (788) ~ (all_560_0_182 = 0) % 38.14/9.84 | (789) all_560_1_183 = 0 % 38.14/9.84 | % 38.14/9.84 | Combining equations (752,789) yields a new equation: % 38.14/9.84 | (790) all_32_0_24 = 0 % 38.14/9.84 | % 38.14/9.84 | Simplifying 790 yields: % 38.14/9.84 | (354) all_32_0_24 = 0 % 38.14/9.84 | % 38.14/9.84 | Equations (354) can reduce 184 to: % 38.14/9.84 | (347) $false % 38.14/9.84 | % 38.14/9.84 |-The branch is then unsatisfiable % 38.14/9.85 |-Branch two: % 38.14/9.85 | (587) all_52_0_48 = 0 % 38.14/9.85 | (794) ~ (all_52_1_49 = 0) % 38.14/9.85 | % 38.14/9.85 | Equations (344) can reduce 794 to: % 38.14/9.85 | (347) $false % 38.14/9.85 | % 38.14/9.85 |-The branch is then unsatisfiable % 38.14/9.85 |-Branch two: % 38.14/9.85 | (796) ~ (distinct_lines(all_1_1_1, all_1_2_2) = 0) % 38.14/9.85 | (417) all_48_0_45 = 0 % 38.14/9.85 | % 38.14/9.85 | Equations (417) can reduce 218 to: % 38.14/9.85 | (347) $false % 38.14/9.85 | % 38.14/9.85 |-The branch is then unsatisfiable % 38.14/9.85 |-Branch two: % 38.14/9.85 | (372) all_50_0_46 = 0 % 38.14/9.85 | (800) ~ (all_50_1_47 = 0) % 38.14/9.85 | % 38.14/9.85 | Equations (343) can reduce 800 to: % 38.14/9.85 | (347) $false % 38.14/9.85 | % 38.14/9.85 |-The branch is then unsatisfiable % 38.14/9.85 |-Branch two: % 38.14/9.85 | (802) ~ (apart_point_and_line(all_1_3_3, all_1_1_1) = 0) % 38.14/9.85 | (803) all_1_0_0 = 0 % 38.14/9.85 | % 38.14/9.85 | Equations (803) can reduce 135 to: % 38.14/9.85 | (347) $false % 38.14/9.85 | % 38.14/9.85 |-The branch is then unsatisfiable % 38.14/9.85 % SZS output end Proof for theBenchmark % 38.14/9.85 % 38.14/9.85 9365ms %------------------------------------------------------------------------------