%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO225+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 03:48:57 EDT 2022 % Result : Theorem 4.66s 1.72s % Output : Proof 6.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO225+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n004.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 05:06:53 EDT 2022 % 0.13/0.33 % CPUTime : % 0.62/0.59 ____ _ % 0.62/0.59 ___ / __ \_____(_)___ ________ __________ % 0.62/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.62/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.62/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.62/0.59 % 0.62/0.59 A Theorem Prover for First-Order Logic % 0.62/0.60 (ePrincess v.1.0) % 0.62/0.60 % 0.62/0.60 (c) Philipp Rümmer, 2009-2015 % 0.62/0.60 (c) Peter Backeman, 2014-2015 % 0.62/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.62/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.62/0.60 Bug reports to peter@backeman.se % 0.62/0.60 % 0.62/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.62/0.60 % 0.62/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.66/0.97 Prover 0: Preprocessing ... % 2.11/1.11 Prover 0: Warning: ignoring some quantifiers % 2.11/1.14 Prover 0: Constructing countermodel ... % 2.58/1.28 Prover 0: gave up % 2.58/1.28 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.58/1.31 Prover 1: Preprocessing ... % 3.26/1.43 Prover 1: Constructing countermodel ... % 3.26/1.45 Prover 1: gave up % 3.26/1.45 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.59/1.48 Prover 2: Preprocessing ... % 3.85/1.61 Prover 2: Warning: ignoring some quantifiers % 4.32/1.62 Prover 2: Constructing countermodel ... % 4.66/1.72 Prover 2: proved (264ms) % 4.66/1.72 % 4.66/1.72 No countermodel exists, formula is valid % 4.66/1.72 % SZS status Theorem for theBenchmark % 4.66/1.72 % 4.66/1.72 Generating proof ... Warning: ignoring some quantifiers % 5.95/2.05 found it (size 64) % 5.95/2.05 % 5.95/2.05 % SZS output start Proof for theBenchmark % 5.95/2.05 Assumed formulas after preprocessing and simplification: % 5.95/2.05 | (0) ? [v0] : ? [v1] : (point(v1) = 0 & point(v0) = 0 & distinct_points(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v3, v4) = v6) | ~ (distinct_points(v2, v3) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v2, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v2, v5) = v6) | ~ (distinct_lines(v4, v5) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | (v8 = 0 & apart_point_and_line(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v4) = v7) | ~ (apart_point_and_line(v2, v5) = v6) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v4) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_lines(v4, v5) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v2, v5) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_points(v2, v3) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v4, v3) = v6) | ~ (distinct_points(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_lines(v3, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (convergent_lines(v3, v4) = v6) | ~ (convergent_lines(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (convergent_lines(v2, v4) = v6) | ~ (distinct_lines(v3, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v3, v4) = v6) | ~ (distinct_lines(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_points(v3, v4) = v6) | ~ (distinct_points(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v4, v3) = v5) | ~ (apart_point_and_line(v2, v3) = 0) | distinct_points(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v4) = v5) | ~ (apart_point_and_line(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = 0) | ~ (distinct_lines(v3, v4) = v5) | apart_point_and_line(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = 0) | ~ (distinct_points(v2, v4) = v5) | apart_point_and_line(v4, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v3, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v3) = 0) | ~ (distinct_lines(v3, v4) = v5) | convergent_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v3, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v2, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v3, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v2, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (orthogonal_through_point(v5, v4) = v3) | ~ (orthogonal_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (parallel_through_point(v5, v4) = v3) | ~ (parallel_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersection_point(v5, v4) = v3) | ~ (intersection_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (line_connecting(v5, v4) = v3) | ~ (line_connecting(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (apart_point_and_line(v5, v4) = v3) | ~ (apart_point_and_line(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (convergent_lines(v5, v4) = v3) | ~ (convergent_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_lines(v5, v4) = v3) | ~ (distinct_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_points(v5, v4) = v3) | ~ (distinct_points(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | ~ (distinct_points(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v3, v5) = 0) | (v6 = 0 & apart_point_and_line(v3, v4) = 0) | (v6 = 0 & apart_point_and_line(v2, v5) = 0) | (v6 = 0 & apart_point_and_line(v2, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (point(v4) = v3) | ~ (point(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (line(v4) = v3) | ~ (line(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (orthogonal_through_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & point(v4) = 0) | ( ~ (v5 = 0) & line(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v4, v3) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v4, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & point(v2) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v3, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : (v3 = 0 | ~ (line(v2) = v3)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | apart_point_and_line(v1, v2) = 0) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v3) = v5)) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v2) = v5)) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & point(v4) = 0 & intersection_point(v2, v3) = v4) | ( ~ (v4 = 0) & line(v3) = v4) | ( ~ (v4 = 0) & line(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v3, v4) = v5)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v2, v4) = v5)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & line(v4) = 0 & line_connecting(v2, v3) = v4) | ( ~ (v4 = 0) & point(v3) = v4) | ( ~ (v4 = 0) & point(v2) = v4))) & ! [v2] : ~ (convergent_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_points(v2, v2) = 0) & ? [v2] : ? [v3] : ? [v4] : orthogonal_through_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : parallel_through_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : intersection_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : line_connecting(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : apart_point_and_line(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : convergent_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : distinct_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : distinct_points(v3, v2) = v4 & ? [v2] : ? [v3] : point(v2) = v3 & ? [v2] : ? [v3] : line(v2) = v3) % 6.45/2.10 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 6.45/2.10 | (1) point(all_0_0_0) = 0 & point(all_0_1_1) = 0 & distinct_points(all_0_1_1, all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(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] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (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(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (line(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (apart_point_and_line(all_0_0_0, v0) = v1) | apart_point_and_line(all_0_1_1, v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (apart_point_and_line(all_0_1_1, v0) = v1) | apart_point_and_line(all_0_0_0, v0) = 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] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [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] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 % 6.64/2.13 | % 6.64/2.13 | Applying alpha-rule on (1) yields: % 6.64/2.13 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 6.64/2.13 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 6.64/2.13 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 6.64/2.13 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 6.64/2.13 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 6.64/2.13 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 6.64/2.13 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 6.64/2.13 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 6.64/2.13 | (10) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) % 6.64/2.13 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 6.64/2.13 | (12) ! [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) % 6.64/2.14 | (13) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 6.64/2.14 | (14) ? [v0] : ? [v1] : line(v0) = v1 % 6.64/2.14 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 6.64/2.14 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 6.64/2.14 | (17) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) % 6.64/2.14 | (18) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 6.64/2.14 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 6.64/2.14 | (20) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 6.64/2.14 | (21) ! [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) % 6.64/2.14 | (22) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 6.64/2.14 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 6.64/2.14 | (24) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 6.64/2.14 | (25) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 6.64/2.14 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 6.64/2.14 | (27) ? [v0] : ? [v1] : point(v0) = v1 % 6.64/2.14 | (28) ! [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)) % 6.64/2.14 | (29) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 6.64/2.14 | (30) ! [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)) % 6.64/2.14 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 6.64/2.14 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 6.64/2.14 | (33) distinct_points(all_0_1_1, all_0_0_0) = 0 % 6.64/2.14 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 6.64/2.14 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 6.64/2.14 | (36) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 % 6.64/2.14 | (37) ! [v0] : ! [v1] : (v1 = 0 | ~ (line(v0) = v1)) % 6.64/2.14 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 6.64/2.15 | (39) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 6.64/2.15 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 6.64/2.15 | (41) ! [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)) % 6.64/2.15 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) % 6.64/2.15 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 6.64/2.15 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) % 6.64/2.15 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 6.64/2.15 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 6.64/2.15 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 6.64/2.15 | (48) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 6.64/2.15 | (49) ! [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)) % 6.64/2.15 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 6.64/2.15 | (51) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 6.64/2.15 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 6.64/2.15 | (53) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 6.64/2.16 | (54) ! [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) % 6.64/2.16 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 6.64/2.16 | (56) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 6.64/2.16 | (57) point(all_0_1_1) = 0 % 6.64/2.16 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 6.64/2.16 | (59) ! [v0] : ! [v1] : (v1 = 0 | ~ (apart_point_and_line(all_0_1_1, v0) = v1) | apart_point_and_line(all_0_0_0, v0) = 0) % 6.64/2.16 | (60) ! [v0] : ! [v1] : (v1 = 0 | ~ (apart_point_and_line(all_0_0_0, v0) = v1) | apart_point_and_line(all_0_1_1, v0) = 0) % 6.64/2.16 | (61) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 6.64/2.16 | (62) ! [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)) % 6.64/2.16 | (63) point(all_0_0_0) = 0 % 6.64/2.16 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 6.64/2.16 | (65) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 6.64/2.16 | (66) ! [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) % 6.64/2.16 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 6.64/2.16 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 6.64/2.16 | (69) ! [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)) % 6.64/2.16 | % 6.64/2.16 | Instantiating formula (48) with all_0_0_0, all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_0_0) = 0, yields: % 6.64/2.16 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(all_0_0_0, v0) = v1) % 6.64/2.16 | % 6.64/2.16 | Instantiating formula (56) with all_0_0_0, all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_0_0) = 0, yields: % 6.64/2.16 | (71) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(all_0_1_1, v0) = v1) % 6.64/2.16 | % 6.64/2.16 | Instantiating formula (10) with all_0_0_0, all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_0_0) = 0, yields: % 6.64/2.16 | (72) ? [v0] : ? [v1] : ((v1 = 0 & line(v0) = 0 & line_connecting(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & point(all_0_0_0) = v0) | ( ~ (v0 = 0) & point(all_0_1_1) = v0)) % 6.64/2.16 | % 6.64/2.16 | Instantiating (72) with all_32_0_30, all_32_1_31 yields: % 6.64/2.16 | (73) (all_32_0_30 = 0 & line(all_32_1_31) = 0 & line_connecting(all_0_1_1, all_0_0_0) = all_32_1_31) | ( ~ (all_32_1_31 = 0) & point(all_0_0_0) = all_32_1_31) | ( ~ (all_32_1_31 = 0) & point(all_0_1_1) = all_32_1_31) % 6.64/2.16 | % 6.64/2.16 | Instantiating (71) with all_33_0_32, all_33_1_33 yields: % 6.64/2.16 | (74) ~ (all_33_0_32 = 0) & line_connecting(all_0_1_1, all_0_0_0) = all_33_1_33 & apart_point_and_line(all_0_1_1, all_33_1_33) = all_33_0_32 % 6.64/2.16 | % 6.64/2.16 | Applying alpha-rule on (74) yields: % 6.64/2.16 | (75) ~ (all_33_0_32 = 0) % 6.64/2.16 | (76) line_connecting(all_0_1_1, all_0_0_0) = all_33_1_33 % 6.64/2.16 | (77) apart_point_and_line(all_0_1_1, all_33_1_33) = all_33_0_32 % 6.64/2.16 | % 6.64/2.16 | Instantiating (70) with all_35_0_34, all_35_1_35 yields: % 6.64/2.16 | (78) ~ (all_35_0_34 = 0) & line_connecting(all_0_1_1, all_0_0_0) = all_35_1_35 & apart_point_and_line(all_0_0_0, all_35_1_35) = all_35_0_34 % 6.64/2.16 | % 6.64/2.16 | Applying alpha-rule on (78) yields: % 6.64/2.16 | (79) ~ (all_35_0_34 = 0) % 6.64/2.16 | (80) line_connecting(all_0_1_1, all_0_0_0) = all_35_1_35 % 6.64/2.16 | (81) apart_point_and_line(all_0_0_0, all_35_1_35) = all_35_0_34 % 6.64/2.16 | % 6.64/2.16 +-Applying beta-rule and splitting (73), into two cases. % 6.64/2.16 |-Branch one: % 6.64/2.16 | (82) (all_32_0_30 = 0 & line(all_32_1_31) = 0 & line_connecting(all_0_1_1, all_0_0_0) = all_32_1_31) | ( ~ (all_32_1_31 = 0) & point(all_0_0_0) = all_32_1_31) % 6.64/2.16 | % 6.64/2.16 +-Applying beta-rule and splitting (82), into two cases. % 6.64/2.16 |-Branch one: % 6.64/2.16 | (83) all_32_0_30 = 0 & line(all_32_1_31) = 0 & line_connecting(all_0_1_1, all_0_0_0) = all_32_1_31 % 6.64/2.16 | % 6.64/2.16 | Applying alpha-rule on (83) yields: % 6.64/2.16 | (84) all_32_0_30 = 0 % 6.64/2.16 | (85) line(all_32_1_31) = 0 % 6.64/2.17 | (86) line_connecting(all_0_1_1, all_0_0_0) = all_32_1_31 % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (40) with all_0_1_1, all_0_0_0, all_33_1_33, all_35_1_35 and discharging atoms line_connecting(all_0_1_1, all_0_0_0) = all_35_1_35, line_connecting(all_0_1_1, all_0_0_0) = all_33_1_33, yields: % 6.64/2.17 | (87) all_35_1_35 = all_33_1_33 % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (40) with all_0_1_1, all_0_0_0, all_32_1_31, all_35_1_35 and discharging atoms line_connecting(all_0_1_1, all_0_0_0) = all_35_1_35, line_connecting(all_0_1_1, all_0_0_0) = all_32_1_31, yields: % 6.64/2.17 | (88) all_35_1_35 = all_32_1_31 % 6.64/2.17 | % 6.64/2.17 | Combining equations (88,87) yields a new equation: % 6.64/2.17 | (89) all_33_1_33 = all_32_1_31 % 6.64/2.17 | % 6.64/2.17 | Combining equations (89,87) yields a new equation: % 6.64/2.17 | (88) all_35_1_35 = all_32_1_31 % 6.64/2.17 | % 6.64/2.17 | From (88) and (81) follows: % 6.64/2.17 | (91) apart_point_and_line(all_0_0_0, all_32_1_31) = all_35_0_34 % 6.64/2.17 | % 6.64/2.17 | From (89) and (77) follows: % 6.64/2.17 | (92) apart_point_and_line(all_0_1_1, all_32_1_31) = all_33_0_32 % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (52) with all_35_0_34, all_35_0_34, all_32_1_31, all_32_1_31, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_0_0, all_32_1_31) = all_35_0_34, distinct_points(all_0_1_1, all_0_0_0) = 0, yields: % 6.64/2.17 | (93) all_35_0_34 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0)) % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (47) with all_35_0_34, all_35_0_34, all_32_1_31, all_32_1_31, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_32_1_31) = all_35_0_34, yields: % 6.64/2.17 | (94) all_35_0_34 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (60) with all_35_0_34, all_32_1_31 and discharging atoms apart_point_and_line(all_0_0_0, all_32_1_31) = all_35_0_34, yields: % 6.64/2.17 | (95) all_35_0_34 = 0 | apart_point_and_line(all_0_1_1, all_32_1_31) = 0 % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (47) with all_33_0_32, all_35_0_34, all_32_1_31, all_32_1_31, all_0_1_1, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_32_1_31) = all_35_0_34, apart_point_and_line(all_0_1_1, all_32_1_31) = all_33_0_32, yields: % 6.64/2.17 | (96) all_35_0_34 = 0 | all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0)) % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (47) with all_35_0_34, all_33_0_32, all_32_1_31, all_32_1_31, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_0_0, all_32_1_31) = all_35_0_34, apart_point_and_line(all_0_1_1, all_32_1_31) = all_33_0_32, yields: % 6.64/2.17 | (97) all_35_0_34 = 0 | all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0)) % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (6) with all_33_0_32, all_33_0_32, all_32_1_31, all_32_1_31, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_32_1_31) = all_33_0_32, distinct_points(all_0_1_1, all_0_0_0) = 0, yields: % 6.64/2.17 | (98) all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0)) % 6.64/2.17 | % 6.64/2.17 | Instantiating formula (47) with all_33_0_32, all_33_0_32, all_32_1_31, all_32_1_31, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_32_1_31) = all_33_0_32, yields: % 6.64/2.17 | (99) all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 6.64/2.17 | % 6.64/2.17 +-Applying beta-rule and splitting (95), into two cases. % 6.64/2.17 |-Branch one: % 6.64/2.17 | (100) apart_point_and_line(all_0_1_1, all_32_1_31) = 0 % 6.64/2.17 | % 6.64/2.17 +-Applying beta-rule and splitting (98), into two cases. % 6.64/2.17 |-Branch one: % 6.64/2.17 | (101) all_33_0_32 = 0 % 6.64/2.17 | % 6.64/2.17 | Equations (101) can reduce 75 to: % 6.64/2.17 | (102) $false % 6.64/2.17 | % 6.64/2.17 |-The branch is then unsatisfiable % 6.64/2.17 |-Branch two: % 6.64/2.17 | (75) ~ (all_33_0_32 = 0) % 6.64/2.17 | (104) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0)) % 6.64/2.17 | % 6.64/2.17 +-Applying beta-rule and splitting (93), into two cases. % 6.64/2.17 |-Branch one: % 6.64/2.17 | (105) all_35_0_34 = 0 % 6.64/2.17 | % 6.64/2.17 | Equations (105) can reduce 79 to: % 6.64/2.17 | (102) $false % 6.64/2.17 | % 6.64/2.17 |-The branch is then unsatisfiable % 6.64/2.17 |-Branch two: % 6.64/2.17 | (79) ~ (all_35_0_34 = 0) % 6.64/2.17 | (108) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0)) % 6.64/2.17 | % 6.64/2.17 +-Applying beta-rule and splitting (94), into two cases. % 6.64/2.17 |-Branch one: % 6.64/2.17 | (105) all_35_0_34 = 0 % 6.64/2.17 | % 6.64/2.17 | Equations (105) can reduce 79 to: % 6.64/2.17 | (102) $false % 6.64/2.17 | % 6.64/2.17 |-The branch is then unsatisfiable % 6.64/2.17 |-Branch two: % 6.64/2.17 | (79) ~ (all_35_0_34 = 0) % 6.64/2.17 | (112) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0)) % 6.64/2.17 | % 6.64/2.17 +-Applying beta-rule and splitting (99), into two cases. % 6.64/2.17 |-Branch one: % 6.64/2.17 | (101) all_33_0_32 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (101) can reduce 75 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 |-Branch two: % 6.64/2.18 | (75) ~ (all_33_0_32 = 0) % 6.64/2.18 | (116) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 6.64/2.18 | % 6.64/2.18 +-Applying beta-rule and splitting (97), into two cases. % 6.64/2.18 |-Branch one: % 6.64/2.18 | (105) all_35_0_34 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (105) can reduce 79 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 |-Branch two: % 6.64/2.18 | (79) ~ (all_35_0_34 = 0) % 6.64/2.18 | (120) all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0)) % 6.64/2.18 | % 6.64/2.18 +-Applying beta-rule and splitting (96), into two cases. % 6.64/2.18 |-Branch one: % 6.64/2.18 | (105) all_35_0_34 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (105) can reduce 79 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 |-Branch two: % 6.64/2.18 | (79) ~ (all_35_0_34 = 0) % 6.64/2.18 | (124) all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0)) % 6.64/2.18 | % 6.64/2.18 +-Applying beta-rule and splitting (120), into two cases. % 6.64/2.18 |-Branch one: % 6.64/2.18 | (101) all_33_0_32 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (101) can reduce 75 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 |-Branch two: % 6.64/2.18 | (75) ~ (all_33_0_32 = 0) % 6.64/2.18 | (128) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0)) % 6.64/2.18 | % 6.64/2.18 +-Applying beta-rule and splitting (124), into two cases. % 6.64/2.18 |-Branch one: % 6.64/2.18 | (101) all_33_0_32 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (101) can reduce 75 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 |-Branch two: % 6.64/2.18 | (75) ~ (all_33_0_32 = 0) % 6.64/2.18 | (132) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_32_1_31) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_32_1_31) = 0) | ( ~ (v0 = 0) & distinct_lines(all_32_1_31, all_32_1_31) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0)) % 6.64/2.18 | % 6.64/2.18 | Instantiating formula (31) with all_0_1_1, all_32_1_31, 0, all_33_0_32 and discharging atoms apart_point_and_line(all_0_1_1, all_32_1_31) = all_33_0_32, apart_point_and_line(all_0_1_1, all_32_1_31) = 0, yields: % 6.64/2.18 | (101) all_33_0_32 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (101) can reduce 75 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 |-Branch two: % 6.64/2.18 | (135) ~ (apart_point_and_line(all_0_1_1, all_32_1_31) = 0) % 6.64/2.18 | (105) all_35_0_34 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (105) can reduce 79 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 |-Branch two: % 6.64/2.18 | (138) ~ (all_32_1_31 = 0) & point(all_0_0_0) = all_32_1_31 % 6.64/2.18 | % 6.64/2.18 | Applying alpha-rule on (138) yields: % 6.64/2.18 | (139) ~ (all_32_1_31 = 0) % 6.64/2.18 | (140) point(all_0_0_0) = all_32_1_31 % 6.64/2.18 | % 6.64/2.18 | Instantiating formula (67) with all_0_0_0, all_32_1_31, 0 and discharging atoms point(all_0_0_0) = all_32_1_31, point(all_0_0_0) = 0, yields: % 6.64/2.18 | (141) all_32_1_31 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (141) can reduce 139 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 |-Branch two: % 6.64/2.18 | (143) ~ (all_32_1_31 = 0) & point(all_0_1_1) = all_32_1_31 % 6.64/2.18 | % 6.64/2.18 | Applying alpha-rule on (143) yields: % 6.64/2.18 | (139) ~ (all_32_1_31 = 0) % 6.64/2.18 | (145) point(all_0_1_1) = all_32_1_31 % 6.64/2.18 | % 6.64/2.18 | Instantiating formula (67) with all_0_1_1, all_32_1_31, 0 and discharging atoms point(all_0_1_1) = all_32_1_31, point(all_0_1_1) = 0, yields: % 6.64/2.18 | (141) all_32_1_31 = 0 % 6.64/2.18 | % 6.64/2.18 | Equations (141) can reduce 139 to: % 6.64/2.18 | (102) $false % 6.64/2.18 | % 6.64/2.18 |-The branch is then unsatisfiable % 6.64/2.18 % SZS output end Proof for theBenchmark % 6.64/2.18 % 6.64/2.18 1569ms %------------------------------------------------------------------------------