%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n010.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 03:48:10 EDT 2022 % Result : Theorem 3.89s 1.58s % Output : Proof 5.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 13:22:23 EDT 2022 % 0.13/0.34 % CPUTime : % 0.48/0.60 ____ _ % 0.48/0.60 ___ / __ \_____(_)___ ________ __________ % 0.48/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.60 % 0.48/0.60 A Theorem Prover for First-Order Logic % 0.48/0.60 (ePrincess v.1.0) % 0.48/0.60 % 0.48/0.60 (c) Philipp Rümmer, 2009-2015 % 0.48/0.60 (c) Peter Backeman, 2014-2015 % 0.48/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.60 Bug reports to peter@backeman.se % 0.48/0.60 % 0.48/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.60 % 0.48/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.34/0.93 Prover 0: Preprocessing ... % 1.95/1.07 Prover 0: Warning: ignoring some quantifiers % 2.01/1.09 Prover 0: Constructing countermodel ... % 3.11/1.39 Prover 0: gave up % 3.11/1.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.11/1.41 Prover 1: Preprocessing ... % 3.43/1.49 Prover 1: Constructing countermodel ... % 3.89/1.58 Prover 1: proved (187ms) % 3.89/1.58 % 3.89/1.58 No countermodel exists, formula is valid % 3.89/1.58 % SZS status Theorem for theBenchmark % 3.89/1.58 % 3.89/1.58 Generating proof ... found it (size 59) % 5.12/1.86 % 5.12/1.86 % SZS output start Proof for theBenchmark % 5.12/1.86 Assumed formulas after preprocessing and simplification: % 5.12/1.86 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & line_connecting(v0, v1) = v6 & apart_point_and_line(v1, v2) = v5 & apart_point_and_line(v0, v2) = v4 & convergent_lines(v2, v3) = 0 & distinct_lines(v2, v6) = v7 & distinct_points(v0, v1) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection_point(v8, v9) = v11) | ~ (distinct_points(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (apart_point_and_line(v10, v9) = v15 & apart_point_and_line(v10, v8) = v14 & convergent_lines(v8, v9) = v13 & ( ~ (v13 = 0) | ( ~ (v15 = 0) & ~ (v14 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | apart_point_and_line(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_points(v8, v10) = v11) | apart_point_and_line(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_lines(v8, v10) = v11) | ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_points(v8, v10) = v11) | ~ (distinct_points(v8, v9) = 0) | distinct_points(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection_point(v11, v10) = v9) | ~ (intersection_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (line_connecting(v11, v10) = v9) | ~ (line_connecting(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (apart_point_and_line(v11, v10) = v9) | ~ (apart_point_and_line(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (convergent_lines(v11, v10) = v9) | ~ (convergent_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_lines(v11, v10) = v9) | ~ (distinct_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_points(v11, v10) = v9) | ~ (distinct_points(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v8, v9) = v11) | ~ (apart_point_and_line(v10, v11) = 0) | ? [v12] : ? [v13] : ? [v14] : (distinct_points(v10, v9) = v14 & distinct_points(v10, v8) = v13 & distinct_points(v8, v9) = v12 & ( ~ (v12 = 0) | (v14 = 0 & v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) | ~ (distinct_points(v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (apart_point_and_line(v9, v11) = v15 & apart_point_and_line(v9, v10) = v14 & apart_point_and_line(v8, v11) = v13 & apart_point_and_line(v8, v10) = v12 & (v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ( ~ (convergent_lines(v8, v9) = 0) | distinct_lines(v8, v9) = 0) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0) & (v5 = 0 | v4 = 0)) % 5.12/1.90 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields: % 5.12/1.90 | (1) ~ (all_0_0_0 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_0_1_1 & apart_point_and_line(all_0_6_6, all_0_5_5) = all_0_2_2 & apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3 & convergent_lines(all_0_5_5, all_0_4_4) = 0 & distinct_lines(all_0_5_5, all_0_1_1) = all_0_0_0 & distinct_points(all_0_7_7, all_0_6_6) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 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(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, 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(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 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] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & (all_0_2_2 = 0 | all_0_3_3 = 0) % 5.12/1.91 | % 5.12/1.91 | Applying alpha-rule on (1) yields: % 5.12/1.91 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 5.12/1.91 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 5.12/1.91 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 5.12/1.91 | (5) distinct_lines(all_0_5_5, all_0_1_1) = all_0_0_0 % 5.12/1.91 | (6) all_0_2_2 = 0 | all_0_3_3 = 0 % 5.12/1.91 | (7) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 5.12/1.91 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))))) % 5.12/1.91 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 5.12/1.91 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 5.12/1.91 | (11) ! [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))) % 5.12/1.91 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 5.12/1.91 | (13) apart_point_and_line(all_0_6_6, all_0_5_5) = all_0_2_2 % 5.12/1.91 | (14) apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3 % 5.12/1.91 | (15) ! [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) % 5.12/1.91 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 5.12/1.91 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 5.12/1.91 | (18) ~ (all_0_0_0 = 0) % 5.12/1.91 | (19) ! [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) % 5.12/1.92 | (20) distinct_points(all_0_7_7, all_0_6_6) = 0 % 5.12/1.92 | (21) line_connecting(all_0_7_7, all_0_6_6) = all_0_1_1 % 5.12/1.92 | (22) convergent_lines(all_0_5_5, all_0_4_4) = 0 % 5.12/1.92 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) % 5.12/1.92 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 5.12/1.92 | (25) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 5.12/1.92 | (26) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) % 5.12/1.92 | (27) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 5.12/1.92 | % 5.12/1.92 | Instantiating formula (27) with all_0_7_7 yields: % 5.12/1.92 | (28) ~ (distinct_points(all_0_7_7, all_0_7_7) = 0) % 5.12/1.92 | % 5.12/1.92 | Instantiating formula (26) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 5.12/1.92 | (29) distinct_lines(all_0_5_5, all_0_4_4) = 0 % 5.12/1.92 | % 5.12/1.92 | Instantiating formula (19) with all_0_0_0, all_0_1_1, all_0_5_5, all_0_6_6 and discharging atoms distinct_lines(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 5.12/1.92 | (30) all_0_0_0 = 0 | ~ (apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | apart_point_and_line(all_0_6_6, all_0_1_1) = 0 % 5.12/1.92 | % 5.12/1.92 | Instantiating formula (19) with all_0_0_0, all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms distinct_lines(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 5.12/1.92 | (31) all_0_0_0 = 0 | ~ (apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | apart_point_and_line(all_0_7_7, all_0_1_1) = 0 % 5.12/1.92 | % 5.12/1.92 | Instantiating formula (11) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms distinct_lines(all_0_5_5, all_0_4_4) = 0, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 5.12/1.92 | (32) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_6_6, all_0_4_4) = v3 & apart_point_and_line(all_0_6_6, all_0_5_5) = v2 & apart_point_and_line(all_0_7_7, all_0_4_4) = v1 & apart_point_and_line(all_0_7_7, all_0_5_5) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0)) % 5.12/1.92 | % 5.12/1.92 | Instantiating (32) with all_22_0_8, all_22_1_9, all_22_2_10, all_22_3_11 yields: % 5.12/1.92 | (33) apart_point_and_line(all_0_6_6, all_0_4_4) = all_22_0_8 & apart_point_and_line(all_0_6_6, all_0_5_5) = all_22_1_9 & apart_point_and_line(all_0_7_7, all_0_4_4) = all_22_2_10 & apart_point_and_line(all_0_7_7, all_0_5_5) = all_22_3_11 & (all_22_0_8 = 0 | all_22_1_9 = 0 | all_22_2_10 = 0 | all_22_3_11 = 0) % 5.12/1.92 | % 5.12/1.92 | Applying alpha-rule on (33) yields: % 5.12/1.92 | (34) apart_point_and_line(all_0_6_6, all_0_5_5) = all_22_1_9 % 5.12/1.92 | (35) all_22_0_8 = 0 | all_22_1_9 = 0 | all_22_2_10 = 0 | all_22_3_11 = 0 % 5.12/1.92 | (36) apart_point_and_line(all_0_7_7, all_0_4_4) = all_22_2_10 % 5.12/1.92 | (37) apart_point_and_line(all_0_7_7, all_0_5_5) = all_22_3_11 % 5.12/1.92 | (38) apart_point_and_line(all_0_6_6, all_0_4_4) = all_22_0_8 % 5.12/1.92 | % 5.12/1.92 | Instantiating formula (12) with all_0_6_6, all_0_5_5, all_22_1_9, all_0_2_2 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_22_1_9, apart_point_and_line(all_0_6_6, all_0_5_5) = all_0_2_2, yields: % 5.12/1.92 | (39) all_22_1_9 = all_0_2_2 % 5.12/1.92 | % 5.12/1.92 | Instantiating formula (12) with all_0_7_7, all_0_5_5, all_22_3_11, all_0_3_3 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_22_3_11, apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3, yields: % 5.12/1.92 | (40) all_22_3_11 = all_0_3_3 % 5.12/1.92 | % 5.12/1.92 | From (39) and (34) follows: % 5.12/1.92 | (13) apart_point_and_line(all_0_6_6, all_0_5_5) = all_0_2_2 % 5.12/1.92 | % 5.12/1.92 | From (40) and (37) follows: % 5.12/1.93 | (14) apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3 % 5.12/1.93 | % 5.12/1.93 | Instantiating formula (23) with all_0_1_1, all_0_6_6, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_1_1, yields: % 5.12/1.93 | (43) ~ (apart_point_and_line(all_0_6_6, all_0_1_1) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_6_6, all_0_6_6) = v2 & distinct_points(all_0_6_6, all_0_7_7) = v1 & distinct_points(all_0_7_7, all_0_6_6) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.12/1.93 | % 5.12/1.93 | Instantiating formula (23) with all_0_1_1, all_0_7_7, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_1_1, yields: % 5.12/1.93 | (44) ~ (apart_point_and_line(all_0_7_7, all_0_1_1) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_7_7, all_0_6_6) = v2 & distinct_points(all_0_7_7, all_0_6_6) = v0 & distinct_points(all_0_7_7, all_0_7_7) = v1 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.12/1.93 | % 5.12/1.93 +-Applying beta-rule and splitting (44), into two cases. % 5.12/1.93 |-Branch one: % 5.12/1.93 | (45) ~ (apart_point_and_line(all_0_7_7, all_0_1_1) = 0) % 5.12/1.93 | % 5.12/1.93 +-Applying beta-rule and splitting (31), into two cases. % 5.12/1.93 |-Branch one: % 5.12/1.93 | (46) ~ (apart_point_and_line(all_0_7_7, all_0_5_5) = 0) % 5.12/1.93 | % 5.12/1.93 | Using (14) and (46) yields: % 5.12/1.93 | (47) ~ (all_0_3_3 = 0) % 5.12/1.93 | % 5.12/1.93 +-Applying beta-rule and splitting (6), into two cases. % 5.12/1.93 |-Branch one: % 5.12/1.93 | (48) all_0_2_2 = 0 % 5.12/1.93 | % 5.12/1.93 | From (48) and (13) follows: % 5.12/1.93 | (49) apart_point_and_line(all_0_6_6, all_0_5_5) = 0 % 5.12/1.93 | % 5.12/1.93 +-Applying beta-rule and splitting (30), into two cases. % 5.12/1.93 |-Branch one: % 5.12/1.93 | (50) ~ (apart_point_and_line(all_0_6_6, all_0_5_5) = 0) % 5.12/1.93 | % 5.12/1.93 | Using (49) and (50) yields: % 5.12/1.93 | (51) $false % 5.12/1.93 | % 5.12/1.93 |-The branch is then unsatisfiable % 5.12/1.93 |-Branch two: % 5.12/1.93 | (49) apart_point_and_line(all_0_6_6, all_0_5_5) = 0 % 5.12/1.93 | (53) all_0_0_0 = 0 | apart_point_and_line(all_0_6_6, all_0_1_1) = 0 % 5.12/1.93 | % 5.12/1.93 +-Applying beta-rule and splitting (53), into two cases. % 5.12/1.93 |-Branch one: % 5.12/1.93 | (54) apart_point_and_line(all_0_6_6, all_0_1_1) = 0 % 5.12/1.93 | % 5.12/1.93 +-Applying beta-rule and splitting (43), into two cases. % 5.12/1.93 |-Branch one: % 5.12/1.93 | (55) ~ (apart_point_and_line(all_0_6_6, all_0_1_1) = 0) % 5.12/1.93 | % 5.12/1.93 | Using (54) and (55) yields: % 5.12/1.93 | (51) $false % 5.12/1.93 | % 5.12/1.93 |-The branch is then unsatisfiable % 5.12/1.93 |-Branch two: % 5.12/1.93 | (54) apart_point_and_line(all_0_6_6, all_0_1_1) = 0 % 5.12/1.93 | (58) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_6_6, all_0_6_6) = v2 & distinct_points(all_0_6_6, all_0_7_7) = v1 & distinct_points(all_0_7_7, all_0_6_6) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.12/1.93 | % 5.12/1.93 | Instantiating (58) with all_82_0_16, all_82_1_17, all_82_2_18 yields: % 5.12/1.93 | (59) distinct_points(all_0_6_6, all_0_6_6) = all_82_0_16 & distinct_points(all_0_6_6, all_0_7_7) = all_82_1_17 & distinct_points(all_0_7_7, all_0_6_6) = all_82_2_18 & ( ~ (all_82_2_18 = 0) | (all_82_0_16 = 0 & all_82_1_17 = 0)) % 5.12/1.93 | % 5.12/1.93 | Applying alpha-rule on (59) yields: % 5.12/1.93 | (60) distinct_points(all_0_6_6, all_0_6_6) = all_82_0_16 % 5.12/1.93 | (61) distinct_points(all_0_6_6, all_0_7_7) = all_82_1_17 % 5.12/1.93 | (62) distinct_points(all_0_7_7, all_0_6_6) = all_82_2_18 % 5.12/1.93 | (63) ~ (all_82_2_18 = 0) | (all_82_0_16 = 0 & all_82_1_17 = 0) % 5.12/1.93 | % 5.12/1.93 | Instantiating formula (27) with all_0_6_6 yields: % 5.12/1.93 | (64) ~ (distinct_points(all_0_6_6, all_0_6_6) = 0) % 5.12/1.93 | % 5.12/1.93 | Instantiating formula (24) with all_0_7_7, all_0_6_6, all_82_2_18, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_82_2_18, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 5.12/1.93 | (65) all_82_2_18 = 0 % 5.12/1.93 | % 5.12/1.93 +-Applying beta-rule and splitting (63), into two cases. % 5.12/1.93 |-Branch one: % 5.12/1.93 | (66) ~ (all_82_2_18 = 0) % 5.12/1.93 | % 5.12/1.93 | Equations (65) can reduce 66 to: % 5.12/1.93 | (67) $false % 5.12/1.93 | % 5.12/1.93 |-The branch is then unsatisfiable % 5.12/1.93 |-Branch two: % 5.12/1.93 | (65) all_82_2_18 = 0 % 5.12/1.93 | (69) all_82_0_16 = 0 & all_82_1_17 = 0 % 5.12/1.93 | % 5.12/1.93 | Applying alpha-rule on (69) yields: % 5.12/1.93 | (70) all_82_0_16 = 0 % 5.12/1.93 | (71) all_82_1_17 = 0 % 5.12/1.93 | % 5.12/1.93 | From (70) and (60) follows: % 5.12/1.93 | (72) distinct_points(all_0_6_6, all_0_6_6) = 0 % 5.12/1.94 | % 5.12/1.94 | Using (72) and (64) yields: % 5.12/1.94 | (51) $false % 5.12/1.94 | % 5.12/1.94 |-The branch is then unsatisfiable % 5.12/1.94 |-Branch two: % 5.12/1.94 | (55) ~ (apart_point_and_line(all_0_6_6, all_0_1_1) = 0) % 5.12/1.94 | (75) all_0_0_0 = 0 % 5.12/1.94 | % 5.12/1.94 | Equations (75) can reduce 18 to: % 5.12/1.94 | (67) $false % 5.12/1.94 | % 5.12/1.94 |-The branch is then unsatisfiable % 5.12/1.94 |-Branch two: % 5.12/1.94 | (77) ~ (all_0_2_2 = 0) % 5.12/1.94 | (78) all_0_3_3 = 0 % 5.12/1.94 | % 5.12/1.94 | Equations (78) can reduce 47 to: % 5.12/1.94 | (67) $false % 5.12/1.94 | % 5.12/1.94 |-The branch is then unsatisfiable % 5.12/1.94 |-Branch two: % 5.12/1.94 | (80) apart_point_and_line(all_0_7_7, all_0_5_5) = 0 % 5.12/1.94 | (81) all_0_0_0 = 0 | apart_point_and_line(all_0_7_7, all_0_1_1) = 0 % 5.12/1.94 | % 5.12/1.94 +-Applying beta-rule and splitting (81), into two cases. % 5.12/1.94 |-Branch one: % 5.12/1.94 | (82) apart_point_and_line(all_0_7_7, all_0_1_1) = 0 % 5.12/1.94 | % 5.12/1.94 | Using (82) and (45) yields: % 5.12/1.94 | (51) $false % 5.12/1.94 | % 5.12/1.94 |-The branch is then unsatisfiable % 5.12/1.94 |-Branch two: % 5.12/1.94 | (45) ~ (apart_point_and_line(all_0_7_7, all_0_1_1) = 0) % 5.12/1.94 | (75) all_0_0_0 = 0 % 5.12/1.94 | % 5.12/1.94 | Equations (75) can reduce 18 to: % 5.12/1.94 | (67) $false % 5.12/1.94 | % 5.12/1.94 |-The branch is then unsatisfiable % 5.12/1.94 |-Branch two: % 5.12/1.94 | (82) apart_point_and_line(all_0_7_7, all_0_1_1) = 0 % 5.12/1.94 | (88) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_7_7, all_0_6_6) = v2 & distinct_points(all_0_7_7, all_0_6_6) = v0 & distinct_points(all_0_7_7, all_0_7_7) = v1 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.48/1.94 | % 5.48/1.94 | Instantiating (88) with all_58_0_19, all_58_1_20, all_58_2_21 yields: % 5.48/1.94 | (89) distinct_points(all_0_7_7, all_0_6_6) = all_58_0_19 & distinct_points(all_0_7_7, all_0_6_6) = all_58_2_21 & distinct_points(all_0_7_7, all_0_7_7) = all_58_1_20 & ( ~ (all_58_2_21 = 0) | (all_58_0_19 = 0 & all_58_1_20 = 0)) % 5.48/1.94 | % 5.48/1.94 | Applying alpha-rule on (89) yields: % 5.48/1.94 | (90) distinct_points(all_0_7_7, all_0_6_6) = all_58_0_19 % 5.48/1.94 | (91) distinct_points(all_0_7_7, all_0_6_6) = all_58_2_21 % 5.48/1.94 | (92) distinct_points(all_0_7_7, all_0_7_7) = all_58_1_20 % 5.48/1.94 | (93) ~ (all_58_2_21 = 0) | (all_58_0_19 = 0 & all_58_1_20 = 0) % 5.48/1.94 | % 5.48/1.94 | Instantiating formula (24) with all_0_7_7, all_0_6_6, all_58_0_19, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_58_0_19, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 5.48/1.94 | (94) all_58_0_19 = 0 % 5.48/1.94 | % 5.48/1.94 | Instantiating formula (24) with all_0_7_7, all_0_6_6, all_58_2_21, all_58_0_19 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_58_0_19, distinct_points(all_0_7_7, all_0_6_6) = all_58_2_21, yields: % 5.48/1.94 | (95) all_58_0_19 = all_58_2_21 % 5.48/1.94 | % 5.48/1.94 | Using (92) and (28) yields: % 5.48/1.94 | (96) ~ (all_58_1_20 = 0) % 5.48/1.94 | % 5.48/1.94 | Combining equations (94,95) yields a new equation: % 5.48/1.94 | (97) all_58_2_21 = 0 % 5.48/1.94 | % 5.48/1.94 +-Applying beta-rule and splitting (93), into two cases. % 5.48/1.94 |-Branch one: % 5.48/1.94 | (98) ~ (all_58_2_21 = 0) % 5.48/1.94 | % 5.48/1.94 | Equations (97) can reduce 98 to: % 5.48/1.94 | (67) $false % 5.48/1.94 | % 5.48/1.94 |-The branch is then unsatisfiable % 5.48/1.94 |-Branch two: % 5.48/1.94 | (97) all_58_2_21 = 0 % 5.48/1.94 | (101) all_58_0_19 = 0 & all_58_1_20 = 0 % 5.48/1.94 | % 5.48/1.94 | Applying alpha-rule on (101) yields: % 5.48/1.94 | (94) all_58_0_19 = 0 % 5.48/1.94 | (103) all_58_1_20 = 0 % 5.48/1.94 | % 5.48/1.94 | Equations (103) can reduce 96 to: % 5.48/1.94 | (67) $false % 5.48/1.94 | % 5.48/1.94 |-The branch is then unsatisfiable % 5.48/1.94 % SZS output end Proof for theBenchmark % 5.48/1.94 % 5.48/1.94 1338ms %------------------------------------------------------------------------------