%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO200+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 03:48:36 EDT 2022 % Result : Theorem 3.46s 1.56s % Output : Proof 5.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO200+2 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 08:58:43 EDT 2022 % 0.12/0.33 % CPUTime : % 0.58/0.59 ____ _ % 0.58/0.59 ___ / __ \_____(_)___ ________ __________ % 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic % 0.58/0.59 (ePrincess v.1.0) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2015 % 0.58/0.59 (c) Peter Backeman, 2014-2015 % 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.59 Bug reports to peter@backeman.se % 0.58/0.59 % 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.59 % 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.92 Prover 0: Preprocessing ... % 1.86/1.04 Prover 0: Warning: ignoring some quantifiers % 1.86/1.05 Prover 0: Constructing countermodel ... % 2.73/1.32 Prover 0: gave up % 2.73/1.32 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.73/1.36 Prover 1: Preprocessing ... % 2.94/1.46 Prover 1: Constructing countermodel ... % 3.46/1.56 Prover 1: proved (235ms) % 3.46/1.56 % 3.46/1.56 No countermodel exists, formula is valid % 3.46/1.56 % SZS status Theorem for theBenchmark % 3.46/1.56 % 3.46/1.56 Generating proof ... found it (size 83) % 4.73/1.84 % 4.73/1.84 % SZS output start Proof for theBenchmark % 4.73/1.84 Assumed formulas after preprocessing and simplification: % 4.73/1.84 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & distinct_lines(v2, v3) = 0 & distinct_points(v0, v1) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (intersection_point(v4, v5) = v7) | ~ (distinct_points(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (apart_point_and_line(v6, v5) = v11 & apart_point_and_line(v6, v4) = v10 & convergent_lines(v4, v5) = v9 & ( ~ (v9 = 0) | ( ~ (v11 = 0) & ~ (v10 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = 0) | ~ (distinct_lines(v5, v6) = v7) | apart_point_and_line(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = 0) | ~ (distinct_points(v4, v6) = v7) | apart_point_and_line(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v4, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | convergent_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v4, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v4, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection_point(v7, v6) = v5) | ~ (intersection_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (line_connecting(v7, v6) = v5) | ~ (line_connecting(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (apart_point_and_line(v7, v6) = v5) | ~ (apart_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (convergent_lines(v7, v6) = v5) | ~ (convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_lines(v7, v6) = v5) | ~ (distinct_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_points(v7, v6) = v5) | ~ (distinct_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (distinct_points(v6, v5) = v10 & distinct_points(v6, v4) = v9 & distinct_points(v4, v5) = v8 & ( ~ (v8 = 0) | (v10 = 0 & v9 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ~ (distinct_points(v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (apart_point_and_line(v5, v7) = v11 & apart_point_and_line(v5, v6) = v10 & apart_point_and_line(v4, v7) = v9 & apart_point_and_line(v4, v6) = v8 & (v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | distinct_lines(v4, v5) = 0) & ! [v4] : ~ (convergent_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_points(v4, v4) = 0)) % 4.73/1.87 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 4.73/1.87 | (1) line_connecting(all_0_2_2, all_0_3_3) = all_0_0_0 & line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1 & distinct_lines(all_0_1_1, all_0_0_0) = 0 & distinct_points(all_0_3_3, all_0_2_2) = 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) % 4.73/1.88 | % 4.73/1.88 | Applying alpha-rule on (1) yields: % 4.73/1.88 | (2) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 4.73/1.89 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.73/1.89 | (4) ! [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)))) % 4.73/1.89 | (5) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.73/1.89 | (6) ! [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) % 4.73/1.89 | (7) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 4.73/1.89 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 4.73/1.89 | (9) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) % 4.73/1.89 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 4.73/1.89 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 4.73/1.89 | (12) line_connecting(all_0_2_2, all_0_3_3) = all_0_0_0 % 4.73/1.89 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 4.73/1.89 | (14) ! [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))))) % 4.73/1.89 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.73/1.89 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 4.73/1.89 | (17) distinct_points(all_0_3_3, all_0_2_2) = 0 % 4.73/1.89 | (18) line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1 % 4.73/1.89 | (19) distinct_lines(all_0_1_1, all_0_0_0) = 0 % 4.73/1.89 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 4.73/1.89 | (21) ! [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) % 4.73/1.89 | (22) ! [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))) % 4.73/1.89 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 4.73/1.89 | % 4.73/1.89 | Instantiating formula (5) with all_0_3_3 yields: % 4.73/1.89 | (24) ~ (distinct_points(all_0_3_3, all_0_3_3) = 0) % 4.73/1.89 | % 4.73/1.89 | Instantiating formula (22) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms distinct_lines(all_0_1_1, all_0_0_0) = 0, distinct_points(all_0_3_3, all_0_2_2) = 0, yields: % 4.73/1.90 | (25) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_2_2, all_0_0_0) = v3 & apart_point_and_line(all_0_2_2, all_0_1_1) = v2 & apart_point_and_line(all_0_3_3, all_0_0_0) = v1 & apart_point_and_line(all_0_3_3, all_0_1_1) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0)) % 4.73/1.90 | % 4.73/1.90 | Instantiating (25) with all_16_0_4, all_16_1_5, all_16_2_6, all_16_3_7 yields: % 4.73/1.90 | (26) apart_point_and_line(all_0_2_2, all_0_0_0) = all_16_0_4 & apart_point_and_line(all_0_2_2, all_0_1_1) = all_16_1_5 & apart_point_and_line(all_0_3_3, all_0_0_0) = all_16_2_6 & apart_point_and_line(all_0_3_3, all_0_1_1) = all_16_3_7 & (all_16_0_4 = 0 | all_16_1_5 = 0 | all_16_2_6 = 0 | all_16_3_7 = 0) % 4.73/1.90 | % 4.73/1.90 | Applying alpha-rule on (26) yields: % 4.73/1.90 | (27) apart_point_and_line(all_0_3_3, all_0_0_0) = all_16_2_6 % 4.73/1.90 | (28) apart_point_and_line(all_0_2_2, all_0_1_1) = all_16_1_5 % 4.73/1.90 | (29) apart_point_and_line(all_0_2_2, all_0_0_0) = all_16_0_4 % 4.73/1.90 | (30) apart_point_and_line(all_0_3_3, all_0_1_1) = all_16_3_7 % 4.73/1.90 | (31) all_16_0_4 = 0 | all_16_1_5 = 0 | all_16_2_6 = 0 | all_16_3_7 = 0 % 4.73/1.90 | % 4.73/1.90 | Instantiating formula (4) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_2_2 and discharging atoms line_connecting(all_0_2_2, all_0_3_3) = all_0_0_0, yields: % 4.73/1.90 | (32) ~ (apart_point_and_line(all_0_2_2, all_0_0_0) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_2_2, all_0_2_2) = v1 & distinct_points(all_0_2_2, all_0_3_3) = v2 & distinct_points(all_0_2_2, all_0_3_3) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 4.73/1.90 | % 4.73/1.90 | Instantiating formula (4) with all_0_1_1, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 4.73/1.90 | (33) ~ (apart_point_and_line(all_0_2_2, all_0_1_1) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_2_2, all_0_2_2) = v2 & distinct_points(all_0_2_2, all_0_3_3) = v1 & distinct_points(all_0_3_3, all_0_2_2) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.08/1.90 | % 5.08/1.90 | Instantiating formula (4) with all_0_0_0, all_0_3_3, all_0_3_3, all_0_2_2 and discharging atoms line_connecting(all_0_2_2, all_0_3_3) = all_0_0_0, yields: % 5.08/1.90 | (34) ~ (apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_2_2, all_0_3_3) = v0 & distinct_points(all_0_3_3, all_0_2_2) = v1 & distinct_points(all_0_3_3, all_0_3_3) = v2 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.08/1.90 | % 5.08/1.90 | Instantiating formula (4) with all_0_1_1, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 5.08/1.90 | (35) ~ (apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_3_3, all_0_2_2) = v2 & distinct_points(all_0_3_3, all_0_2_2) = v0 & distinct_points(all_0_3_3, all_0_3_3) = v1 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.08/1.90 | % 5.08/1.90 +-Applying beta-rule and splitting (35), into two cases. % 5.08/1.90 |-Branch one: % 5.08/1.90 | (36) ~ (apart_point_and_line(all_0_3_3, all_0_1_1) = 0) % 5.08/1.90 | % 5.08/1.90 | Using (30) and (36) yields: % 5.08/1.90 | (37) ~ (all_16_3_7 = 0) % 5.08/1.90 | % 5.08/1.90 +-Applying beta-rule and splitting (34), into two cases. % 5.08/1.90 |-Branch one: % 5.08/1.90 | (38) ~ (apart_point_and_line(all_0_3_3, all_0_0_0) = 0) % 5.08/1.90 | % 5.08/1.90 | Using (27) and (38) yields: % 5.08/1.90 | (39) ~ (all_16_2_6 = 0) % 5.08/1.90 | % 5.08/1.90 +-Applying beta-rule and splitting (32), into two cases. % 5.08/1.90 |-Branch one: % 5.08/1.90 | (40) ~ (apart_point_and_line(all_0_2_2, all_0_0_0) = 0) % 5.08/1.90 | % 5.08/1.90 | Using (29) and (40) yields: % 5.08/1.90 | (41) ~ (all_16_0_4 = 0) % 5.08/1.90 | % 5.08/1.90 +-Applying beta-rule and splitting (31), into two cases. % 5.08/1.90 |-Branch one: % 5.08/1.90 | (42) all_16_0_4 = 0 % 5.08/1.90 | % 5.08/1.90 | Equations (42) can reduce 41 to: % 5.08/1.90 | (43) $false % 5.08/1.90 | % 5.08/1.90 |-The branch is then unsatisfiable % 5.08/1.90 |-Branch two: % 5.08/1.90 | (41) ~ (all_16_0_4 = 0) % 5.08/1.90 | (45) all_16_1_5 = 0 | all_16_2_6 = 0 | all_16_3_7 = 0 % 5.08/1.91 | % 5.08/1.91 +-Applying beta-rule and splitting (45), into two cases. % 5.08/1.91 |-Branch one: % 5.08/1.91 | (46) all_16_1_5 = 0 % 5.08/1.91 | % 5.08/1.91 | From (46) and (28) follows: % 5.08/1.91 | (47) apart_point_and_line(all_0_2_2, all_0_1_1) = 0 % 5.08/1.91 | % 5.08/1.91 +-Applying beta-rule and splitting (33), into two cases. % 5.08/1.91 |-Branch one: % 5.08/1.91 | (48) ~ (apart_point_and_line(all_0_2_2, all_0_1_1) = 0) % 5.08/1.91 | % 5.08/1.91 | Using (47) and (48) yields: % 5.08/1.91 | (49) $false % 5.08/1.91 | % 5.08/1.91 |-The branch is then unsatisfiable % 5.08/1.91 |-Branch two: % 5.08/1.91 | (47) apart_point_and_line(all_0_2_2, all_0_1_1) = 0 % 5.08/1.91 | (51) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_2_2, all_0_2_2) = v2 & distinct_points(all_0_2_2, all_0_3_3) = v1 & distinct_points(all_0_3_3, all_0_2_2) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.08/1.91 | % 5.08/1.91 | Instantiating (51) with all_63_0_8, all_63_1_9, all_63_2_10 yields: % 5.08/1.91 | (52) distinct_points(all_0_2_2, all_0_2_2) = all_63_0_8 & distinct_points(all_0_2_2, all_0_3_3) = all_63_1_9 & distinct_points(all_0_3_3, all_0_2_2) = all_63_2_10 & ( ~ (all_63_2_10 = 0) | (all_63_0_8 = 0 & all_63_1_9 = 0)) % 5.08/1.91 | % 5.08/1.91 | Applying alpha-rule on (52) yields: % 5.08/1.91 | (53) distinct_points(all_0_2_2, all_0_2_2) = all_63_0_8 % 5.08/1.91 | (54) distinct_points(all_0_2_2, all_0_3_3) = all_63_1_9 % 5.08/1.91 | (55) distinct_points(all_0_3_3, all_0_2_2) = all_63_2_10 % 5.08/1.91 | (56) ~ (all_63_2_10 = 0) | (all_63_0_8 = 0 & all_63_1_9 = 0) % 5.08/1.91 | % 5.08/1.91 | Instantiating formula (5) with all_0_2_2 yields: % 5.08/1.91 | (57) ~ (distinct_points(all_0_2_2, all_0_2_2) = 0) % 5.08/1.91 | % 5.08/1.91 | Instantiating formula (13) with all_0_3_3, all_0_2_2, all_63_2_10, 0 and discharging atoms distinct_points(all_0_3_3, all_0_2_2) = all_63_2_10, distinct_points(all_0_3_3, all_0_2_2) = 0, yields: % 5.08/1.91 | (58) all_63_2_10 = 0 % 5.08/1.91 | % 5.08/1.91 +-Applying beta-rule and splitting (56), into two cases. % 5.08/1.91 |-Branch one: % 5.08/1.91 | (59) ~ (all_63_2_10 = 0) % 5.08/1.91 | % 5.08/1.91 | Equations (58) can reduce 59 to: % 5.08/1.91 | (43) $false % 5.08/1.91 | % 5.08/1.91 |-The branch is then unsatisfiable % 5.08/1.91 |-Branch two: % 5.08/1.91 | (58) all_63_2_10 = 0 % 5.08/1.91 | (62) all_63_0_8 = 0 & all_63_1_9 = 0 % 5.08/1.91 | % 5.08/1.91 | Applying alpha-rule on (62) yields: % 5.08/1.91 | (63) all_63_0_8 = 0 % 5.08/1.91 | (64) all_63_1_9 = 0 % 5.08/1.91 | % 5.08/1.91 | From (63) and (53) follows: % 5.08/1.91 | (65) distinct_points(all_0_2_2, all_0_2_2) = 0 % 5.08/1.91 | % 5.08/1.91 | Using (65) and (57) yields: % 5.08/1.91 | (49) $false % 5.08/1.91 | % 5.08/1.91 |-The branch is then unsatisfiable % 5.08/1.91 |-Branch two: % 5.08/1.91 | (67) ~ (all_16_1_5 = 0) % 5.08/1.91 | (68) all_16_2_6 = 0 | all_16_3_7 = 0 % 5.08/1.91 | % 5.08/1.91 +-Applying beta-rule and splitting (68), into two cases. % 5.08/1.91 |-Branch one: % 5.08/1.91 | (69) all_16_2_6 = 0 % 5.08/1.91 | % 5.08/1.91 | Equations (69) can reduce 39 to: % 5.08/1.91 | (43) $false % 5.08/1.91 | % 5.08/1.91 |-The branch is then unsatisfiable % 5.08/1.91 |-Branch two: % 5.08/1.91 | (39) ~ (all_16_2_6 = 0) % 5.08/1.91 | (72) all_16_3_7 = 0 % 5.08/1.91 | % 5.08/1.91 | Equations (72) can reduce 37 to: % 5.08/1.91 | (43) $false % 5.08/1.91 | % 5.08/1.91 |-The branch is then unsatisfiable % 5.08/1.91 |-Branch two: % 5.08/1.91 | (74) apart_point_and_line(all_0_2_2, all_0_0_0) = 0 % 5.08/1.91 | (75) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_2_2, all_0_2_2) = v1 & distinct_points(all_0_2_2, all_0_3_3) = v2 & distinct_points(all_0_2_2, all_0_3_3) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.08/1.91 | % 5.08/1.91 | Instantiating (75) with all_47_0_11, all_47_1_12, all_47_2_13 yields: % 5.08/1.91 | (76) distinct_points(all_0_2_2, all_0_2_2) = all_47_1_12 & distinct_points(all_0_2_2, all_0_3_3) = all_47_0_11 & distinct_points(all_0_2_2, all_0_3_3) = all_47_2_13 & ( ~ (all_47_2_13 = 0) | (all_47_0_11 = 0 & all_47_1_12 = 0)) % 5.08/1.91 | % 5.08/1.91 | Applying alpha-rule on (76) yields: % 5.08/1.91 | (77) distinct_points(all_0_2_2, all_0_2_2) = all_47_1_12 % 5.08/1.91 | (78) distinct_points(all_0_2_2, all_0_3_3) = all_47_0_11 % 5.08/1.91 | (79) distinct_points(all_0_2_2, all_0_3_3) = all_47_2_13 % 5.08/1.92 | (80) ~ (all_47_2_13 = 0) | (all_47_0_11 = 0 & all_47_1_12 = 0) % 5.08/1.92 | % 5.08/1.92 | Instantiating formula (20) with all_0_2_2, all_0_0_0, 0, all_16_0_4 and discharging atoms apart_point_and_line(all_0_2_2, all_0_0_0) = all_16_0_4, apart_point_and_line(all_0_2_2, all_0_0_0) = 0, yields: % 5.08/1.92 | (42) all_16_0_4 = 0 % 5.08/1.92 | % 5.08/1.92 | Instantiating formula (5) with all_0_2_2 yields: % 5.08/1.92 | (57) ~ (distinct_points(all_0_2_2, all_0_2_2) = 0) % 5.08/1.92 | % 5.08/1.92 | Instantiating formula (13) with all_0_2_2, all_0_3_3, all_47_2_13, all_47_0_11 and discharging atoms distinct_points(all_0_2_2, all_0_3_3) = all_47_0_11, distinct_points(all_0_2_2, all_0_3_3) = all_47_2_13, yields: % 5.08/1.92 | (83) all_47_0_11 = all_47_2_13 % 5.08/1.92 | % 5.08/1.92 | From (42) and (29) follows: % 5.08/1.92 | (74) apart_point_and_line(all_0_2_2, all_0_0_0) = 0 % 5.08/1.92 | % 5.08/1.92 | From (83) and (78) follows: % 5.08/1.92 | (79) distinct_points(all_0_2_2, all_0_3_3) = all_47_2_13 % 5.08/1.92 | % 5.08/1.92 | Using (77) and (57) yields: % 5.08/1.92 | (86) ~ (all_47_1_12 = 0) % 5.08/1.92 | % 5.08/1.92 +-Applying beta-rule and splitting (80), into two cases. % 5.08/1.92 |-Branch one: % 5.08/1.92 | (87) ~ (all_47_2_13 = 0) % 5.08/1.92 | % 5.08/1.92 | Instantiating formula (6) with all_47_2_13, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_0_0) = 0, distinct_points(all_0_2_2, all_0_3_3) = all_47_2_13, ~ (apart_point_and_line(all_0_3_3, all_0_0_0) = 0), yields: % 5.08/1.92 | (88) all_47_2_13 = 0 % 5.08/1.92 | % 5.08/1.92 | Equations (88) can reduce 87 to: % 5.08/1.92 | (43) $false % 5.08/1.92 | % 5.08/1.92 |-The branch is then unsatisfiable % 5.08/1.92 |-Branch two: % 5.08/1.92 | (88) all_47_2_13 = 0 % 5.08/1.92 | (91) all_47_0_11 = 0 & all_47_1_12 = 0 % 5.08/1.92 | % 5.08/1.92 | Applying alpha-rule on (91) yields: % 5.08/1.92 | (92) all_47_0_11 = 0 % 5.08/1.92 | (93) all_47_1_12 = 0 % 5.08/1.92 | % 5.08/1.92 | Equations (93) can reduce 86 to: % 5.08/1.92 | (43) $false % 5.08/1.92 | % 5.08/1.92 |-The branch is then unsatisfiable % 5.08/1.92 |-Branch two: % 5.08/1.92 | (95) apart_point_and_line(all_0_3_3, all_0_0_0) = 0 % 5.08/1.92 | (96) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_2_2, all_0_3_3) = v0 & distinct_points(all_0_3_3, all_0_2_2) = v1 & distinct_points(all_0_3_3, all_0_3_3) = v2 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.08/1.92 | % 5.08/1.92 | Instantiating (96) with all_36_0_14, all_36_1_15, all_36_2_16 yields: % 5.08/1.92 | (97) distinct_points(all_0_2_2, all_0_3_3) = all_36_2_16 & distinct_points(all_0_3_3, all_0_2_2) = all_36_1_15 & distinct_points(all_0_3_3, all_0_3_3) = all_36_0_14 & ( ~ (all_36_2_16 = 0) | (all_36_0_14 = 0 & all_36_1_15 = 0)) % 5.08/1.92 | % 5.08/1.92 | Applying alpha-rule on (97) yields: % 5.08/1.92 | (98) distinct_points(all_0_2_2, all_0_3_3) = all_36_2_16 % 5.08/1.92 | (99) distinct_points(all_0_3_3, all_0_2_2) = all_36_1_15 % 5.08/1.92 | (100) distinct_points(all_0_3_3, all_0_3_3) = all_36_0_14 % 5.08/1.92 | (101) ~ (all_36_2_16 = 0) | (all_36_0_14 = 0 & all_36_1_15 = 0) % 5.08/1.92 | % 5.08/1.92 | Instantiating formula (13) with all_0_3_3, all_0_2_2, all_36_1_15, 0 and discharging atoms distinct_points(all_0_3_3, all_0_2_2) = all_36_1_15, distinct_points(all_0_3_3, all_0_2_2) = 0, yields: % 5.08/1.92 | (102) all_36_1_15 = 0 % 5.08/1.92 | % 5.08/1.92 | Using (100) and (24) yields: % 5.08/1.92 | (103) ~ (all_36_0_14 = 0) % 5.08/1.92 | % 5.08/1.92 | From (102) and (99) follows: % 5.08/1.92 | (17) distinct_points(all_0_3_3, all_0_2_2) = 0 % 5.08/1.92 | % 5.08/1.92 +-Applying beta-rule and splitting (101), into two cases. % 5.08/1.92 |-Branch one: % 5.08/1.92 | (105) ~ (all_36_2_16 = 0) % 5.08/1.92 | % 5.08/1.92 | Instantiating formula (8) with all_36_0_14, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms distinct_points(all_0_3_3, all_0_2_2) = 0, distinct_points(all_0_3_3, all_0_3_3) = all_36_0_14, yields: % 5.08/1.92 | (106) all_36_0_14 = 0 | distinct_points(all_0_2_2, all_0_3_3) = 0 % 5.08/1.92 | % 5.08/1.92 +-Applying beta-rule and splitting (106), into two cases. % 5.08/1.92 |-Branch one: % 5.08/1.92 | (107) distinct_points(all_0_2_2, all_0_3_3) = 0 % 5.08/1.92 | % 5.08/1.92 | Instantiating formula (13) with all_0_2_2, all_0_3_3, 0, all_36_2_16 and discharging atoms distinct_points(all_0_2_2, all_0_3_3) = all_36_2_16, distinct_points(all_0_2_2, all_0_3_3) = 0, yields: % 5.08/1.93 | (108) all_36_2_16 = 0 % 5.08/1.93 | % 5.08/1.93 | Equations (108) can reduce 105 to: % 5.08/1.93 | (43) $false % 5.08/1.93 | % 5.08/1.93 |-The branch is then unsatisfiable % 5.08/1.93 |-Branch two: % 5.08/1.93 | (110) ~ (distinct_points(all_0_2_2, all_0_3_3) = 0) % 5.08/1.93 | (111) all_36_0_14 = 0 % 5.08/1.93 | % 5.08/1.93 | Equations (111) can reduce 103 to: % 5.08/1.93 | (43) $false % 5.08/1.93 | % 5.08/1.93 |-The branch is then unsatisfiable % 5.08/1.93 |-Branch two: % 5.08/1.93 | (108) all_36_2_16 = 0 % 5.08/1.93 | (114) all_36_0_14 = 0 & all_36_1_15 = 0 % 5.08/1.93 | % 5.08/1.93 | Applying alpha-rule on (114) yields: % 5.08/1.93 | (111) all_36_0_14 = 0 % 5.08/1.93 | (102) all_36_1_15 = 0 % 5.08/1.93 | % 5.08/1.93 | Equations (111) can reduce 103 to: % 5.08/1.93 | (43) $false % 5.08/1.93 | % 5.08/1.93 |-The branch is then unsatisfiable % 5.08/1.93 |-Branch two: % 5.08/1.93 | (118) apart_point_and_line(all_0_3_3, all_0_1_1) = 0 % 5.08/1.93 | (119) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_3_3, all_0_2_2) = v2 & distinct_points(all_0_3_3, all_0_2_2) = v0 & distinct_points(all_0_3_3, all_0_3_3) = v1 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.08/1.93 | % 5.08/1.93 | Instantiating (119) with all_25_0_17, all_25_1_18, all_25_2_19 yields: % 5.08/1.93 | (120) distinct_points(all_0_3_3, all_0_2_2) = all_25_0_17 & distinct_points(all_0_3_3, all_0_2_2) = all_25_2_19 & distinct_points(all_0_3_3, all_0_3_3) = all_25_1_18 & ( ~ (all_25_2_19 = 0) | (all_25_0_17 = 0 & all_25_1_18 = 0)) % 5.08/1.93 | % 5.08/1.93 | Applying alpha-rule on (120) yields: % 5.08/1.93 | (121) distinct_points(all_0_3_3, all_0_2_2) = all_25_0_17 % 5.08/1.93 | (122) distinct_points(all_0_3_3, all_0_2_2) = all_25_2_19 % 5.08/1.93 | (123) distinct_points(all_0_3_3, all_0_3_3) = all_25_1_18 % 5.08/1.93 | (124) ~ (all_25_2_19 = 0) | (all_25_0_17 = 0 & all_25_1_18 = 0) % 5.08/1.93 | % 5.08/1.93 | Instantiating formula (13) with all_0_3_3, all_0_2_2, all_25_0_17, 0 and discharging atoms distinct_points(all_0_3_3, all_0_2_2) = all_25_0_17, distinct_points(all_0_3_3, all_0_2_2) = 0, yields: % 5.08/1.93 | (125) all_25_0_17 = 0 % 5.08/1.93 | % 5.08/1.93 | Instantiating formula (13) with all_0_3_3, all_0_2_2, all_25_2_19, all_25_0_17 and discharging atoms distinct_points(all_0_3_3, all_0_2_2) = all_25_0_17, distinct_points(all_0_3_3, all_0_2_2) = all_25_2_19, yields: % 5.08/1.93 | (126) all_25_0_17 = all_25_2_19 % 5.08/1.93 | % 5.08/1.93 | Using (123) and (24) yields: % 5.08/1.93 | (127) ~ (all_25_1_18 = 0) % 5.08/1.93 | % 5.08/1.93 | Combining equations (125,126) yields a new equation: % 5.08/1.93 | (128) all_25_2_19 = 0 % 5.08/1.93 | % 5.08/1.93 +-Applying beta-rule and splitting (124), into two cases. % 5.08/1.93 |-Branch one: % 5.08/1.93 | (129) ~ (all_25_2_19 = 0) % 5.08/1.93 | % 5.08/1.93 | Equations (128) can reduce 129 to: % 5.08/1.93 | (43) $false % 5.08/1.93 | % 5.08/1.93 |-The branch is then unsatisfiable % 5.08/1.93 |-Branch two: % 5.08/1.93 | (128) all_25_2_19 = 0 % 5.08/1.93 | (132) all_25_0_17 = 0 & all_25_1_18 = 0 % 5.08/1.93 | % 5.08/1.93 | Applying alpha-rule on (132) yields: % 5.08/1.93 | (125) all_25_0_17 = 0 % 5.08/1.93 | (134) all_25_1_18 = 0 % 5.08/1.93 | % 5.08/1.93 | Equations (134) can reduce 127 to: % 5.08/1.93 | (43) $false % 5.08/1.93 | % 5.08/1.93 |-The branch is then unsatisfiable % 5.08/1.93 % SZS output end Proof for theBenchmark % 5.08/1.94 % 5.08/1.94 1325ms %------------------------------------------------------------------------------