%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO179+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n013.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 03:48:16 EDT 2022 % Result : Theorem 3.60s 1.52s % Output : Proof 4.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO179+1 : TPTP v8.1.0. Released v3.3.0. % 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n013.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 : Fri Jun 17 15:29:29 EDT 2022 % 0.13/0.34 % CPUTime : % 0.57/0.60 ____ _ % 0.57/0.60 ___ / __ \_____(_)___ ________ __________ % 0.57/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.60 % 0.57/0.60 A Theorem Prover for First-Order Logic % 0.57/0.60 (ePrincess v.1.0) % 0.57/0.60 % 0.57/0.60 (c) Philipp Rümmer, 2009-2015 % 0.57/0.60 (c) Peter Backeman, 2014-2015 % 0.57/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.60 Bug reports to peter@backeman.se % 0.57/0.60 % 0.57/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.60 % 0.57/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.69/0.95 Prover 0: Preprocessing ... % 2.01/1.08 Prover 0: Warning: ignoring some quantifiers % 2.01/1.10 Prover 0: Constructing countermodel ... % 2.56/1.29 Prover 0: gave up % 2.56/1.29 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.56/1.32 Prover 1: Preprocessing ... % 3.16/1.41 Prover 1: Constructing countermodel ... % 3.60/1.52 Prover 1: proved (225ms) % 3.60/1.52 % 3.60/1.52 No countermodel exists, formula is valid % 3.60/1.52 % SZS status Theorem for theBenchmark % 3.60/1.52 % 3.60/1.52 Generating proof ... found it (size 62) % 4.90/1.85 % 4.90/1.85 % SZS output start Proof for theBenchmark % 4.90/1.85 Assumed formulas after preprocessing and simplification: % 4.90/1.85 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (line_connecting(v2, v1) = v6 & line_connecting(v2, v0) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & distinct_lines(v3, v6) = v7 & distinct_lines(v3, v4) = v5 & distinct_points(v0, v1) = 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 | ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | distinct_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] : ( ~ (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] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ~ (apart_point_and_line(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ~ (apart_point_and_line(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ (apart_point_and_line(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ (apart_point_and_line(v8, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v8, v9) = v11)) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0) & ( ~ (v7 = 0) | ~ (v5 = 0))) % 4.90/1.88 | 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: % 4.90/1.88 | (1) line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1 & line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3 & line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0 & distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0 & distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2 & distinct_points(all_0_7_7, all_0_6_6) = 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 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_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] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ( ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0)) % 4.90/1.89 | % 4.90/1.89 | Applying alpha-rule on (1) yields: % 4.90/1.89 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 4.90/1.89 | (3) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 4.90/1.89 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 4.90/1.89 | (5) distinct_points(all_0_7_7, all_0_6_6) = 0 % 4.90/1.89 | (6) ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0) % 4.90/1.89 | (7) line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1 % 4.90/1.89 | (8) distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2 % 4.90/1.89 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 4.90/1.89 | (10) ! [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) % 4.90/1.89 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 4.90/1.89 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 4.90/1.89 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.90/1.89 | (14) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 4.90/1.89 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 4.90/1.89 | (16) line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4 % 4.90/1.89 | (17) line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3 % 4.90/1.89 | (18) ! [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) % 4.90/1.89 | (19) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 4.90/1.89 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.90/1.89 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 4.90/1.89 | (22) apart_point_and_line(all_0_5_5, all_0_4_4) = 0 % 4.90/1.89 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 4.90/1.89 | (24) distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0 % 4.90/1.89 | (25) ! [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))) % 4.90/1.90 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 4.90/1.90 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 4.90/1.90 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.90/1.90 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 4.90/1.90 | % 4.90/1.90 | Instantiating formula (23) with all_0_4_4, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 4.90/1.90 | (30) all_0_0_0 = all_0_2_2 | ~ (distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0) % 4.90/1.90 | % 4.90/1.90 | Instantiating formula (21) with all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4, yields: % 4.90/1.90 | (31) ~ (apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 4.90/1.90 | % 4.90/1.90 | Instantiating formula (2) with all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4, yields: % 4.90/1.90 | (32) ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 4.90/1.90 | % 4.90/1.90 | Instantiating formula (18) with all_0_0_0, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0, yields: % 4.90/1.90 | (33) all_0_0_0 = 0 | apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 4.90/1.90 | % 4.90/1.90 | Instantiating formula (18) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 4.90/1.90 | (34) all_0_2_2 = 0 | apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 4.90/1.90 | % 4.90/1.90 +-Applying beta-rule and splitting (30), into two cases. % 4.90/1.90 |-Branch one: % 4.90/1.90 | (35) ~ (distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0) % 4.90/1.90 | % 4.90/1.90 +-Applying beta-rule and splitting (32), into two cases. % 4.90/1.90 |-Branch one: % 4.90/1.90 | (36) ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0) % 4.90/1.90 | % 4.90/1.90 +-Applying beta-rule and splitting (31), into two cases. % 4.90/1.90 |-Branch one: % 4.90/1.90 | (37) ~ (apart_point_and_line(all_0_6_6, all_0_4_4) = 0) % 4.90/1.90 | % 4.90/1.90 | Using (8) and (35) yields: % 4.90/1.90 | (38) ~ (all_0_0_0 = all_0_2_2) % 4.90/1.90 | % 4.90/1.90 +-Applying beta-rule and splitting (6), into two cases. % 4.90/1.90 |-Branch one: % 4.90/1.90 | (39) ~ (all_0_0_0 = 0) % 4.90/1.90 | % 4.90/1.90 +-Applying beta-rule and splitting (33), into two cases. % 4.90/1.90 |-Branch one: % 4.90/1.90 | (40) apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 4.90/1.90 | % 4.90/1.90 | Instantiating formula (2) with all_0_1_1, all_0_6_6, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields: % 4.90/1.90 | (41) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0) % 4.90/1.90 | % 4.90/1.90 | Instantiating (41) with all_46_0_8 yields: % 4.90/1.90 | (42) ~ (all_46_0_8 = 0) & distinct_points(all_0_5_5, all_0_6_6) = all_46_0_8 % 4.90/1.90 | % 4.90/1.90 | Applying alpha-rule on (42) yields: % 4.90/1.90 | (43) ~ (all_46_0_8 = 0) % 4.90/1.90 | (44) distinct_points(all_0_5_5, all_0_6_6) = all_46_0_8 % 4.90/1.90 | % 4.90/1.90 | Instantiating formula (10) with all_46_0_8, all_0_6_6, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_points(all_0_5_5, all_0_6_6) = all_46_0_8, ~ (apart_point_and_line(all_0_6_6, all_0_4_4) = 0), yields: % 4.90/1.90 | (45) all_46_0_8 = 0 % 4.90/1.90 | % 4.90/1.90 | Equations (45) can reduce 43 to: % 4.90/1.90 | (46) $false % 4.90/1.90 | % 4.90/1.90 |-The branch is then unsatisfiable % 4.90/1.90 |-Branch two: % 4.90/1.90 | (47) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) % 4.90/1.91 | (48) all_0_0_0 = 0 % 4.90/1.91 | % 4.90/1.91 | Equations (48) can reduce 39 to: % 4.90/1.91 | (46) $false % 4.90/1.91 | % 4.90/1.91 |-The branch is then unsatisfiable % 4.90/1.91 |-Branch two: % 4.90/1.91 | (48) all_0_0_0 = 0 % 4.90/1.91 | (51) ~ (all_0_2_2 = 0) % 4.90/1.91 | % 4.90/1.91 | Equations (48) can reduce 38 to: % 4.90/1.91 | (52) ~ (all_0_2_2 = 0) % 4.90/1.91 | % 4.90/1.91 | Simplifying 52 yields: % 4.90/1.91 | (51) ~ (all_0_2_2 = 0) % 4.90/1.91 | % 4.90/1.91 +-Applying beta-rule and splitting (34), into two cases. % 4.90/1.91 |-Branch one: % 4.90/1.91 | (54) apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 4.90/1.91 | % 4.90/1.91 | Instantiating formula (2) with all_0_3_3, all_0_7_7, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_3_3) = 0, yields: % 4.90/1.91 | (55) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0) % 4.90/1.91 | % 4.90/1.91 | Instantiating (55) with all_62_0_17 yields: % 4.90/1.91 | (56) ~ (all_62_0_17 = 0) & distinct_points(all_0_5_5, all_0_7_7) = all_62_0_17 % 4.90/1.91 | % 4.90/1.91 | Applying alpha-rule on (56) yields: % 4.90/1.91 | (57) ~ (all_62_0_17 = 0) % 4.90/1.91 | (58) distinct_points(all_0_5_5, all_0_7_7) = all_62_0_17 % 4.90/1.91 | % 4.90/1.91 | Instantiating formula (10) with all_62_0_17, all_0_7_7, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_points(all_0_5_5, all_0_7_7) = all_62_0_17, ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0), yields: % 4.90/1.91 | (59) all_62_0_17 = 0 % 4.90/1.91 | % 4.90/1.91 | Equations (59) can reduce 57 to: % 4.90/1.91 | (46) $false % 4.90/1.91 | % 4.90/1.91 |-The branch is then unsatisfiable % 4.90/1.91 |-Branch two: % 4.90/1.91 | (61) ~ (apart_point_and_line(all_0_5_5, all_0_3_3) = 0) % 4.90/1.91 | (62) all_0_2_2 = 0 % 4.90/1.91 | % 4.90/1.91 | Equations (62) can reduce 51 to: % 4.90/1.91 | (46) $false % 4.90/1.91 | % 4.90/1.91 |-The branch is then unsatisfiable % 4.90/1.91 |-Branch two: % 4.90/1.91 | (64) apart_point_and_line(all_0_6_6, all_0_4_4) = 0 % 4.90/1.91 | (65) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 4.90/1.91 | % 4.90/1.91 | Instantiating (65) with all_26_0_18 yields: % 4.90/1.91 | (66) ~ (all_26_0_18 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_26_0_18 % 4.90/1.91 | % 4.90/1.91 | Applying alpha-rule on (66) yields: % 4.90/1.91 | (67) ~ (all_26_0_18 = 0) % 4.90/1.91 | (68) distinct_points(all_0_7_7, all_0_6_6) = all_26_0_18 % 4.90/1.91 | % 4.90/1.91 | Instantiating formula (15) with all_0_7_7, all_0_6_6, all_26_0_18, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_26_0_18, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 4.90/1.91 | (69) all_26_0_18 = 0 % 4.90/1.91 | % 4.90/1.91 | Equations (69) can reduce 67 to: % 4.90/1.91 | (46) $false % 4.90/1.91 | % 4.90/1.91 |-The branch is then unsatisfiable % 4.90/1.91 |-Branch two: % 4.90/1.91 | (71) apart_point_and_line(all_0_7_7, all_0_4_4) = 0 % 4.90/1.91 | (65) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 4.90/1.91 | % 4.90/1.91 | Instantiating (65) with all_22_0_19 yields: % 4.90/1.91 | (73) ~ (all_22_0_19 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_22_0_19 % 4.90/1.91 | % 4.90/1.91 | Applying alpha-rule on (73) yields: % 4.90/1.91 | (74) ~ (all_22_0_19 = 0) % 4.90/1.91 | (75) distinct_points(all_0_7_7, all_0_6_6) = all_22_0_19 % 4.90/1.91 | % 4.90/1.91 | Instantiating formula (15) with all_0_7_7, all_0_6_6, all_22_0_19, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_22_0_19, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 4.90/1.91 | (76) all_22_0_19 = 0 % 4.90/1.91 | % 4.90/1.91 | Equations (76) can reduce 74 to: % 4.90/1.91 | (46) $false % 4.90/1.91 | % 4.90/1.91 |-The branch is then unsatisfiable % 4.90/1.91 |-Branch two: % 4.90/1.91 | (78) distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0 % 4.90/1.91 | (79) all_0_0_0 = all_0_2_2 % 4.90/1.91 | % 4.90/1.91 +-Applying beta-rule and splitting (6), into two cases. % 4.90/1.91 |-Branch one: % 4.90/1.91 | (39) ~ (all_0_0_0 = 0) % 4.90/1.91 | % 4.90/1.91 | Equations (79) can reduce 39 to: % 4.90/1.91 | (51) ~ (all_0_2_2 = 0) % 4.90/1.91 | % 4.90/1.91 +-Applying beta-rule and splitting (34), into two cases. % 4.90/1.91 |-Branch one: % 4.90/1.91 | (54) apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 4.90/1.91 | % 4.90/1.91 +-Applying beta-rule and splitting (32), into two cases. % 4.90/1.91 |-Branch one: % 4.90/1.91 | (36) ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0) % 4.90/1.91 | % 4.90/1.91 | Instantiating formula (2) with all_0_3_3, all_0_7_7, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_3_3) = 0, yields: % 4.90/1.91 | (55) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0) % 4.90/1.92 | % 4.90/1.92 | Instantiating (55) with all_47_0_20 yields: % 4.90/1.92 | (85) ~ (all_47_0_20 = 0) & distinct_points(all_0_5_5, all_0_7_7) = all_47_0_20 % 4.90/1.92 | % 4.90/1.92 | Applying alpha-rule on (85) yields: % 4.90/1.92 | (86) ~ (all_47_0_20 = 0) % 4.90/1.92 | (87) distinct_points(all_0_5_5, all_0_7_7) = all_47_0_20 % 4.90/1.92 | % 4.90/1.92 | Instantiating formula (10) with all_47_0_20, all_0_7_7, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_points(all_0_5_5, all_0_7_7) = all_47_0_20, ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0), yields: % 4.90/1.92 | (88) all_47_0_20 = 0 % 4.90/1.92 | % 4.90/1.92 | Equations (88) can reduce 86 to: % 4.90/1.92 | (46) $false % 4.90/1.92 | % 4.90/1.92 |-The branch is then unsatisfiable % 4.90/1.92 |-Branch two: % 4.90/1.92 | (71) apart_point_and_line(all_0_7_7, all_0_4_4) = 0 % 4.90/1.92 | (65) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 4.90/1.92 | % 4.90/1.92 | Instantiating (65) with all_34_0_22 yields: % 4.90/1.92 | (92) ~ (all_34_0_22 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_34_0_22 % 4.90/1.92 | % 4.90/1.92 | Applying alpha-rule on (92) yields: % 4.90/1.92 | (93) ~ (all_34_0_22 = 0) % 4.90/1.92 | (94) distinct_points(all_0_7_7, all_0_6_6) = all_34_0_22 % 4.90/1.92 | % 4.90/1.92 | Instantiating formula (15) with all_0_7_7, all_0_6_6, all_34_0_22, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_34_0_22, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 4.90/1.92 | (95) all_34_0_22 = 0 % 4.90/1.92 | % 4.90/1.92 | Equations (95) can reduce 93 to: % 4.90/1.92 | (46) $false % 4.90/1.92 | % 4.90/1.92 |-The branch is then unsatisfiable % 4.90/1.92 |-Branch two: % 4.90/1.92 | (61) ~ (apart_point_and_line(all_0_5_5, all_0_3_3) = 0) % 4.90/1.92 | (62) all_0_2_2 = 0 % 4.90/1.92 | % 4.90/1.92 | Equations (62) can reduce 51 to: % 4.90/1.92 | (46) $false % 4.90/1.92 | % 4.90/1.92 |-The branch is then unsatisfiable % 4.90/1.92 |-Branch two: % 4.90/1.92 | (48) all_0_0_0 = 0 % 4.90/1.92 | (51) ~ (all_0_2_2 = 0) % 4.90/1.92 | % 4.90/1.92 | Combining equations (48,79) yields a new equation: % 4.90/1.92 | (62) all_0_2_2 = 0 % 4.90/1.92 | % 4.90/1.92 | Equations (62) can reduce 51 to: % 4.90/1.92 | (46) $false % 4.90/1.92 | % 4.90/1.92 |-The branch is then unsatisfiable % 4.90/1.92 % SZS output end Proof for theBenchmark % 4.90/1.92 % 4.90/1.92 1309ms %------------------------------------------------------------------------------