%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO179+2 : 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 3.33s 1.45s % Output : Proof 5.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n013.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 00:55:59 EDT 2022 % 0.12/0.33 % CPUTime : % 0.49/0.57 ____ _ % 0.49/0.57 ___ / __ \_____(_)___ ________ __________ % 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.57 % 0.49/0.57 A Theorem Prover for First-Order Logic % 0.49/0.57 (ePrincess v.1.0) % 0.49/0.57 % 0.49/0.57 (c) Philipp Rümmer, 2009-2015 % 0.49/0.57 (c) Peter Backeman, 2014-2015 % 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.57 Bug reports to peter@backeman.se % 0.49/0.57 % 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.57 % 0.49/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.89 Prover 0: Preprocessing ... % 1.90/1.01 Prover 0: Warning: ignoring some quantifiers % 1.90/1.03 Prover 0: Constructing countermodel ... % 2.66/1.25 Prover 0: gave up % 2.66/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.78/1.28 Prover 1: Preprocessing ... % 3.04/1.36 Prover 1: Constructing countermodel ... % 3.33/1.45 Prover 1: proved (199ms) % 3.33/1.45 % 3.33/1.45 No countermodel exists, formula is valid % 3.33/1.45 % SZS status Theorem for theBenchmark % 3.33/1.45 % 3.33/1.45 Generating proof ... found it (size 85) % 5.23/1.89 % 5.23/1.89 % SZS output start Proof for theBenchmark % 5.23/1.89 Assumed formulas after preprocessing and simplification: % 5.23/1.89 | (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] : ! [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) & ( ~ (v7 = 0) | ~ (v5 = 0))) % 5.23/1.92 | 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: % 5.23/1.92 | (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] : ! [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_0_0 = 0) | ~ (all_0_2_2 = 0)) % 5.23/1.93 | % 5.23/1.93 | Applying alpha-rule on (1) yields: % 5.23/1.93 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 5.23/1.93 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 5.23/1.93 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 5.23/1.93 | (5) ! [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))) % 5.23/1.93 | (6) line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3 % 5.23/1.93 | (7) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) % 5.23/1.93 | (8) ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0) % 5.23/1.93 | (9) ! [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)))) % 5.23/1.93 | (10) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 5.23/1.93 | (11) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 5.23/1.93 | (12) ! [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) % 5.23/1.93 | (13) apart_point_and_line(all_0_5_5, all_0_4_4) = 0 % 5.23/1.93 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 5.23/1.94 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 5.23/1.94 | (16) line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1 % 5.23/1.94 | (17) distinct_points(all_0_7_7, all_0_6_6) = 0 % 5.23/1.94 | (18) distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0 % 5.23/1.94 | (19) line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4 % 5.23/1.94 | (20) distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2 % 5.23/1.94 | (21) ! [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))))) % 5.23/1.94 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 5.23/1.94 | (23) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 5.23/1.94 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 5.62/1.94 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 5.62/1.94 | (26) ! [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) % 5.62/1.94 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 5.62/1.94 | % 5.62/1.94 | Instantiating formula (15) 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: % 5.62/1.94 | (28) all_0_0_0 = all_0_2_2 | ~ (distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0) % 5.62/1.94 | % 5.62/1.94 | Instantiating formula (9) with all_0_4_4, all_0_5_5, 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, apart_point_and_line(all_0_5_5, all_0_4_4) = 0, yields: % 5.62/1.94 | (29) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_6_6) = v2 & distinct_points(all_0_5_5, all_0_7_7) = v1 & distinct_points(all_0_7_7, all_0_6_6) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.62/1.94 | % 5.62/1.94 | Instantiating formula (26) 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: % 5.62/1.94 | (30) all_0_0_0 = 0 | apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 5.62/1.94 | % 5.62/1.94 | Instantiating formula (26) 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: % 5.62/1.94 | (31) all_0_2_2 = 0 | apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 5.62/1.94 | % 5.62/1.94 | Instantiating (29) with all_16_0_8, all_16_1_9, all_16_2_10 yields: % 5.62/1.94 | (32) distinct_points(all_0_5_5, all_0_6_6) = all_16_0_8 & distinct_points(all_0_5_5, all_0_7_7) = all_16_1_9 & distinct_points(all_0_7_7, all_0_6_6) = all_16_2_10 & ( ~ (all_16_2_10 = 0) | (all_16_0_8 = 0 & all_16_1_9 = 0)) % 5.62/1.94 | % 5.62/1.94 | Applying alpha-rule on (32) yields: % 5.62/1.94 | (33) distinct_points(all_0_5_5, all_0_6_6) = all_16_0_8 % 5.62/1.94 | (34) distinct_points(all_0_5_5, all_0_7_7) = all_16_1_9 % 5.62/1.94 | (35) distinct_points(all_0_7_7, all_0_6_6) = all_16_2_10 % 5.62/1.94 | (36) ~ (all_16_2_10 = 0) | (all_16_0_8 = 0 & all_16_1_9 = 0) % 5.62/1.94 | % 5.62/1.94 | Instantiating formula (3) with all_0_7_7, all_0_6_6, all_16_2_10, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_16_2_10, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 5.62/1.95 | (37) all_16_2_10 = 0 % 5.62/1.95 | % 5.62/1.95 +-Applying beta-rule and splitting (36), into two cases. % 5.62/1.95 |-Branch one: % 5.62/1.95 | (38) ~ (all_16_2_10 = 0) % 5.62/1.95 | % 5.62/1.95 | Equations (37) can reduce 38 to: % 5.62/1.95 | (39) $false % 5.62/1.95 | % 5.62/1.95 |-The branch is then unsatisfiable % 5.62/1.95 |-Branch two: % 5.62/1.95 | (37) all_16_2_10 = 0 % 5.62/1.95 | (41) all_16_0_8 = 0 & all_16_1_9 = 0 % 5.62/1.95 | % 5.62/1.95 | Applying alpha-rule on (41) yields: % 5.62/1.95 | (42) all_16_0_8 = 0 % 5.62/1.95 | (43) all_16_1_9 = 0 % 5.62/1.95 | % 5.62/1.95 | From (42) and (33) follows: % 5.62/1.95 | (44) distinct_points(all_0_5_5, all_0_6_6) = 0 % 5.62/1.95 | % 5.62/1.95 | From (43) and (34) follows: % 5.62/1.95 | (45) distinct_points(all_0_5_5, all_0_7_7) = 0 % 5.62/1.95 | % 5.62/1.95 +-Applying beta-rule and splitting (28), into two cases. % 5.62/1.95 |-Branch one: % 5.62/1.95 | (46) ~ (distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0) % 5.62/1.95 | % 5.62/1.95 | Using (20) and (46) yields: % 5.62/1.95 | (47) ~ (all_0_0_0 = all_0_2_2) % 5.62/1.95 | % 5.62/1.95 +-Applying beta-rule and splitting (8), into two cases. % 5.62/1.95 |-Branch one: % 5.62/1.95 | (48) ~ (all_0_0_0 = 0) % 5.62/1.95 | % 5.62/1.95 +-Applying beta-rule and splitting (30), into two cases. % 5.62/1.95 |-Branch one: % 5.62/1.95 | (49) apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 5.62/1.95 | % 5.62/1.95 | Instantiating formula (9) with all_0_1_1, all_0_5_5, 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: % 5.62/1.95 | (50) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_5_5) = v1 & distinct_points(all_0_5_5, all_0_6_6) = v2 & distinct_points(all_0_5_5, all_0_6_6) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.62/1.95 | % 5.62/1.95 | Instantiating (50) with all_61_0_11, all_61_1_12, all_61_2_13 yields: % 5.62/1.95 | (51) distinct_points(all_0_5_5, all_0_5_5) = all_61_1_12 & distinct_points(all_0_5_5, all_0_6_6) = all_61_0_11 & distinct_points(all_0_5_5, all_0_6_6) = all_61_2_13 & ( ~ (all_61_2_13 = 0) | (all_61_0_11 = 0 & all_61_1_12 = 0)) % 5.62/1.95 | % 5.62/1.95 | Applying alpha-rule on (51) yields: % 5.62/1.95 | (52) distinct_points(all_0_5_5, all_0_5_5) = all_61_1_12 % 5.62/1.95 | (53) distinct_points(all_0_5_5, all_0_6_6) = all_61_0_11 % 5.62/1.95 | (54) distinct_points(all_0_5_5, all_0_6_6) = all_61_2_13 % 5.62/1.95 | (55) ~ (all_61_2_13 = 0) | (all_61_0_11 = 0 & all_61_1_12 = 0) % 5.62/1.95 | % 5.62/1.95 | Instantiating formula (10) with all_0_5_5 yields: % 5.62/1.95 | (56) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0) % 5.62/1.95 | % 5.62/1.95 | Instantiating formula (3) with all_0_5_5, all_0_6_6, all_61_0_11, 0 and discharging atoms distinct_points(all_0_5_5, all_0_6_6) = all_61_0_11, distinct_points(all_0_5_5, all_0_6_6) = 0, yields: % 5.62/1.95 | (57) all_61_0_11 = 0 % 5.62/1.95 | % 5.62/1.95 | Instantiating formula (3) with all_0_5_5, all_0_6_6, all_61_2_13, all_61_0_11 and discharging atoms distinct_points(all_0_5_5, all_0_6_6) = all_61_0_11, distinct_points(all_0_5_5, all_0_6_6) = all_61_2_13, yields: % 5.62/1.95 | (58) all_61_0_11 = all_61_2_13 % 5.62/1.95 | % 5.62/1.95 | Combining equations (57,58) yields a new equation: % 5.62/1.95 | (59) all_61_2_13 = 0 % 5.62/1.95 | % 5.62/1.95 +-Applying beta-rule and splitting (55), into two cases. % 5.62/1.95 |-Branch one: % 5.62/1.95 | (60) ~ (all_61_2_13 = 0) % 5.62/1.95 | % 5.62/1.95 | Equations (59) can reduce 60 to: % 5.62/1.95 | (39) $false % 5.62/1.95 | % 5.62/1.95 |-The branch is then unsatisfiable % 5.62/1.95 |-Branch two: % 5.62/1.95 | (59) all_61_2_13 = 0 % 5.62/1.95 | (63) all_61_0_11 = 0 & all_61_1_12 = 0 % 5.62/1.95 | % 5.62/1.95 | Applying alpha-rule on (63) yields: % 5.62/1.95 | (57) all_61_0_11 = 0 % 5.62/1.95 | (65) all_61_1_12 = 0 % 5.62/1.95 | % 5.62/1.95 | From (65) and (52) follows: % 5.62/1.95 | (66) distinct_points(all_0_5_5, all_0_5_5) = 0 % 5.62/1.95 | % 5.62/1.95 | Using (66) and (56) yields: % 5.62/1.95 | (67) $false % 5.62/1.95 | % 5.62/1.95 |-The branch is then unsatisfiable % 5.62/1.96 |-Branch two: % 5.62/1.96 | (68) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) % 5.62/1.96 | (69) all_0_0_0 = 0 % 5.62/1.96 | % 5.62/1.96 | Equations (69) can reduce 48 to: % 5.62/1.96 | (39) $false % 5.62/1.96 | % 5.62/1.96 |-The branch is then unsatisfiable % 5.62/1.96 |-Branch two: % 5.62/1.96 | (69) all_0_0_0 = 0 % 5.62/1.96 | (72) ~ (all_0_2_2 = 0) % 5.62/1.96 | % 5.62/1.96 | Equations (69) can reduce 47 to: % 5.62/1.96 | (73) ~ (all_0_2_2 = 0) % 5.62/1.96 | % 5.62/1.96 | Simplifying 73 yields: % 5.62/1.96 | (72) ~ (all_0_2_2 = 0) % 5.62/1.96 | % 5.62/1.96 +-Applying beta-rule and splitting (31), into two cases. % 5.62/1.96 |-Branch one: % 5.62/1.96 | (75) apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 5.62/1.96 | % 5.62/1.96 | Instantiating formula (9) with all_0_3_3, all_0_5_5, 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: % 5.62/1.96 | (76) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_5_5) = v1 & distinct_points(all_0_5_5, all_0_7_7) = v2 & distinct_points(all_0_5_5, all_0_7_7) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.62/1.96 | % 5.62/1.96 | Instantiating (76) with all_85_0_38, all_85_1_39, all_85_2_40 yields: % 5.62/1.96 | (77) distinct_points(all_0_5_5, all_0_5_5) = all_85_1_39 & distinct_points(all_0_5_5, all_0_7_7) = all_85_0_38 & distinct_points(all_0_5_5, all_0_7_7) = all_85_2_40 & ( ~ (all_85_2_40 = 0) | (all_85_0_38 = 0 & all_85_1_39 = 0)) % 5.62/1.96 | % 5.62/1.96 | Applying alpha-rule on (77) yields: % 5.62/1.96 | (78) distinct_points(all_0_5_5, all_0_5_5) = all_85_1_39 % 5.62/1.96 | (79) distinct_points(all_0_5_5, all_0_7_7) = all_85_0_38 % 5.62/1.96 | (80) distinct_points(all_0_5_5, all_0_7_7) = all_85_2_40 % 5.62/1.96 | (81) ~ (all_85_2_40 = 0) | (all_85_0_38 = 0 & all_85_1_39 = 0) % 5.62/1.96 | % 5.62/1.96 | Instantiating formula (10) with all_0_5_5 yields: % 5.62/1.96 | (56) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0) % 5.62/1.96 | % 5.62/1.96 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_85_0_38, 0 and discharging atoms distinct_points(all_0_5_5, all_0_7_7) = all_85_0_38, distinct_points(all_0_5_5, all_0_7_7) = 0, yields: % 5.62/1.96 | (83) all_85_0_38 = 0 % 5.62/1.96 | % 5.62/1.96 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_85_2_40, all_85_0_38 and discharging atoms distinct_points(all_0_5_5, all_0_7_7) = all_85_0_38, distinct_points(all_0_5_5, all_0_7_7) = all_85_2_40, yields: % 5.62/1.96 | (84) all_85_0_38 = all_85_2_40 % 5.62/1.96 | % 5.62/1.96 | Combining equations (83,84) yields a new equation: % 5.62/1.96 | (85) all_85_2_40 = 0 % 5.62/1.96 | % 5.62/1.96 +-Applying beta-rule and splitting (81), into two cases. % 5.62/1.96 |-Branch one: % 5.62/1.96 | (86) ~ (all_85_2_40 = 0) % 5.62/1.96 | % 5.62/1.96 | Equations (85) can reduce 86 to: % 5.62/1.96 | (39) $false % 5.62/1.96 | % 5.62/1.96 |-The branch is then unsatisfiable % 5.62/1.96 |-Branch two: % 5.62/1.96 | (85) all_85_2_40 = 0 % 5.62/1.96 | (89) all_85_0_38 = 0 & all_85_1_39 = 0 % 5.62/1.96 | % 5.62/1.96 | Applying alpha-rule on (89) yields: % 5.62/1.96 | (83) all_85_0_38 = 0 % 5.62/1.96 | (91) all_85_1_39 = 0 % 5.62/1.96 | % 5.62/1.96 | From (91) and (78) follows: % 5.62/1.96 | (66) distinct_points(all_0_5_5, all_0_5_5) = 0 % 5.62/1.96 | % 5.62/1.96 | Using (66) and (56) yields: % 5.62/1.96 | (67) $false % 5.62/1.96 | % 5.62/1.96 |-The branch is then unsatisfiable % 5.62/1.96 |-Branch two: % 5.62/1.96 | (94) ~ (apart_point_and_line(all_0_5_5, all_0_3_3) = 0) % 5.62/1.96 | (95) all_0_2_2 = 0 % 5.62/1.96 | % 5.62/1.96 | Equations (95) can reduce 72 to: % 5.62/1.96 | (39) $false % 5.62/1.96 | % 5.62/1.96 |-The branch is then unsatisfiable % 5.62/1.96 |-Branch two: % 5.62/1.96 | (97) distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0 % 5.62/1.96 | (98) all_0_0_0 = all_0_2_2 % 5.62/1.96 | % 5.62/1.96 +-Applying beta-rule and splitting (8), into two cases. % 5.62/1.96 |-Branch one: % 5.62/1.96 | (48) ~ (all_0_0_0 = 0) % 5.62/1.96 | % 5.62/1.96 | Equations (98) can reduce 48 to: % 5.62/1.96 | (72) ~ (all_0_2_2 = 0) % 5.62/1.96 | % 5.62/1.96 +-Applying beta-rule and splitting (31), into two cases. % 5.62/1.96 |-Branch one: % 5.62/1.96 | (75) apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 5.62/1.97 | % 5.62/1.97 +-Applying beta-rule and splitting (30), into two cases. % 5.62/1.97 |-Branch one: % 5.62/1.97 | (49) apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 5.62/1.97 | % 5.62/1.97 | Instantiating formula (9) with all_0_1_1, all_0_5_5, 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: % 5.62/1.97 | (50) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_5_5) = v1 & distinct_points(all_0_5_5, all_0_6_6) = v2 & distinct_points(all_0_5_5, all_0_6_6) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.62/1.97 | % 5.62/1.97 | Instantiating formula (9) with all_0_3_3, all_0_5_5, 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: % 5.62/1.97 | (76) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_0_5_5, all_0_5_5) = v1 & distinct_points(all_0_5_5, all_0_7_7) = v2 & distinct_points(all_0_5_5, all_0_7_7) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 5.62/1.97 | % 5.62/1.97 | Instantiating (76) with all_58_0_41, all_58_1_42, all_58_2_43 yields: % 5.62/1.97 | (105) distinct_points(all_0_5_5, all_0_5_5) = all_58_1_42 & distinct_points(all_0_5_5, all_0_7_7) = all_58_0_41 & distinct_points(all_0_5_5, all_0_7_7) = all_58_2_43 & ( ~ (all_58_2_43 = 0) | (all_58_0_41 = 0 & all_58_1_42 = 0)) % 5.62/1.97 | % 5.62/1.97 | Applying alpha-rule on (105) yields: % 5.62/1.97 | (106) distinct_points(all_0_5_5, all_0_5_5) = all_58_1_42 % 5.62/1.97 | (107) distinct_points(all_0_5_5, all_0_7_7) = all_58_0_41 % 5.62/1.97 | (108) distinct_points(all_0_5_5, all_0_7_7) = all_58_2_43 % 5.62/1.97 | (109) ~ (all_58_2_43 = 0) | (all_58_0_41 = 0 & all_58_1_42 = 0) % 5.62/1.97 | % 5.62/1.97 | Instantiating (50) with all_60_0_44, all_60_1_45, all_60_2_46 yields: % 5.62/1.97 | (110) distinct_points(all_0_5_5, all_0_5_5) = all_60_1_45 & distinct_points(all_0_5_5, all_0_6_6) = all_60_0_44 & distinct_points(all_0_5_5, all_0_6_6) = all_60_2_46 & ( ~ (all_60_2_46 = 0) | (all_60_0_44 = 0 & all_60_1_45 = 0)) % 5.62/1.97 | % 5.62/1.97 | Applying alpha-rule on (110) yields: % 5.62/1.97 | (111) distinct_points(all_0_5_5, all_0_5_5) = all_60_1_45 % 5.62/1.97 | (112) distinct_points(all_0_5_5, all_0_6_6) = all_60_0_44 % 5.62/1.97 | (113) distinct_points(all_0_5_5, all_0_6_6) = all_60_2_46 % 5.62/1.97 | (114) ~ (all_60_2_46 = 0) | (all_60_0_44 = 0 & all_60_1_45 = 0) % 5.62/1.97 | % 5.62/1.97 | Instantiating formula (10) with all_0_5_5 yields: % 5.62/1.97 | (56) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0) % 5.62/1.97 | % 5.62/1.97 | Instantiating formula (3) with all_0_5_5, all_0_5_5, all_58_1_42, all_60_1_45 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = all_60_1_45, distinct_points(all_0_5_5, all_0_5_5) = all_58_1_42, yields: % 5.62/1.97 | (116) all_60_1_45 = all_58_1_42 % 5.62/1.97 | % 5.62/1.97 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_58_0_41, 0 and discharging atoms distinct_points(all_0_5_5, all_0_7_7) = all_58_0_41, distinct_points(all_0_5_5, all_0_7_7) = 0, yields: % 5.62/1.97 | (117) all_58_0_41 = 0 % 5.62/1.97 | % 5.62/1.97 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_58_2_43, all_58_0_41 and discharging atoms distinct_points(all_0_5_5, all_0_7_7) = all_58_0_41, distinct_points(all_0_5_5, all_0_7_7) = all_58_2_43, yields: % 5.62/1.97 | (118) all_58_0_41 = all_58_2_43 % 5.62/1.97 | % 5.62/1.97 | Combining equations (117,118) yields a new equation: % 5.62/1.97 | (119) all_58_2_43 = 0 % 5.62/1.97 | % 5.62/1.97 | From (116) and (111) follows: % 5.62/1.97 | (106) distinct_points(all_0_5_5, all_0_5_5) = all_58_1_42 % 5.62/1.97 | % 5.62/1.97 +-Applying beta-rule and splitting (109), into two cases. % 5.62/1.97 |-Branch one: % 5.62/1.97 | (121) ~ (all_58_2_43 = 0) % 5.62/1.97 | % 5.62/1.97 | Equations (119) can reduce 121 to: % 5.62/1.97 | (39) $false % 5.62/1.97 | % 5.62/1.97 |-The branch is then unsatisfiable % 5.62/1.97 |-Branch two: % 5.62/1.97 | (119) all_58_2_43 = 0 % 5.62/1.97 | (124) all_58_0_41 = 0 & all_58_1_42 = 0 % 5.62/1.97 | % 5.62/1.97 | Applying alpha-rule on (124) yields: % 5.62/1.97 | (117) all_58_0_41 = 0 % 5.62/1.97 | (126) all_58_1_42 = 0 % 5.62/1.97 | % 5.62/1.97 | From (126) and (106) follows: % 5.62/1.97 | (66) distinct_points(all_0_5_5, all_0_5_5) = 0 % 5.62/1.97 | % 5.62/1.97 | Using (66) and (56) yields: % 5.62/1.97 | (67) $false % 5.62/1.97 | % 5.62/1.97 |-The branch is then unsatisfiable % 5.62/1.97 |-Branch two: % 5.62/1.97 | (68) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) % 5.62/1.98 | (69) all_0_0_0 = 0 % 5.62/1.98 | % 5.62/1.98 | Combining equations (69,98) yields a new equation: % 5.62/1.98 | (95) all_0_2_2 = 0 % 5.62/1.98 | % 5.62/1.98 | Equations (95) can reduce 72 to: % 5.62/1.98 | (39) $false % 5.62/1.98 | % 5.62/1.98 |-The branch is then unsatisfiable % 5.62/1.98 |-Branch two: % 5.62/1.98 | (94) ~ (apart_point_and_line(all_0_5_5, all_0_3_3) = 0) % 5.62/1.98 | (95) all_0_2_2 = 0 % 5.62/1.98 | % 5.62/1.98 | Equations (95) can reduce 72 to: % 5.62/1.98 | (39) $false % 5.62/1.98 | % 5.62/1.98 |-The branch is then unsatisfiable % 5.62/1.98 |-Branch two: % 5.62/1.98 | (69) all_0_0_0 = 0 % 5.62/1.98 | (72) ~ (all_0_2_2 = 0) % 5.62/1.98 | % 5.62/1.98 | Combining equations (69,98) yields a new equation: % 5.62/1.98 | (95) all_0_2_2 = 0 % 5.62/1.98 | % 5.62/1.98 | Equations (95) can reduce 72 to: % 5.62/1.98 | (39) $false % 5.62/1.98 | % 5.62/1.98 |-The branch is then unsatisfiable % 5.62/1.98 % SZS output end Proof for theBenchmark % 5.62/1.98 % 5.62/1.98 1395ms %------------------------------------------------------------------------------