%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO204+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n014.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 03:48:39 EDT 2022 % Result : Theorem 3.07s 1.40s % Output : Proof 5.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO204+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n014.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sat Jun 18 08:39:04 EDT 2022 % 0.12/0.34 % CPUTime : % 0.54/0.53 ____ _ % 0.54/0.53 ___ / __ \_____(_)___ ________ __________ % 0.54/0.53 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.53 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.53 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.53 % 0.54/0.53 A Theorem Prover for First-Order Logic % 0.54/0.53 (ePrincess v.1.0) % 0.54/0.53 % 0.54/0.53 (c) Philipp Rümmer, 2009-2015 % 0.54/0.53 (c) Peter Backeman, 2014-2015 % 0.54/0.53 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.53 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.53 Bug reports to peter@backeman.se % 0.54/0.53 % 0.54/0.53 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.53 % 0.54/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.58/0.58 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.54/0.88 Prover 0: Preprocessing ... % 1.86/1.01 Prover 0: Warning: ignoring some quantifiers % 1.86/1.03 Prover 0: Constructing countermodel ... % 2.41/1.16 Prover 0: gave up % 2.41/1.16 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.41/1.19 Prover 1: Preprocessing ... % 2.82/1.31 Prover 1: Constructing countermodel ... % 3.07/1.40 Prover 1: proved (240ms) % 3.07/1.40 % 3.07/1.40 No countermodel exists, formula is valid % 3.07/1.40 % SZS status Theorem for theBenchmark % 3.07/1.40 % 3.07/1.40 Generating proof ... found it (size 81) % 4.86/1.77 % 4.86/1.77 % SZS output start Proof for theBenchmark % 4.86/1.77 Assumed formulas after preprocessing and simplification: % 4.86/1.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v3 = 0) & line_connecting(v0, v2) = v6 & line_connecting(v0, v1) = v5 & distinct_lines(v5, v6) = v7 & distinct_points(v1, v2) = v3 & distinct_points(v0, v2) = v4 & 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, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | convergent_lines(v8, 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) & ( ~ (v4 = 0) | v7 = 0)) % 4.86/1.81 | 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: % 4.86/1.81 | (1) ~ (all_0_4_4 = 0) & line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1 & line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_0 & distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4 & distinct_points(all_0_7_7, all_0_5_5) = all_0_3_3 & 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, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(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_3_3 = 0) | all_0_0_0 = 0) % 5.13/1.82 | % 5.13/1.82 | Applying alpha-rule on (1) yields: % 5.13/1.82 | (2) ! [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))) % 5.13/1.82 | (3) distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_0 % 5.13/1.82 | (4) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 5.13/1.82 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 5.13/1.82 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 5.13/1.82 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 5.13/1.82 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 5.13/1.82 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 5.13/1.82 | (10) ~ (all_0_3_3 = 0) | all_0_0_0 = 0 % 5.13/1.82 | (11) distinct_points(all_0_7_7, all_0_5_5) = all_0_3_3 % 5.13/1.82 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 5.13/1.82 | (13) distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4 % 5.13/1.82 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 5.13/1.82 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 5.13/1.83 | (16) ! [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) % 5.13/1.83 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 5.13/1.83 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 5.13/1.83 | (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) % 5.13/1.83 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 5.13/1.83 | (21) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 5.13/1.83 | (22) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 5.13/1.83 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 5.13/1.83 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 5.13/1.83 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 5.13/1.83 | (26) ~ (all_0_4_4 = 0) % 5.13/1.83 | (27) line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1 % 5.13/1.83 | (28) distinct_points(all_0_7_7, all_0_6_6) = 0 % 5.13/1.83 | (29) line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2 % 5.13/1.83 | % 5.13/1.83 | Instantiating formula (8) with all_0_7_7, all_0_6_6, 0, all_0_3_3 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 5.13/1.83 | (30) all_0_3_3 = 0 | ~ (distinct_points(all_0_7_7, all_0_6_6) = all_0_3_3) % 5.13/1.83 | % 5.13/1.83 | Instantiating formula (18) with all_0_3_3, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_5_5) = all_0_3_3, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 5.13/1.83 | (31) all_0_3_3 = 0 | distinct_points(all_0_6_6, all_0_5_5) = 0 % 5.13/1.83 | % 5.13/1.83 +-Applying beta-rule and splitting (31), into two cases. % 5.13/1.83 |-Branch one: % 5.13/1.83 | (32) distinct_points(all_0_6_6, all_0_5_5) = 0 % 5.13/1.83 | % 5.13/1.83 | Instantiating formula (8) with all_0_6_6, all_0_5_5, 0, all_0_4_4 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4, distinct_points(all_0_6_6, all_0_5_5) = 0, yields: % 5.13/1.83 | (33) all_0_4_4 = 0 % 5.13/1.83 | % 5.13/1.83 | Equations (33) can reduce 26 to: % 5.13/1.83 | (34) $false % 5.13/1.83 | % 5.13/1.83 |-The branch is then unsatisfiable % 5.13/1.83 |-Branch two: % 5.13/1.83 | (35) ~ (distinct_points(all_0_6_6, all_0_5_5) = 0) % 5.13/1.83 | (36) all_0_3_3 = 0 % 5.13/1.83 | % 5.13/1.83 | From (36) and (11) follows: % 5.13/1.84 | (37) distinct_points(all_0_7_7, all_0_5_5) = 0 % 5.13/1.84 | % 5.13/1.84 +-Applying beta-rule and splitting (10), into two cases. % 5.13/1.84 |-Branch one: % 5.13/1.84 | (38) ~ (all_0_3_3 = 0) % 5.13/1.84 | % 5.13/1.84 | Equations (36) can reduce 38 to: % 5.13/1.84 | (34) $false % 5.13/1.84 | % 5.13/1.84 |-The branch is then unsatisfiable % 5.13/1.84 |-Branch two: % 5.13/1.84 | (36) all_0_3_3 = 0 % 5.13/1.84 | (41) all_0_0_0 = 0 % 5.13/1.84 | % 5.13/1.84 | From (41) and (3) follows: % 5.13/1.84 | (42) distinct_lines(all_0_2_2, all_0_1_1) = 0 % 5.13/1.84 | % 5.13/1.84 | Instantiating formula (2) with all_0_1_1, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 5.13/1.84 | (43) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_6_6, all_0_1_1) = v3 & apart_point_and_line(all_0_6_6, all_0_2_2) = v2 & apart_point_and_line(all_0_7_7, all_0_1_1) = v1 & apart_point_and_line(all_0_7_7, all_0_2_2) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0)) % 5.13/1.84 | % 5.13/1.84 | Instantiating formula (2) with all_0_1_1, all_0_2_2, all_0_5_5, all_0_7_7 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, distinct_points(all_0_7_7, all_0_5_5) = 0, yields: % 5.13/1.84 | (44) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_5_5, all_0_1_1) = v3 & apart_point_and_line(all_0_5_5, all_0_2_2) = v2 & apart_point_and_line(all_0_7_7, all_0_1_1) = v1 & apart_point_and_line(all_0_7_7, all_0_2_2) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0)) % 5.13/1.84 | % 5.13/1.84 | Instantiating (44) with all_39_0_8, all_39_1_9, all_39_2_10, all_39_3_11 yields: % 5.13/1.84 | (45) apart_point_and_line(all_0_5_5, all_0_1_1) = all_39_0_8 & apart_point_and_line(all_0_5_5, all_0_2_2) = all_39_1_9 & apart_point_and_line(all_0_7_7, all_0_1_1) = all_39_2_10 & apart_point_and_line(all_0_7_7, all_0_2_2) = all_39_3_11 & (all_39_0_8 = 0 | all_39_1_9 = 0 | all_39_2_10 = 0 | all_39_3_11 = 0) % 5.13/1.84 | % 5.13/1.84 | Applying alpha-rule on (45) yields: % 5.13/1.84 | (46) apart_point_and_line(all_0_7_7, all_0_2_2) = all_39_3_11 % 5.13/1.84 | (47) apart_point_and_line(all_0_5_5, all_0_1_1) = all_39_0_8 % 5.13/1.84 | (48) apart_point_and_line(all_0_7_7, all_0_1_1) = all_39_2_10 % 5.13/1.84 | (49) apart_point_and_line(all_0_5_5, all_0_2_2) = all_39_1_9 % 5.13/1.84 | (50) all_39_0_8 = 0 | all_39_1_9 = 0 | all_39_2_10 = 0 | all_39_3_11 = 0 % 5.13/1.84 | % 5.13/1.84 | Instantiating (43) with all_41_0_12, all_41_1_13, all_41_2_14, all_41_3_15 yields: % 5.13/1.84 | (51) apart_point_and_line(all_0_6_6, all_0_1_1) = all_41_0_12 & apart_point_and_line(all_0_6_6, all_0_2_2) = all_41_1_13 & apart_point_and_line(all_0_7_7, all_0_1_1) = all_41_2_14 & apart_point_and_line(all_0_7_7, all_0_2_2) = all_41_3_15 & (all_41_0_12 = 0 | all_41_1_13 = 0 | all_41_2_14 = 0 | all_41_3_15 = 0) % 5.13/1.84 | % 5.13/1.84 | Applying alpha-rule on (51) yields: % 5.13/1.84 | (52) apart_point_and_line(all_0_6_6, all_0_2_2) = all_41_1_13 % 5.13/1.84 | (53) apart_point_and_line(all_0_6_6, all_0_1_1) = all_41_0_12 % 5.13/1.84 | (54) all_41_0_12 = 0 | all_41_1_13 = 0 | all_41_2_14 = 0 | all_41_3_15 = 0 % 5.13/1.84 | (55) apart_point_and_line(all_0_7_7, all_0_1_1) = all_41_2_14 % 5.13/1.84 | (56) apart_point_and_line(all_0_7_7, all_0_2_2) = all_41_3_15 % 5.13/1.84 | % 5.13/1.84 | Instantiating formula (25) with all_0_7_7, all_0_1_1, all_39_2_10, all_41_2_14 and discharging atoms apart_point_and_line(all_0_7_7, all_0_1_1) = all_41_2_14, apart_point_and_line(all_0_7_7, all_0_1_1) = all_39_2_10, yields: % 5.13/1.84 | (57) all_41_2_14 = all_39_2_10 % 5.13/1.84 | % 5.13/1.84 | Instantiating formula (25) with all_0_7_7, all_0_2_2, all_39_3_11, all_41_3_15 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_41_3_15, apart_point_and_line(all_0_7_7, all_0_2_2) = all_39_3_11, yields: % 5.13/1.84 | (58) all_41_3_15 = all_39_3_11 % 5.13/1.84 | % 5.13/1.84 | From (57) and (55) follows: % 5.13/1.84 | (48) apart_point_and_line(all_0_7_7, all_0_1_1) = all_39_2_10 % 5.13/1.84 | % 5.13/1.84 | From (58) and (56) follows: % 5.13/1.84 | (46) apart_point_and_line(all_0_7_7, all_0_2_2) = all_39_3_11 % 5.13/1.84 | % 5.13/1.84 | Instantiating formula (23) with all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1, yields: % 5.13/1.84 | (61) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0) % 5.13/1.84 | % 5.13/1.84 | Instantiating formula (16) with all_0_4_4, all_0_5_5, all_0_1_1, all_0_6_6 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 5.13/1.84 | (62) all_0_4_4 = 0 | ~ (apart_point_and_line(all_0_6_6, all_0_1_1) = 0) | apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 5.13/1.84 | % 5.13/1.85 | Instantiating formula (23) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 5.13/1.85 | (63) ~ (apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 5.13/1.85 | % 5.13/1.85 | Instantiating formula (6) with all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1, yields: % 5.13/1.85 | (64) ~ (apart_point_and_line(all_0_7_7, all_0_1_1) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0) % 5.13/1.85 | % 5.13/1.85 | Instantiating formula (6) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 5.13/1.85 | (65) ~ (apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (30), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (66) ~ (distinct_points(all_0_7_7, all_0_6_6) = all_0_3_3) % 5.13/1.85 | % 5.13/1.85 | From (36) and (66) follows: % 5.13/1.85 | (67) ~ (distinct_points(all_0_7_7, all_0_6_6) = 0) % 5.13/1.85 | % 5.13/1.85 | Using (28) and (67) yields: % 5.13/1.85 | (68) $false % 5.13/1.85 | % 5.13/1.85 |-The branch is then unsatisfiable % 5.13/1.85 |-Branch two: % 5.13/1.85 | (69) distinct_points(all_0_7_7, all_0_6_6) = all_0_3_3 % 5.13/1.85 | (36) all_0_3_3 = 0 % 5.13/1.85 | % 5.13/1.85 | From (36) and (69) follows: % 5.13/1.85 | (28) distinct_points(all_0_7_7, all_0_6_6) = 0 % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (65), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (72) ~ (apart_point_and_line(all_0_7_7, all_0_2_2) = 0) % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (64), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (73) ~ (apart_point_and_line(all_0_7_7, all_0_1_1) = 0) % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (63), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (74) ~ (apart_point_and_line(all_0_6_6, all_0_2_2) = 0) % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (61), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (75) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (62), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (76) ~ (apart_point_and_line(all_0_6_6, all_0_1_1) = 0) % 5.13/1.85 | % 5.13/1.85 | Using (53) and (76) yields: % 5.13/1.85 | (77) ~ (all_41_0_12 = 0) % 5.13/1.85 | % 5.13/1.85 | Using (52) and (74) yields: % 5.13/1.85 | (78) ~ (all_41_1_13 = 0) % 5.13/1.85 | % 5.13/1.85 | Using (48) and (73) yields: % 5.13/1.85 | (79) ~ (all_39_2_10 = 0) % 5.13/1.85 | % 5.13/1.85 | Using (46) and (72) yields: % 5.13/1.85 | (80) ~ (all_39_3_11 = 0) % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (54), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (81) all_41_0_12 = 0 % 5.13/1.85 | % 5.13/1.85 | Equations (81) can reduce 77 to: % 5.13/1.85 | (34) $false % 5.13/1.85 | % 5.13/1.85 |-The branch is then unsatisfiable % 5.13/1.85 |-Branch two: % 5.13/1.85 | (77) ~ (all_41_0_12 = 0) % 5.13/1.85 | (84) all_41_1_13 = 0 | all_41_2_14 = 0 | all_41_3_15 = 0 % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (84), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (85) all_41_1_13 = 0 % 5.13/1.85 | % 5.13/1.85 | Equations (85) can reduce 78 to: % 5.13/1.85 | (34) $false % 5.13/1.85 | % 5.13/1.85 |-The branch is then unsatisfiable % 5.13/1.85 |-Branch two: % 5.13/1.85 | (78) ~ (all_41_1_13 = 0) % 5.13/1.85 | (88) all_41_2_14 = 0 | all_41_3_15 = 0 % 5.13/1.85 | % 5.13/1.85 +-Applying beta-rule and splitting (88), into two cases. % 5.13/1.85 |-Branch one: % 5.13/1.85 | (89) all_41_2_14 = 0 % 5.13/1.85 | % 5.13/1.85 | Combining equations (89,57) yields a new equation: % 5.13/1.85 | (90) all_39_2_10 = 0 % 5.13/1.85 | % 5.13/1.85 | Equations (90) can reduce 79 to: % 5.13/1.85 | (34) $false % 5.13/1.85 | % 5.13/1.85 |-The branch is then unsatisfiable % 5.13/1.85 |-Branch two: % 5.13/1.85 | (92) ~ (all_41_2_14 = 0) % 5.13/1.85 | (93) all_41_3_15 = 0 % 5.13/1.85 | % 5.13/1.85 | Combining equations (58,93) yields a new equation: % 5.13/1.85 | (94) all_39_3_11 = 0 % 5.13/1.85 | % 5.13/1.85 | Simplifying 94 yields: % 5.13/1.85 | (95) all_39_3_11 = 0 % 5.13/1.85 | % 5.13/1.85 | Equations (95) can reduce 80 to: % 5.13/1.85 | (34) $false % 5.13/1.85 | % 5.13/1.85 |-The branch is then unsatisfiable % 5.13/1.86 |-Branch two: % 5.13/1.86 | (97) apart_point_and_line(all_0_6_6, all_0_1_1) = 0 % 5.13/1.86 | (98) all_0_4_4 = 0 | apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 5.13/1.86 | % 5.13/1.86 +-Applying beta-rule and splitting (98), into two cases. % 5.13/1.86 |-Branch one: % 5.13/1.86 | (99) apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 5.13/1.86 | % 5.13/1.86 | Using (99) and (75) yields: % 5.13/1.86 | (68) $false % 5.13/1.86 | % 5.13/1.86 |-The branch is then unsatisfiable % 5.13/1.86 |-Branch two: % 5.13/1.86 | (75) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) % 5.13/1.86 | (33) all_0_4_4 = 0 % 5.13/1.86 | % 5.13/1.86 | Equations (33) can reduce 26 to: % 5.13/1.86 | (34) $false % 5.13/1.86 | % 5.13/1.86 |-The branch is then unsatisfiable % 5.13/1.86 |-Branch two: % 5.13/1.86 | (99) apart_point_and_line(all_0_5_5, all_0_1_1) = 0 % 5.32/1.86 | (105) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0) % 5.32/1.86 | % 5.32/1.86 | Instantiating (105) with all_70_0_16 yields: % 5.32/1.86 | (106) ~ (all_70_0_16 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_70_0_16 % 5.32/1.86 | % 5.32/1.86 | Applying alpha-rule on (106) yields: % 5.32/1.86 | (107) ~ (all_70_0_16 = 0) % 5.32/1.86 | (108) distinct_points(all_0_7_7, all_0_5_5) = all_70_0_16 % 5.32/1.86 | % 5.32/1.86 | Instantiating formula (8) with all_0_7_7, all_0_5_5, all_70_0_16, 0 and discharging atoms distinct_points(all_0_7_7, all_0_5_5) = all_70_0_16, distinct_points(all_0_7_7, all_0_5_5) = 0, yields: % 5.32/1.86 | (109) all_70_0_16 = 0 % 5.32/1.86 | % 5.32/1.86 | Equations (109) can reduce 107 to: % 5.32/1.86 | (34) $false % 5.32/1.86 | % 5.32/1.86 |-The branch is then unsatisfiable % 5.32/1.86 |-Branch two: % 5.32/1.86 | (111) apart_point_and_line(all_0_6_6, all_0_2_2) = 0 % 5.32/1.86 | (112) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 5.32/1.86 | % 5.32/1.86 | Instantiating (112) with all_66_0_17 yields: % 5.32/1.86 | (113) ~ (all_66_0_17 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_66_0_17 % 5.32/1.86 | % 5.32/1.86 | Applying alpha-rule on (113) yields: % 5.32/1.86 | (114) ~ (all_66_0_17 = 0) % 5.32/1.86 | (115) distinct_points(all_0_7_7, all_0_6_6) = all_66_0_17 % 5.32/1.86 | % 5.32/1.86 | Instantiating formula (8) with all_0_7_7, all_0_6_6, all_66_0_17, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_66_0_17, distinct_points(all_0_7_7, all_0_6_6) = 0, yields: % 5.32/1.86 | (116) all_66_0_17 = 0 % 5.32/1.86 | % 5.32/1.86 | Equations (116) can reduce 114 to: % 5.32/1.86 | (34) $false % 5.32/1.86 | % 5.32/1.86 |-The branch is then unsatisfiable % 5.32/1.86 |-Branch two: % 5.32/1.86 | (118) apart_point_and_line(all_0_7_7, all_0_1_1) = 0 % 5.32/1.86 | (105) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0) % 5.32/1.86 | % 5.32/1.86 | Instantiating (105) with all_62_0_18 yields: % 5.32/1.86 | (120) ~ (all_62_0_18 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_62_0_18 % 5.32/1.86 | % 5.32/1.86 | Applying alpha-rule on (120) yields: % 5.32/1.86 | (121) ~ (all_62_0_18 = 0) % 5.32/1.86 | (122) distinct_points(all_0_7_7, all_0_5_5) = all_62_0_18 % 5.32/1.86 | % 5.32/1.86 | Instantiating formula (8) with all_0_7_7, all_0_5_5, all_62_0_18, 0 and discharging atoms distinct_points(all_0_7_7, all_0_5_5) = all_62_0_18, distinct_points(all_0_7_7, all_0_5_5) = 0, yields: % 5.32/1.86 | (123) all_62_0_18 = 0 % 5.32/1.86 | % 5.32/1.86 | Equations (123) can reduce 121 to: % 5.32/1.86 | (34) $false % 5.32/1.86 | % 5.32/1.86 |-The branch is then unsatisfiable % 5.32/1.86 |-Branch two: % 5.32/1.86 | (125) apart_point_and_line(all_0_7_7, all_0_2_2) = 0 % 5.32/1.86 | (112) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0) % 5.32/1.86 | % 5.32/1.86 | Instantiating (112) with all_58_0_19 yields: % 5.32/1.86 | (127) ~ (all_58_0_19 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_58_0_19 % 5.32/1.87 | % 5.32/1.87 | Applying alpha-rule on (127) yields: % 5.32/1.87 | (128) ~ (all_58_0_19 = 0) % 5.32/1.87 | (129) distinct_points(all_0_7_7, all_0_6_6) = all_58_0_19 % 5.32/1.87 | % 5.32/1.87 | Instantiating formula (8) 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: % 5.32/1.87 | (130) all_58_0_19 = 0 % 5.32/1.87 | % 5.32/1.87 | Equations (130) can reduce 128 to: % 5.32/1.87 | (34) $false % 5.32/1.87 | % 5.32/1.87 |-The branch is then unsatisfiable % 5.32/1.87 % SZS output end Proof for theBenchmark % 5.32/1.87 % 5.32/1.87 1329ms %------------------------------------------------------------------------------