%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO196+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 03:48:32 EDT 2022 % Result : Theorem 7.44s 2.42s % Output : Proof 8.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO196+2 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n020.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sat Jun 18 04:13:04 EDT 2022 % 0.14/0.34 % CPUTime : % 0.61/0.61 ____ _ % 0.61/0.61 ___ / __ \_____(_)___ ________ __________ % 0.61/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.61 % 0.61/0.61 A Theorem Prover for First-Order Logic % 0.61/0.61 (ePrincess v.1.0) % 0.61/0.61 % 0.61/0.61 (c) Philipp Rümmer, 2009-2015 % 0.61/0.61 (c) Peter Backeman, 2014-2015 % 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.61 Bug reports to peter@backeman.se % 0.61/0.61 % 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.61 % 0.61/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.64/0.97 Prover 0: Preprocessing ... % 1.99/1.11 Prover 0: Warning: ignoring some quantifiers % 1.99/1.12 Prover 0: Constructing countermodel ... % 7.44/2.42 Prover 0: proved (1728ms) % 7.44/2.42 % 7.44/2.42 No countermodel exists, formula is valid % 7.44/2.42 % SZS status Theorem for theBenchmark % 7.44/2.42 % 7.44/2.42 Generating proof ... Warning: ignoring some quantifiers % 8.27/2.62 found it (size 22) % 8.27/2.62 % 8.27/2.62 % SZS output start Proof for theBenchmark % 8.27/2.62 Assumed formulas after preprocessing and simplification: % 8.27/2.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(v2, v3) = v5 & intersection_point(v0, v1) = v4 & convergent_lines(v2, v3) & convergent_lines(v0, v1) & ~ apart_point_and_line(v4, v3) & ~ apart_point_and_line(v4, v2) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v6, v7) = v9) | ~ apart_point_and_line(v8, v7) | ~ convergent_lines(v6, v7) | distinct_points(v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v6, v7) = v9) | ~ apart_point_and_line(v8, v6) | ~ convergent_lines(v6, v7) | distinct_points(v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v6, v7) = v9) | ~ apart_point_and_line(v8, v9) | ~ distinct_points(v6, v7) | distinct_points(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v6, v7) = v9) | ~ apart_point_and_line(v8, v9) | ~ distinct_points(v6, v7) | distinct_points(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ distinct_lines(v8, v9) | ~ distinct_points(v6, v7) | apart_point_and_line(v7, v9) | apart_point_and_line(v7, v8) | apart_point_and_line(v6, v9) | apart_point_and_line(v6, v8)) & ? [v6] : ! [v7] : ! [v8] : ( ~ apart_point_and_line(v7, v8) | apart_point_and_line(v7, v6) | distinct_lines(v8, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ apart_point_and_line(v7, v8) | apart_point_and_line(v6, v8) | distinct_points(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ convergent_lines(v7, v8) | convergent_lines(v8, v6) | convergent_lines(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ distinct_lines(v7, v8) | distinct_lines(v8, v6) | distinct_lines(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ distinct_points(v7, v8) | distinct_points(v8, v6) | distinct_points(v7, v6)) & ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | distinct_lines(v6, v7)) & ! [v6] : ~ convergent_lines(v6, v6) & ! [v6] : ~ distinct_lines(v6, v6) & ! [v6] : ~ distinct_points(v6, v6) & (apart_point_and_line(v5, v1) | apart_point_and_line(v5, v0))) % 8.27/2.67 | 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 yields: % 8.27/2.67 | (1) intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0 & intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1 & convergent_lines(all_0_3_3, all_0_2_2) & convergent_lines(all_0_5_5, all_0_4_4) & ~ apart_point_and_line(all_0_1_1, all_0_2_2) & ~ apart_point_and_line(all_0_1_1, all_0_3_3) & ! [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] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) & ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1)) & ! [v0] : ~ convergent_lines(v0, v0) & ! [v0] : ~ distinct_lines(v0, v0) & ! [v0] : ~ distinct_points(v0, v0) & (apart_point_and_line(all_0_0_0, all_0_4_4) | apart_point_and_line(all_0_0_0, all_0_5_5)) % 8.72/2.67 | % 8.72/2.67 | Applying alpha-rule on (1) yields: % 8.72/2.67 | (2) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0)) % 8.72/2.67 | (3) apart_point_and_line(all_0_0_0, all_0_4_4) | apart_point_and_line(all_0_0_0, all_0_5_5) % 8.72/2.67 | (4) ! [v0] : ~ distinct_points(v0, v0) % 8.72/2.67 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1)) % 8.72/2.67 | (6) intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0 % 8.72/2.67 | (7) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1)) % 8.72/2.67 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) % 8.72/2.67 | (9) convergent_lines(all_0_3_3, all_0_2_2) % 8.72/2.67 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 8.72/2.67 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0)) % 8.72/2.67 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) % 8.72/2.67 | (13) ~ apart_point_and_line(all_0_1_1, all_0_2_2) % 8.72/2.67 | (14) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0)) % 8.72/2.68 | (15) convergent_lines(all_0_5_5, all_0_4_4) % 8.72/2.68 | (16) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) % 8.72/2.68 | (17) ! [v0] : ~ distinct_lines(v0, v0) % 8.72/2.68 | (18) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) % 8.72/2.68 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 8.72/2.68 | (20) ~ apart_point_and_line(all_0_1_1, all_0_3_3) % 8.72/2.68 | (21) ! [v0] : ~ convergent_lines(v0, v0) % 8.72/2.68 | (22) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) % 8.72/2.68 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) % 8.72/2.68 | (24) intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1 % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (7) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2), yields: % 8.72/2.68 | (25) distinct_lines(all_0_3_3, all_0_2_2) % 8.72/2.68 | % 8.72/2.68 +-Applying beta-rule and splitting (3), into two cases. % 8.72/2.68 |-Branch one: % 8.72/2.68 | (26) apart_point_and_line(all_0_0_0, all_0_4_4) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (23) with all_0_1_1, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1, apart_point_and_line(all_0_0_0, all_0_4_4), convergent_lines(all_0_5_5, all_0_4_4), yields: % 8.72/2.68 | (27) distinct_points(all_0_0_0, all_0_1_1) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (12) with all_0_2_2, all_0_3_3, all_0_1_1, all_0_0_0 and discharging atoms distinct_lines(all_0_3_3, all_0_2_2), distinct_points(all_0_0_0, all_0_1_1), ~ apart_point_and_line(all_0_1_1, all_0_2_2), ~ apart_point_and_line(all_0_1_1, all_0_3_3), yields: % 8.72/2.68 | (28) apart_point_and_line(all_0_0_0, all_0_2_2) | apart_point_and_line(all_0_0_0, all_0_3_3) % 8.72/2.68 | % 8.72/2.68 +-Applying beta-rule and splitting (28), into two cases. % 8.72/2.68 |-Branch one: % 8.72/2.68 | (29) apart_point_and_line(all_0_0_0, all_0_2_2) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (23) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_2_2), convergent_lines(all_0_3_3, all_0_2_2), yields: % 8.72/2.68 | (30) distinct_points(all_0_0_0, all_0_0_0) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (4) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields: % 8.72/2.68 | (31) $false % 8.72/2.68 | % 8.72/2.68 |-The branch is then unsatisfiable % 8.72/2.68 |-Branch two: % 8.72/2.68 | (32) ~ apart_point_and_line(all_0_0_0, all_0_2_2) % 8.72/2.68 | (33) apart_point_and_line(all_0_0_0, all_0_3_3) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (8) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_3_3), convergent_lines(all_0_3_3, all_0_2_2), yields: % 8.72/2.68 | (30) distinct_points(all_0_0_0, all_0_0_0) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (4) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields: % 8.72/2.68 | (31) $false % 8.72/2.68 | % 8.72/2.68 |-The branch is then unsatisfiable % 8.72/2.68 |-Branch two: % 8.72/2.68 | (36) ~ apart_point_and_line(all_0_0_0, all_0_4_4) % 8.72/2.68 | (37) apart_point_and_line(all_0_0_0, all_0_5_5) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (8) with all_0_1_1, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1, apart_point_and_line(all_0_0_0, all_0_5_5), convergent_lines(all_0_5_5, all_0_4_4), yields: % 8.72/2.68 | (27) distinct_points(all_0_0_0, all_0_1_1) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (12) with all_0_2_2, all_0_3_3, all_0_1_1, all_0_0_0 and discharging atoms distinct_lines(all_0_3_3, all_0_2_2), distinct_points(all_0_0_0, all_0_1_1), ~ apart_point_and_line(all_0_1_1, all_0_2_2), ~ apart_point_and_line(all_0_1_1, all_0_3_3), yields: % 8.72/2.68 | (28) apart_point_and_line(all_0_0_0, all_0_2_2) | apart_point_and_line(all_0_0_0, all_0_3_3) % 8.72/2.68 | % 8.72/2.68 +-Applying beta-rule and splitting (28), into two cases. % 8.72/2.68 |-Branch one: % 8.72/2.68 | (29) apart_point_and_line(all_0_0_0, all_0_2_2) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (23) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_2_2), convergent_lines(all_0_3_3, all_0_2_2), yields: % 8.72/2.68 | (30) distinct_points(all_0_0_0, all_0_0_0) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (4) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields: % 8.72/2.68 | (31) $false % 8.72/2.68 | % 8.72/2.68 |-The branch is then unsatisfiable % 8.72/2.68 |-Branch two: % 8.72/2.68 | (32) ~ apart_point_and_line(all_0_0_0, all_0_2_2) % 8.72/2.68 | (33) apart_point_and_line(all_0_0_0, all_0_3_3) % 8.72/2.68 | % 8.72/2.68 | Instantiating formula (8) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_3_3), convergent_lines(all_0_3_3, all_0_2_2), yields: % 8.72/2.69 | (30) distinct_points(all_0_0_0, all_0_0_0) % 8.72/2.69 | % 8.72/2.69 | Instantiating formula (4) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields: % 8.72/2.69 | (31) $false % 8.72/2.69 | % 8.72/2.69 |-The branch is then unsatisfiable % 8.72/2.69 % SZS output end Proof for theBenchmark % 8.72/2.69 % 8.72/2.69 2056ms %------------------------------------------------------------------------------