%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 03:48:34 EDT 2022 % Result : Theorem 14.85s 4.45s % Output : Proof 15.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n023.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 07:31:49 EDT 2022 % 0.12/0.33 % CPUTime : % 0.48/0.58 ____ _ % 0.48/0.58 ___ / __ \_____(_)___ ________ __________ % 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.58 % 0.48/0.58 A Theorem Prover for First-Order Logic % 0.48/0.58 (ePrincess v.1.0) % 0.48/0.58 % 0.48/0.58 (c) Philipp Rümmer, 2009-2015 % 0.48/0.58 (c) Peter Backeman, 2014-2015 % 0.48/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.58 Bug reports to peter@backeman.se % 0.48/0.58 % 0.48/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.58 % 0.48/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.67/0.94 Prover 0: Preprocessing ... % 1.97/1.07 Prover 0: Warning: ignoring some quantifiers % 2.04/1.09 Prover 0: Constructing countermodel ... % 14.85/4.45 Prover 0: proved (3817ms) % 14.85/4.45 % 14.85/4.45 No countermodel exists, formula is valid % 14.85/4.45 % SZS status Theorem for theBenchmark % 14.85/4.45 % 14.85/4.45 Generating proof ... Warning: ignoring some quantifiers % 15.85/4.65 found it (size 16) % 15.85/4.65 % 15.85/4.65 % SZS output start Proof for theBenchmark % 15.85/4.65 Assumed formulas after preprocessing and simplification: % 15.85/4.65 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v1) & convergent_lines(v2, v1) & convergent_lines(v0, v2) & convergent_lines(v0, v1) & ~ apart_point_and_line(v3, v2) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v5, v6) = v8) | ~ apart_point_and_line(v7, v6) | ~ convergent_lines(v5, v6) | distinct_points(v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v5, v6) = v8) | ~ apart_point_and_line(v7, v5) | ~ convergent_lines(v5, v6) | distinct_points(v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v8) | ~ apart_point_and_line(v7, v8) | ~ distinct_points(v5, v6) | distinct_points(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v8) | ~ apart_point_and_line(v7, v8) | ~ distinct_points(v5, v6) | distinct_points(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ distinct_lines(v7, v8) | ~ distinct_points(v5, v6) | apart_point_and_line(v6, v8) | apart_point_and_line(v6, v7) | apart_point_and_line(v5, v8) | apart_point_and_line(v5, v7)) & ? [v5] : ! [v6] : ! [v7] : ( ~ apart_point_and_line(v6, v7) | apart_point_and_line(v6, v5) | distinct_lines(v7, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ apart_point_and_line(v6, v7) | apart_point_and_line(v5, v7) | distinct_points(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | convergent_lines(v7, v5) | convergent_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ distinct_lines(v6, v7) | distinct_lines(v7, v5) | distinct_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ distinct_points(v6, v7) | distinct_points(v7, v5) | distinct_points(v6, v5)) & ! [v5] : ! [v6] : ( ~ convergent_lines(v5, v6) | distinct_lines(v5, v6)) & ! [v5] : ~ convergent_lines(v5, v5) & ! [v5] : ~ distinct_lines(v5, v5) & ! [v5] : ~ distinct_points(v5, v5)) % 15.97/4.69 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 15.97/4.69 | (1) intersection_point(all_0_4_4, all_0_2_2) = all_0_0_0 & intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1 & apart_point_and_line(all_0_0_0, all_0_3_3) & convergent_lines(all_0_2_2, all_0_3_3) & convergent_lines(all_0_4_4, all_0_2_2) & convergent_lines(all_0_4_4, all_0_3_3) & ~ apart_point_and_line(all_0_1_1, all_0_2_2) & ! [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) % 15.97/4.70 | % 15.97/4.70 | Applying alpha-rule on (1) yields: % 15.97/4.70 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) % 15.97/4.70 | (3) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) % 15.97/4.70 | (4) convergent_lines(all_0_4_4, all_0_3_3) % 15.97/4.70 | (5) convergent_lines(all_0_2_2, all_0_3_3) % 15.97/4.70 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1)) % 15.97/4.70 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0)) % 15.97/4.70 | (8) intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1 % 15.97/4.70 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 15.97/4.70 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 15.97/4.70 | (11) ! [v0] : ~ convergent_lines(v0, v0) % 15.97/4.70 | (12) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0)) % 15.97/4.70 | (13) ! [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)) % 15.97/4.70 | (14) apart_point_and_line(all_0_0_0, all_0_3_3) % 15.97/4.70 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) % 15.97/4.70 | (16) ! [v0] : ~ distinct_points(v0, v0) % 15.97/4.70 | (17) intersection_point(all_0_4_4, all_0_2_2) = all_0_0_0 % 15.97/4.70 | (18) ! [v0] : ~ distinct_lines(v0, v0) % 15.97/4.71 | (19) ~ apart_point_and_line(all_0_1_1, all_0_2_2) % 15.97/4.71 | (20) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) % 15.97/4.71 | (21) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0)) % 15.97/4.71 | (22) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) % 15.97/4.71 | (23) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1)) % 15.97/4.71 | (24) convergent_lines(all_0_4_4, all_0_2_2) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (23) with all_0_2_2, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2), yields: % 15.97/4.71 | (25) distinct_lines(all_0_4_4, all_0_2_2) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (15) with all_0_1_1, all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_0_0, all_0_3_3), convergent_lines(all_0_4_4, all_0_3_3), yields: % 15.97/4.71 | (26) distinct_points(all_0_0_0, all_0_1_1) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (13) with all_0_2_2, all_0_4_4, all_0_1_1, all_0_0_0 and discharging atoms distinct_lines(all_0_4_4, 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), yields: % 15.97/4.71 | (27) apart_point_and_line(all_0_0_0, all_0_2_2) | apart_point_and_line(all_0_0_0, all_0_4_4) | apart_point_and_line(all_0_1_1, all_0_4_4) % 15.97/4.71 | % 15.97/4.71 +-Applying beta-rule and splitting (27), into two cases. % 15.97/4.71 |-Branch one: % 15.97/4.71 | (28) apart_point_and_line(all_0_0_0, all_0_2_2) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (15) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_2_2), convergent_lines(all_0_4_4, all_0_2_2), yields: % 15.97/4.71 | (29) distinct_points(all_0_0_0, all_0_0_0) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (16) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields: % 15.97/4.71 | (30) $false % 15.97/4.71 | % 15.97/4.71 |-The branch is then unsatisfiable % 15.97/4.71 |-Branch two: % 15.97/4.71 | (31) ~ apart_point_and_line(all_0_0_0, all_0_2_2) % 15.97/4.71 | (32) apart_point_and_line(all_0_0_0, all_0_4_4) | apart_point_and_line(all_0_1_1, all_0_4_4) % 15.97/4.71 | % 15.97/4.71 +-Applying beta-rule and splitting (32), into two cases. % 15.97/4.71 |-Branch one: % 15.97/4.71 | (33) apart_point_and_line(all_0_0_0, all_0_4_4) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (2) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_4_4), convergent_lines(all_0_4_4, all_0_2_2), yields: % 15.97/4.71 | (29) distinct_points(all_0_0_0, all_0_0_0) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (16) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields: % 15.97/4.71 | (30) $false % 15.97/4.71 | % 15.97/4.71 |-The branch is then unsatisfiable % 15.97/4.71 |-Branch two: % 15.97/4.71 | (36) ~ apart_point_and_line(all_0_0_0, all_0_4_4) % 15.97/4.71 | (37) apart_point_and_line(all_0_1_1, all_0_4_4) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (2) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_1_1, all_0_4_4), convergent_lines(all_0_4_4, all_0_3_3), yields: % 15.97/4.71 | (38) distinct_points(all_0_1_1, all_0_1_1) % 15.97/4.71 | % 15.97/4.71 | Instantiating formula (16) with all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_1_1), yields: % 15.97/4.71 | (30) $false % 15.97/4.71 | % 15.97/4.71 |-The branch is then unsatisfiable % 15.97/4.71 % SZS output end Proof for theBenchmark % 15.97/4.71 % 15.97/4.71 4121ms %------------------------------------------------------------------------------