%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET926+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 : Tue Jul 19 00:23:13 EDT 2022 % Result : Theorem 1.73s 1.13s % Output : Proof 2.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET926+1 : TPTP v8.1.0. Released v3.2.0. % 0.00/0.11 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n005.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Sun Jul 10 09:49:52 EDT 2022 % 0.11/0.33 % CPUTime : % 0.55/0.59 ____ _ % 0.55/0.59 ___ / __ \_____(_)___ ________ __________ % 0.55/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.59 % 0.55/0.59 A Theorem Prover for First-Order Logic % 0.61/0.59 (ePrincess v.1.0) % 0.61/0.59 % 0.61/0.59 (c) Philipp Rümmer, 2009-2015 % 0.61/0.59 (c) Peter Backeman, 2014-2015 % 0.61/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.59 Bug reports to peter@backeman.se % 0.61/0.59 % 0.61/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.59 % 0.61/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.33/0.91 Prover 0: Preprocessing ... % 1.57/1.04 Prover 0: Constructing countermodel ... % 1.73/1.13 Prover 0: proved (491ms) % 1.73/1.13 % 1.73/1.13 No countermodel exists, formula is valid % 1.73/1.13 % SZS status Theorem for theBenchmark % 1.73/1.13 % 1.73/1.13 Generating proof ... found it (size 9) % 2.33/1.29 % 2.33/1.29 % SZS output start Proof for theBenchmark % 2.33/1.29 Assumed formulas after preprocessing and simplification: % 2.33/1.29 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ~ (v3 = empty_set) & singleton(v0) = v2 & set_difference(v2, v1) = v3 & empty(v5) & empty(empty_set) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (singleton(v6) = v8) | ~ (set_difference(v8, v7) = v9) | in(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (singleton(v6) = v8) | ~ (set_difference(v8, v7) = v9) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_difference(v9, v8) = v7) | ~ (set_difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (singleton(v6) = v8) | ~ (set_difference(v8, v7) = v8) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (singleton(v6) = v8) | ~ (set_difference(v8, v7) = empty_set) | in(v6, v7)) & ! [v6] : ! [v7] : ( ~ in(v7, v6) | ~ in(v6, v7))) % 2.50/1.32 | 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: % 2.50/1.32 | (1) ~ (all_0_2_2 = all_0_3_3) & ~ (all_0_2_2 = empty_set) & singleton(all_0_5_5) = all_0_3_3 & set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = empty_set) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.50/1.33 | % 2.50/1.33 | Applying alpha-rule on (1) yields: % 2.50/1.33 | (2) set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 % 2.50/1.33 | (3) ~ (all_0_2_2 = empty_set) % 2.50/1.33 | (4) empty(empty_set) % 2.50/1.33 | (5) ~ empty(all_0_1_1) % 2.50/1.33 | (6) singleton(all_0_5_5) = all_0_3_3 % 2.50/1.33 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v2) | ~ in(v0, v1)) % 2.50/1.33 | (8) ~ (all_0_2_2 = all_0_3_3) % 2.50/1.33 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ in(v0, v1)) % 2.50/1.33 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | in(v0, v1)) % 2.50/1.33 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.50/1.33 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 2.50/1.33 | (13) empty(all_0_0_0) % 2.50/1.33 | (14) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.50/1.33 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = empty_set) | in(v0, v1)) % 2.50/1.34 | % 2.50/1.34 | Instantiating formula (10) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, set_difference(all_0_3_3, all_0_4_4) = all_0_2_2, yields: % 2.50/1.34 | (16) all_0_2_2 = all_0_3_3 | in(all_0_5_5, all_0_4_4) % 2.50/1.34 | % 2.50/1.34 +-Applying beta-rule and splitting (16), into two cases. % 2.50/1.34 |-Branch one: % 2.50/1.34 | (17) in(all_0_5_5, all_0_4_4) % 2.50/1.34 | % 2.50/1.34 | Instantiating formula (9) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, set_difference(all_0_3_3, all_0_4_4) = all_0_2_2, in(all_0_5_5, all_0_4_4), yields: % 2.50/1.34 | (18) all_0_2_2 = empty_set % 2.50/1.34 | % 2.50/1.34 | Equations (18) can reduce 3 to: % 2.50/1.34 | (19) $false % 2.50/1.34 | % 2.50/1.34 |-The branch is then unsatisfiable % 2.50/1.34 |-Branch two: % 2.50/1.34 | (20) ~ in(all_0_5_5, all_0_4_4) % 2.50/1.34 | (21) all_0_2_2 = all_0_3_3 % 2.50/1.34 | % 2.50/1.34 | Equations (21) can reduce 8 to: % 2.50/1.34 | (19) $false % 2.50/1.34 | % 2.50/1.34 |-The branch is then unsatisfiable % 2.50/1.34 % SZS output end Proof for theBenchmark % 2.50/1.34 % 2.50/1.34 739ms %------------------------------------------------------------------------------