%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU123+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 08:46:44 EDT 2022 % Result : Theorem 2.44s 1.28s % Output : Proof 3.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU123+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n007.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 : Mon Jun 20 05:21:29 EDT 2022 % 0.14/0.34 % CPUTime : % 0.20/0.59 ____ _ % 0.20/0.59 ___ / __ \_____(_)___ ________ __________ % 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic % 0.20/0.59 (ePrincess v.1.0) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2015 % 0.20/0.59 (c) Peter Backeman, 2014-2015 % 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.37/0.92 Prover 0: Preprocessing ... % 1.61/1.00 Prover 0: Warning: ignoring some quantifiers % 1.61/1.02 Prover 0: Constructing countermodel ... % 1.75/1.14 Prover 0: gave up % 1.75/1.14 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.75/1.16 Prover 1: Preprocessing ... % 2.35/1.24 Prover 1: Constructing countermodel ... % 2.44/1.28 Prover 1: proved (136ms) % 2.44/1.28 % 2.44/1.28 No countermodel exists, formula is valid % 2.44/1.28 % SZS status Theorem for theBenchmark % 2.44/1.28 % 2.44/1.28 Generating proof ... found it (size 11) % 2.81/1.43 % 2.81/1.43 % SZS output start Proof for theBenchmark % 2.81/1.43 Assumed formulas after preprocessing and simplification: % 2.81/1.43 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v2 = 0) & ~ (v0 = empty_set) & empty(v3) = 0 & empty(v1) = v2 & empty(empty_set) = 0 & subset(v0, empty_set) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (in(v7, v6) = v5) | ~ (in(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (empty(v6) = v5) | ~ (empty(v6) = v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (empty(v5) = 0) | ~ (empty(v4) = 0)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (subset(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & subset(v5, v4) = v6)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v4, v4) = v5)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(empty_set, v4) = v5)) & ! [v4] : ! [v5] : ( ~ (in(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & empty(v5) = v6)) & ! [v4] : ! [v5] : ( ~ (in(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & in(v5, v4) = v6)) & ! [v4] : (v4 = empty_set | ~ (empty(v4) = 0))) % 2.98/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 2.98/1.46 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = empty_set) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(all_0_3_3, empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 3.03/1.46 | % 3.03/1.46 | Applying alpha-rule on (1) yields: % 3.03/1.46 | (2) ~ (all_0_1_1 = 0) % 3.03/1.46 | (3) empty(all_0_2_2) = all_0_1_1 % 3.03/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 3.03/1.46 | (5) ~ (all_0_3_3 = empty_set) % 3.03/1.46 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) % 3.03/1.47 | (7) empty(empty_set) = 0 % 3.03/1.47 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 3.03/1.47 | (9) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 3.03/1.47 | (10) empty(all_0_0_0) = 0 % 3.03/1.47 | (11) subset(all_0_3_3, empty_set) = 0 % 3.03/1.47 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 3.03/1.47 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 3.03/1.47 | (14) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 3.03/1.47 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 3.03/1.47 | (16) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 3.03/1.47 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 3.03/1.47 | % 3.03/1.47 | Instantiating formula (17) with empty_set, all_0_3_3 and discharging atoms subset(all_0_3_3, empty_set) = 0, yields: % 3.03/1.47 | (18) all_0_3_3 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_3_3) = v0) % 3.03/1.47 | % 3.03/1.47 +-Applying beta-rule and splitting (18), into two cases. % 3.03/1.47 |-Branch one: % 3.03/1.47 | (19) all_0_3_3 = empty_set % 3.03/1.47 | % 3.03/1.47 | Equations (19) can reduce 5 to: % 3.03/1.47 | (20) $false % 3.03/1.47 | % 3.03/1.47 |-The branch is then unsatisfiable % 3.03/1.47 |-Branch two: % 3.03/1.47 | (5) ~ (all_0_3_3 = empty_set) % 3.03/1.47 | (22) ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_3_3) = v0) % 3.03/1.47 | % 3.03/1.47 | Instantiating (22) with all_18_0_4 yields: % 3.03/1.47 | (23) ~ (all_18_0_4 = 0) & subset(empty_set, all_0_3_3) = all_18_0_4 % 3.03/1.47 | % 3.03/1.47 | Applying alpha-rule on (23) yields: % 3.03/1.47 | (24) ~ (all_18_0_4 = 0) % 3.03/1.47 | (25) subset(empty_set, all_0_3_3) = all_18_0_4 % 3.03/1.47 | % 3.03/1.47 | Instantiating formula (6) with all_18_0_4, all_0_3_3 and discharging atoms subset(empty_set, all_0_3_3) = all_18_0_4, yields: % 3.03/1.47 | (26) all_18_0_4 = 0 % 3.03/1.47 | % 3.03/1.47 | Equations (26) can reduce 24 to: % 3.03/1.47 | (20) $false % 3.03/1.47 | % 3.03/1.47 |-The branch is then unsatisfiable % 3.03/1.47 % SZS output end Proof for theBenchmark % 3.03/1.48 % 3.03/1.48 871ms %------------------------------------------------------------------------------