%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET604+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n018.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 00:20:41 EDT 2022 % Result : Theorem 2.41s 1.31s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET604+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n018.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 : Sun Jul 10 14:10:42 EDT 2022 % 0.12/0.34 % 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 % 0.20/0.60 (ePrincess v.1.0) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2015 % 0.20/0.60 (c) Peter Backeman, 2014-2015 % 0.20/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.60 Bug reports to peter@backeman.se % 0.20/0.60 % 0.20/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.38/0.89 Prover 0: Preprocessing ... % 1.64/1.02 Prover 0: Warning: ignoring some quantifiers % 1.64/1.04 Prover 0: Constructing countermodel ... % 2.17/1.19 Prover 0: gave up % 2.17/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.17/1.21 Prover 1: Preprocessing ... % 2.41/1.28 Prover 1: Constructing countermodel ... % 2.41/1.31 Prover 1: proved (119ms) % 2.41/1.31 % 2.41/1.31 No countermodel exists, formula is valid % 2.41/1.31 % SZS status Theorem for theBenchmark % 2.41/1.31 % 2.41/1.31 Generating proof ... found it (size 11) % 3.26/1.46 % 3.26/1.46 % SZS output start Proof for theBenchmark % 3.26/1.46 Assumed formulas after preprocessing and simplification: % 3.26/1.46 | (0) ? [v0] : ? [v1] : ( ~ (v1 = empty_set) & difference(empty_set, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (member(v4, v5) = v6) | ~ (difference(v2, v3) = v5) | ? [v7] : ? [v8] : (member(v4, v3) = v8 & member(v4, v2) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (member(v5, v4) = v3) | ~ (member(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (difference(v5, v4) = v3) | ~ (difference(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (subset(v5, v4) = v3) | ~ (subset(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (member(v4, v5) = 0) | ~ (difference(v2, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & member(v4, v3) = v6 & member(v4, v2) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v4 = empty_set | ~ (difference(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & subset(v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & member(v5, v3) = v6 & member(v5, v2) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (empty(v4) = v3) | ~ (empty(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (member(v4, v2) = 0) | ~ (subset(v2, v3) = 0) | member(v4, v3) = 0) & ! [v2] : ! [v3] : (v3 = v2 | ~ (subset(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v3, v2) = v4)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (empty(v2) = v3) | ? [v4] : member(v4, v2) = 0) & ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v2) = v3)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(empty_set, v2) = v3)) & ! [v2] : ! [v3] : ( ~ (empty(v2) = 0) | ~ (member(v3, v2) = 0)) & ! [v2] : ! [v3] : ( ~ (difference(v2, v3) = empty_set) | subset(v2, v3) = 0) & ! [v2] : ~ (member(v2, empty_set) = 0)) % 3.26/1.50 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 3.26/1.50 | (1) ~ (all_0_0_0 = empty_set) & difference(empty_set, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (difference(v0, v1) = v3) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (difference(v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0)) & ! [v0] : ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ~ (member(v0, empty_set) = 0) % 3.26/1.50 | % 3.26/1.51 | Applying alpha-rule on (1) yields: % 3.26/1.51 | (2) ! [v0] : ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1) = 0) % 3.26/1.51 | (3) ~ (all_0_0_0 = empty_set) % 3.26/1.51 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 3.26/1.51 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) % 3.26/1.51 | (6) difference(empty_set, all_0_1_1) = all_0_0_0 % 3.26/1.51 | (7) ! [v0] : ~ (member(v0, empty_set) = 0) % 3.26/1.51 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 3.26/1.51 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 3.26/1.51 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 3.26/1.51 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (difference(v0, v1) = v3) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 3.45/1.51 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0) % 3.45/1.51 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 3.45/1.51 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (difference(v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) % 3.45/1.51 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 3.45/1.51 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) % 3.45/1.51 | (17) ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0)) % 3.45/1.51 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 3.45/1.51 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 3.45/1.51 | % 3.45/1.51 | Instantiating formula (18) with all_0_0_0, all_0_1_1, empty_set and discharging atoms difference(empty_set, all_0_1_1) = all_0_0_0, yields: % 3.45/1.51 | (20) all_0_0_0 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_1_1) = v0) % 3.45/1.51 | % 3.45/1.51 +-Applying beta-rule and splitting (20), into two cases. % 3.45/1.51 |-Branch one: % 3.45/1.51 | (21) all_0_0_0 = empty_set % 3.45/1.51 | % 3.45/1.51 | Equations (21) can reduce 3 to: % 3.45/1.51 | (22) $false % 3.45/1.51 | % 3.45/1.51 |-The branch is then unsatisfiable % 3.45/1.51 |-Branch two: % 3.45/1.51 | (3) ~ (all_0_0_0 = empty_set) % 3.45/1.51 | (24) ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_1_1) = v0) % 3.45/1.52 | % 3.45/1.52 | Instantiating (24) with all_10_0_2 yields: % 3.45/1.52 | (25) ~ (all_10_0_2 = 0) & subset(empty_set, all_0_1_1) = all_10_0_2 % 3.45/1.52 | % 3.45/1.52 | Applying alpha-rule on (25) yields: % 3.45/1.52 | (26) ~ (all_10_0_2 = 0) % 3.45/1.52 | (27) subset(empty_set, all_0_1_1) = all_10_0_2 % 3.45/1.52 | % 3.45/1.52 | Instantiating formula (16) with all_10_0_2, all_0_1_1 and discharging atoms subset(empty_set, all_0_1_1) = all_10_0_2, yields: % 3.45/1.52 | (28) all_10_0_2 = 0 % 3.45/1.52 | % 3.45/1.52 | Equations (28) can reduce 26 to: % 3.45/1.52 | (22) $false % 3.45/1.52 | % 3.45/1.52 |-The branch is then unsatisfiable % 3.45/1.52 % SZS output end Proof for theBenchmark % 3.45/1.52 % 3.45/1.52 911ms %------------------------------------------------------------------------------