%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0. % 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 00:16:54 EDT 2022 % Result : Theorem 2.37s 1.21s % Output : Proof 2.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n005.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 : Sun Jul 10 21:44:37 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.58 ____ _ % 0.18/0.58 ___ / __ \_____(_)___ ________ __________ % 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.21/0.86 Prover 0: Preprocessing ... % 1.51/0.95 Prover 0: Warning: ignoring some quantifiers % 1.51/0.96 Prover 0: Constructing countermodel ... % 1.71/1.09 Prover 0: gave up % 1.98/1.09 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.98/1.10 Prover 1: Preprocessing ... % 2.37/1.19 Prover 1: Constructing countermodel ... % 2.37/1.21 Prover 1: proved (121ms) % 2.37/1.21 % 2.37/1.21 No countermodel exists, formula is valid % 2.37/1.21 % SZS status Theorem for theBenchmark % 2.37/1.21 % 2.37/1.21 Generating proof ... found it (size 11) % 2.74/1.37 % 2.74/1.37 % SZS output start Proof for theBenchmark % 2.74/1.37 Assumed formulas after preprocessing and simplification: % 2.74/1.37 | (0) ? [v0] : ( ~ (v0 = empty_set) & subset(v0, empty_set) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (member(v4, v3) = v2) | ~ (member(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (subset(v4, v3) = v2) | ~ (subset(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v2) = v5 & member(v4, v1) = 0)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (empty(v3) = v2) | ~ (empty(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v3, v1) = 0) | ~ (subset(v1, v2) = 0) | member(v3, v2) = 0) & ! [v1] : ! [v2] : (v2 = v1 | ~ (subset(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & subset(v2, v1) = v3)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (empty(v1) = v2) | ? [v3] : member(v3, v1) = 0) & ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(empty_set, v1) = v2)) & ! [v1] : ! [v2] : ( ~ (empty(v1) = 0) | ~ (member(v2, v1) = 0)) & ! [v1] : ~ (member(v1, empty_set) = 0)) % 2.93/1.40 | Instantiating (0) with all_0_0_0 yields: % 2.93/1.40 | (1) ~ (all_0_0_0 = empty_set) & subset(all_0_0_0, empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [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] : ~ (member(v0, empty_set) = 0) % 2.93/1.40 | % 2.93/1.40 | Applying alpha-rule on (1) yields: % 2.93/1.40 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 2.93/1.40 | (3) subset(all_0_0_0, empty_set) = 0 % 2.93/1.40 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 2.93/1.41 | (5) ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0)) % 2.93/1.41 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 2.93/1.41 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 2.93/1.41 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 2.93/1.41 | (9) ! [v0] : ~ (member(v0, empty_set) = 0) % 2.93/1.41 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) % 2.93/1.41 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 2.93/1.41 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0) % 2.93/1.41 | (13) ~ (all_0_0_0 = empty_set) % 2.93/1.41 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) % 2.93/1.41 | % 2.93/1.41 | Instantiating formula (7) with empty_set, all_0_0_0 and discharging atoms subset(all_0_0_0, empty_set) = 0, yields: % 2.93/1.41 | (15) all_0_0_0 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_0_0) = v0) % 2.93/1.41 | % 2.93/1.41 +-Applying beta-rule and splitting (15), into two cases. % 2.93/1.41 |-Branch one: % 2.93/1.41 | (16) all_0_0_0 = empty_set % 2.93/1.41 | % 2.93/1.41 | Equations (16) can reduce 13 to: % 2.93/1.41 | (17) $false % 2.93/1.41 | % 2.93/1.41 |-The branch is then unsatisfiable % 2.93/1.41 |-Branch two: % 2.93/1.41 | (13) ~ (all_0_0_0 = empty_set) % 2.93/1.41 | (19) ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_0_0) = v0) % 2.93/1.41 | % 2.93/1.41 | Instantiating (19) with all_10_0_1 yields: % 2.93/1.41 | (20) ~ (all_10_0_1 = 0) & subset(empty_set, all_0_0_0) = all_10_0_1 % 2.93/1.41 | % 2.93/1.41 | Applying alpha-rule on (20) yields: % 2.93/1.41 | (21) ~ (all_10_0_1 = 0) % 2.93/1.41 | (22) subset(empty_set, all_0_0_0) = all_10_0_1 % 2.93/1.41 | % 2.93/1.41 | Instantiating formula (10) with all_10_0_1, all_0_0_0 and discharging atoms subset(empty_set, all_0_0_0) = all_10_0_1, yields: % 2.93/1.41 | (23) all_10_0_1 = 0 % 2.93/1.41 | % 2.93/1.41 | Equations (23) can reduce 21 to: % 2.93/1.41 | (17) $false % 2.93/1.41 | % 2.93/1.41 |-The branch is then unsatisfiable % 2.93/1.42 % SZS output end Proof for theBenchmark % 2.93/1.42 % 2.93/1.42 823ms %------------------------------------------------------------------------------