%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET605+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 00:20:42 EDT 2022 % Result : Theorem 2.15s 1.15s % Output : Proof 2.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SET605+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 02:06:13 EDT 2022 % 0.13/0.33 % CPUTime : % 0.53/0.57 ____ _ % 0.53/0.57 ___ / __ \_____(_)___ ________ __________ % 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.57 % 0.53/0.57 A Theorem Prover for First-Order Logic % 0.53/0.57 (ePrincess v.1.0) % 0.53/0.57 % 0.53/0.57 (c) Philipp Rümmer, 2009-2015 % 0.53/0.57 (c) Peter Backeman, 2014-2015 % 0.53/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.57 Bug reports to peter@backeman.se % 0.53/0.57 % 0.53/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.57 % 0.53/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.37/0.88 Prover 0: Preprocessing ... % 1.86/1.04 Prover 0: Warning: ignoring some quantifiers % 1.86/1.06 Prover 0: Constructing countermodel ... % 2.15/1.15 Prover 0: proved (524ms) % 2.15/1.15 % 2.15/1.15 No countermodel exists, formula is valid % 2.15/1.15 % SZS status Theorem for theBenchmark % 2.15/1.15 % 2.15/1.15 Generating proof ... Warning: ignoring some quantifiers % 2.79/1.34 found it (size 6) % 2.79/1.34 % 2.79/1.34 % SZS output start Proof for theBenchmark % 2.79/1.34 Assumed formulas after preprocessing and simplification: % 2.79/1.34 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = empty_set) & difference(v0, v2) = v3 & union(v0, v1) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (difference(v7, v6) = v5) | ~ (difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v7) | ~ member(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v7) | member(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v4) | member(v6, v7) | member(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v7) | member(v6, v5) | member(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v5) | member(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v4) | member(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = empty_set | ~ (difference(v4, v5) = v6) | ~ subset(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v5, v4) = v6) | union(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | union(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | subset(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ member(v6, v4) | ~ subset(v4, v5) | member(v6, v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ subset(v5, v4) | ~ subset(v4, v5)) & ! [v4] : ! [v5] : ( ~ (difference(v4, v5) = empty_set) | subset(v4, v5)) & ! [v4] : ! [v5] : ( ~ empty(v4) | ~ member(v5, v4)) & ! [v4] : ~ member(v4, empty_set) & ? [v4] : ? [v5] : (v5 = v4 | ? [v6] : (( ~ member(v6, v5) | ~ member(v6, v4)) & (member(v6, v5) | member(v6, v4)))) & ? [v4] : ? [v5] : (subset(v4, v5) | ? [v6] : (member(v6, v4) & ~ member(v6, v5))) & ? [v4] : (empty(v4) | ? [v5] : member(v5, v4)) & ? [v4] : subset(v4, v4)) % 2.86/1.38 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 2.86/1.38 | (1) ~ (all_0_0_0 = empty_set) & difference(all_0_3_3, all_0_1_1) = all_0_0_0 & union(all_0_3_3, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) & ! [v0] : ~ member(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ? [v0] : subset(v0, v0) % 2.86/1.39 | % 2.86/1.39 | Applying alpha-rule on (1) yields: % 2.86/1.39 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (difference(v0, v1) = v2) | ~ subset(v0, v1)) % 2.86/1.39 | (3) ~ (all_0_0_0 = empty_set) % 2.86/1.39 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) % 2.86/1.39 | (5) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) % 2.86/1.39 | (6) ? [v0] : subset(v0, v0) % 2.86/1.39 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) % 2.86/1.39 | (8) ! [v0] : ~ member(v0, empty_set) % 2.86/1.39 | (9) ! [v0] : ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1)) % 2.86/1.39 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 2.86/1.39 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) % 2.86/1.39 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) % 2.86/1.39 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | subset(v0, v2)) % 2.86/1.39 | (14) ? [v0] : (empty(v0) | ? [v1] : member(v1, v0)) % 2.86/1.39 | (15) union(all_0_3_3, all_0_2_2) = all_0_1_1 % 2.86/1.39 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) % 2.86/1.39 | (17) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 2.86/1.39 | (18) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 2.86/1.40 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) % 2.86/1.40 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 2.86/1.40 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 2.86/1.40 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 2.86/1.40 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 2.86/1.40 | (24) difference(all_0_3_3, all_0_1_1) = all_0_0_0 % 2.86/1.40 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 2.86/1.40 | % 2.86/1.40 | Instantiating formula (13) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 2.86/1.40 | (26) subset(all_0_3_3, all_0_1_1) % 2.86/1.40 | % 2.86/1.40 | Instantiating formula (2) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms difference(all_0_3_3, all_0_1_1) = all_0_0_0, subset(all_0_3_3, all_0_1_1), yields: % 2.86/1.40 | (27) all_0_0_0 = empty_set % 2.86/1.40 | % 2.86/1.40 | Equations (27) can reduce 3 to: % 2.86/1.40 | (28) $false % 2.86/1.40 | % 2.86/1.40 |-The branch is then unsatisfiable % 2.86/1.40 % SZS output end Proof for theBenchmark % 2.86/1.40 % 2.86/1.40 817ms %------------------------------------------------------------------------------