%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU169+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 08:47:16 EDT 2022 % Result : Theorem 2.38s 1.28s % Output : Proof 3.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU169+1 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 22:21:58 EDT 2022 % 0.13/0.35 % CPUTime : % 0.53/0.59 ____ _ % 0.53/0.59 ___ / __ \_____(_)___ ________ __________ % 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.59 % 0.53/0.59 A Theorem Prover for First-Order Logic % 0.53/0.60 (ePrincess v.1.0) % 0.53/0.60 % 0.53/0.60 (c) Philipp Rümmer, 2009-2015 % 0.53/0.60 (c) Peter Backeman, 2014-2015 % 0.53/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.60 Bug reports to peter@backeman.se % 0.53/0.60 % 0.53/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.60 % 0.53/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.33/0.93 Prover 0: Preprocessing ... % 1.70/1.07 Prover 0: Warning: ignoring some quantifiers % 1.83/1.09 Prover 0: Constructing countermodel ... % 2.38/1.28 Prover 0: proved (629ms) % 2.38/1.28 % 2.38/1.28 No countermodel exists, formula is valid % 2.38/1.28 % SZS status Theorem for theBenchmark % 2.38/1.28 % 2.38/1.28 Generating proof ... Warning: ignoring some quantifiers % 3.15/1.49 found it (size 9) % 3.15/1.49 % 3.15/1.49 % SZS output start Proof for theBenchmark % 3.15/1.49 Assumed formulas after preprocessing and simplification: % 3.15/1.49 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (powerset(v0) = v2 & element(v1, v2) & empty(v5) & empty(empty_set) & in(v3, v1) & ~ empty(v4) & ~ in(v3, v0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (powerset(v8) = v7) | ~ (powerset(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (powerset(v6) = v7) | ~ subset(v8, v6) | in(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (powerset(v6) = v7) | ~ in(v8, v7) | subset(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ subset(v6, v7) | ~ in(v8, v6) | in(v8, v7)) & ? [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (powerset(v7) = v8) | ? [v9] : (( ~ subset(v9, v7) | ~ in(v9, v6)) & (subset(v9, v7) | in(v9, v6)))) & ! [v6] : ! [v7] : (v7 = v6 | ~ empty(v7) | ~ empty(v6)) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ~ empty(v7)) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | empty(v6) | ? [v8] : (element(v8, v7) & ~ empty(v8))) & ! [v6] : ! [v7] : ( ~ element(v7, v6) | ~ empty(v6) | empty(v7)) & ! [v6] : ! [v7] : ( ~ element(v7, v6) | empty(v6) | in(v7, v6)) & ! [v6] : ! [v7] : ( ~ empty(v7) | ~ empty(v6) | element(v7, v6)) & ! [v6] : ! [v7] : ( ~ empty(v7) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ( ~ in(v7, v6) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ( ~ in(v7, v6) | element(v7, v6) | empty(v6)) & ! [v6] : (v6 = empty_set | ~ empty(v6)) & ? [v6] : ? [v7] : element(v7, v6) & ? [v6] : ? [v7] : (subset(v6, v7) | ? [v8] : (in(v8, v6) & ~ in(v8, v7))) & ? [v6] : subset(v6, v6)) % 3.15/1.52 | 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: % 3.15/1.52 | (1) powerset(all_0_5_5) = all_0_3_3 & element(all_0_4_4, all_0_3_3) & empty(all_0_0_0) & empty(empty_set) & in(all_0_2_2, all_0_4_4) & ~ empty(all_0_1_1) & ~ in(all_0_2_2, all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : subset(v0, v0) % 3.15/1.53 | % 3.34/1.53 | Applying alpha-rule on (1) yields: % 3.34/1.53 | (2) ? [v0] : subset(v0, v0) % 3.34/1.53 | (3) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) % 3.34/1.53 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 3.34/1.53 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.34/1.53 | (6) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) % 3.34/1.53 | (7) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.34/1.53 | (8) ~ empty(all_0_1_1) % 3.34/1.53 | (9) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.34/1.53 | (10) empty(all_0_0_0) % 3.34/1.53 | (11) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 3.34/1.53 | (12) powerset(all_0_5_5) = all_0_3_3 % 3.34/1.53 | (13) in(all_0_2_2, all_0_4_4) % 3.34/1.53 | (14) ? [v0] : ? [v1] : element(v1, v0) % 3.34/1.53 | (15) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 3.34/1.53 | (16) element(all_0_4_4, all_0_3_3) % 3.34/1.53 | (17) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 3.34/1.53 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 3.34/1.54 | (19) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) % 3.34/1.54 | (20) ~ in(all_0_2_2, all_0_5_5) % 3.34/1.54 | (21) empty(empty_set) % 3.34/1.54 | (22) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 3.34/1.54 | (23) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) % 3.34/1.54 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 3.34/1.54 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 3.34/1.54 | (26) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 3.34/1.54 | % 3.34/1.54 | Instantiating formula (3) with all_0_4_4, all_0_3_3 and discharging atoms element(all_0_4_4, all_0_3_3), yields: % 3.34/1.54 | (27) empty(all_0_3_3) | in(all_0_4_4, all_0_3_3) % 3.34/1.54 | % 3.34/1.54 +-Applying beta-rule and splitting (27), into two cases. % 3.34/1.54 |-Branch one: % 3.34/1.54 | (28) empty(all_0_3_3) % 3.34/1.54 | % 3.34/1.54 | Instantiating formula (15) with all_0_3_3, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_3_3, empty(all_0_3_3), yields: % 3.34/1.54 | (29) $false % 3.34/1.54 | % 3.34/1.54 |-The branch is then unsatisfiable % 3.34/1.54 |-Branch two: % 3.34/1.54 | (30) ~ empty(all_0_3_3) % 3.34/1.54 | (31) in(all_0_4_4, all_0_3_3) % 3.34/1.54 | % 3.34/1.54 | Instantiating formula (24) with all_0_4_4, all_0_3_3, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_3_3, in(all_0_4_4, all_0_3_3), yields: % 3.34/1.54 | (32) subset(all_0_4_4, all_0_5_5) % 3.34/1.54 | % 3.34/1.54 | Instantiating formula (4) with all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_5_5), in(all_0_2_2, all_0_4_4), ~ in(all_0_2_2, all_0_5_5), yields: % 3.34/1.54 | (29) $false % 3.34/1.54 | % 3.34/1.54 |-The branch is then unsatisfiable % 3.34/1.54 % SZS output end Proof for theBenchmark % 3.34/1.54 % 3.34/1.54 935ms %------------------------------------------------------------------------------