%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU115+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %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 : 300s % DateTime : Fri Oct 3 08:00:53 PM UTC 2025 % Result : Theorem 3.82s 4.05s % Output : Proof 3.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU115+1 : TPTP v9.2.0. Released v3.2.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n005.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 : 300 % 0.13/0.34 % DateTime : Fri Oct 3 04:29:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.82/4.05 SZS status Theorem for theBenchmark.p % 3.82/4.05 SZS output start Proof for theBenchmark.p % 3.82/4.05 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), empty A → finite A) True % 3.82/4.05 Clause #27 (by assumption #[]): Eq (empty empty_set) True % 3.82/4.05 Clause #31 (by assumption #[]): Eq (Not (Eq (finite_subsets empty_set) (singleton empty_set))) True % 3.82/4.05 Clause #32 (by assumption #[]): Eq (∀ (A : Iota), finite A → Eq (finite_subsets A) (powerset A)) True % 3.82/4.05 Clause #33 (by assumption #[]): Eq (Eq (powerset empty_set) (singleton empty_set)) True % 3.82/4.05 Clause #38 (by clausification #[9]): ∀ (a : Iota), Eq (empty a → finite a) True % 3.82/4.05 Clause #39 (by clausification #[38]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (finite a) True) % 3.82/4.05 Clause #40 (by superposition #[39, 27]): Or (Eq (finite empty_set) True) (Eq False True) % 3.82/4.05 Clause #41 (by clausification #[40]): Eq (finite empty_set) True % 3.82/4.05 Clause #60 (by clausification #[33]): Eq (powerset empty_set) (singleton empty_set) % 3.82/4.05 Clause #98 (by clausification #[31]): Eq (Eq (finite_subsets empty_set) (singleton empty_set)) False % 3.82/4.05 Clause #99 (by clausification #[98]): Ne (finite_subsets empty_set) (singleton empty_set) % 3.82/4.05 Clause #100 (by forward demodulation #[99, 60]): Ne (finite_subsets empty_set) (powerset empty_set) % 3.82/4.05 Clause #105 (by clausification #[32]): ∀ (a : Iota), Eq (finite a → Eq (finite_subsets a) (powerset a)) True % 3.82/4.05 Clause #106 (by clausification #[105]): ∀ (a : Iota), Or (Eq (finite a) False) (Eq (Eq (finite_subsets a) (powerset a)) True) % 3.82/4.05 Clause #107 (by clausification #[106]): ∀ (a : Iota), Or (Eq (finite a) False) (Eq (finite_subsets a) (powerset a)) % 3.82/4.05 Clause #108 (by superposition #[107, 41]): Or (Eq (finite_subsets empty_set) (powerset empty_set)) (Eq False True) % 3.82/4.05 Clause #109 (by clausification #[108]): Eq (finite_subsets empty_set) (powerset empty_set) % 3.82/4.05 Clause #110 (by forward contextual literal cutting #[109, 100]): False % 3.82/4.05 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------