%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET194+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 07:59:47 PM UTC 2025 % Result : Theorem 4.06s 4.25s % Output : Proof 4.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET194+3 : TPTP v9.2.0. Released v2.2.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n019.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 : Thu Oct 2 14:01:53 EDT 2025 % 0.13/0.34 % CPUTime : % 4.06/4.25 SZS status Theorem for theBenchmark.p % 4.06/4.25 SZS output start Proof for theBenchmark.p % 4.06/4.25 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (union B C)) (Or (member D B) (member D C))) True % 4.06/4.25 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 4.06/4.25 Clause #5 (by assumption #[]): Eq (Not (∀ (B C : Iota), subset B (union B C))) True % 4.06/4.25 Clause #7 (by clausification #[5]): Eq (∀ (B C : Iota), subset B (union B C)) False % 4.06/4.25 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), subset (skS.0 0 a) (union (skS.0 0 a) C))) True % 4.06/4.25 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (C : Iota), subset (skS.0 0 a) (union (skS.0 0 a) C)) False % 4.06/4.25 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 0 a) (union (skS.0 0 a) (skS.0 1 a a_1)))) True % 4.06/4.25 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (union (skS.0 0 a) (skS.0 1 a a_1))) False % 4.06/4.25 Clause #15 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 4.06/4.25 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 4.06/4.25 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False) % 4.06/4.25 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 4.06/4.25 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 2 a a_1 a_2) a → member (skS.0 2 a a_1 a_2) a_1)) True) % 4.06/4.25 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 4.06/4.25 Or (Eq (subset a a_1) True) (Eq (member (skS.0 2 a a_1 a_2) a → member (skS.0 2 a a_1 a_2) a_1) False) % 4.06/4.25 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 2 a a_1 a_2) a) True) % 4.06/4.25 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 2 a a_1 a_2) a_1) False) % 4.06/4.25 Clause #26 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (union a C)) (Or (member D a) (member D C))) True % 4.06/4.25 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (union a a_1)) (Or (member D a) (member D a_1))) True % 4.06/4.25 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (union a_1 a_2)) (Or (member a a_1) (member a a_2))) True % 4.06/4.25 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (Or (member a a_1) (member a a_2)) False) % 4.06/4.25 Clause #32 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (member a a_1) False) % 4.06/4.25 Clause #34 (by superposition #[32, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 4.06/4.25 Or (Eq (member (skS.0 2 a a_1 a_2) (union a a_3)) True) (Or (Eq (subset a a_1) True) (Eq False True)) % 4.06/4.25 Clause #56 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (member (skS.0 2 a a_1 a_2) (union a a_3)) True) (Eq (subset a a_1) True) % 4.06/4.25 Clause #57 (by superposition #[56, 22]): ∀ (a a_1 : Iota), Or (Eq (subset a (union a a_1)) True) (Or (Eq (subset a (union a a_1)) True) (Eq True False)) % 4.06/4.25 Clause #61 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (subset a (union a a_1)) True) (Eq (subset a (union a a_1)) True) % 4.06/4.25 Clause #62 (by eliminate duplicate literals #[61]): ∀ (a a_1 : Iota), Eq (subset a (union a a_1)) True % 4.06/4.25 Clause #63 (by superposition #[62, 11]): Eq True False % 4.06/4.25 Clause #69 (by clausification #[63]): False % 4.06/4.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------