%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET924+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:00:42 PM UTC 2025 % Result : Theorem 3.83s 4.00s % Output : Proof 3.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET924+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n010.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 14:38:23 EDT 2025 % 0.14/0.36 % CPUTime : % 3.83/4.00 SZS status Theorem for theBenchmark.p % 3.83/4.00 SZS output start Proof for theBenchmark.p % 3.83/4.00 Clause #3 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) (singleton A)) (Not (in A B)))) True % 3.83/4.00 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) (singleton A)) (Not (in A B))) True % 3.83/4.00 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) (singleton a)) (Not (in a B))) True % 3.83/4.00 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) (singleton a)) (Not (in a a_1))) True % 3.83/4.00 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) (singleton a)) True) (Eq (Not (in a a_1)) False) % 3.83/4.00 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) (singleton a)) False) (Eq (Not (in a a_1)) True) % 3.83/4.00 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (set_difference (singleton a) a_1) (singleton a)) % 3.83/4.00 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (set_difference (singleton a) a_1) (singleton a)) (Eq (in a a_1) True) % 3.83/4.00 Clause #19 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) True) (Ne (set_difference (singleton a) a_1) (singleton a)) % 3.83/4.00 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Ne (set_difference (singleton a) a_1) (singleton a)) (Eq (in a a_1) False) % 3.83/4.00 Clause #22 (by clausification #[3]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) (singleton A)) (Not (in A B))) False % 3.83/4.00 Clause #23 (by clausification #[22]): ∀ (a : Iota), % 3.83/4.00 Eq % 3.83/4.00 (Not % 3.83/4.00 (∀ (B : Iota), % 3.83/4.00 Iff (Eq (set_difference (singleton (skS.0 2 a)) B) (singleton (skS.0 2 a))) (Not (in (skS.0 2 a) B)))) % 3.83/4.00 True % 3.83/4.00 Clause #24 (by clausification #[23]): ∀ (a : Iota), % 3.83/4.00 Eq % 3.83/4.00 (∀ (B : Iota), Iff (Eq (set_difference (singleton (skS.0 2 a)) B) (singleton (skS.0 2 a))) (Not (in (skS.0 2 a) B))) % 3.83/4.00 False % 3.83/4.00 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), % 3.83/4.00 Eq % 3.83/4.00 (Not % 3.83/4.00 (Iff (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) % 3.83/4.00 (Not (in (skS.0 2 a) (skS.0 3 a a_1))))) % 3.83/4.00 True % 3.83/4.00 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), % 3.83/4.00 Eq % 3.83/4.00 (Iff (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) % 3.83/4.00 (Not (in (skS.0 2 a) (skS.0 3 a a_1)))) % 3.83/4.00 False % 3.83/4.00 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), % 3.83/4.00 Or (Eq (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) False) % 3.83/4.00 (Eq (Not (in (skS.0 2 a) (skS.0 3 a a_1))) False) % 3.83/4.00 Clause #28 (by clausification #[26]): ∀ (a a_1 : Iota), % 3.83/4.00 Or (Eq (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) True) % 3.83/4.00 (Eq (Not (in (skS.0 2 a) (skS.0 3 a a_1))) True) % 3.83/4.00 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), % 3.83/4.00 Or (Eq (Not (in (skS.0 2 a) (skS.0 3 a a_1))) False) % 3.83/4.00 (Ne (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) % 3.83/4.00 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 3.83/4.00 Or (Ne (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) % 3.83/4.00 (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True) % 3.83/4.00 Clause #31 (by forward contextual literal cutting #[30, 18]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True % 3.83/4.00 Clause #34 (by clausification #[28]): ∀ (a a_1 : Iota), % 3.83/4.00 Or (Eq (Not (in (skS.0 2 a) (skS.0 3 a a_1))) True) % 3.83/4.00 (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) % 3.83/4.00 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 3.83/4.00 Or (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) % 3.83/4.00 (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) False) % 3.83/4.00 Clause #36 (by forward demodulation #[35, 31]): ∀ (a a_1 : Iota), % 3.83/4.00 Or (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) (Eq True False) % 3.83/4.00 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a)) % 3.85/4.00 Clause #38 (by superposition #[37, 20]): ∀ (a a_1 : Iota), Or (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) False) % 3.85/4.00 Clause #39 (by eliminate resolved literals #[38]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) False % 3.85/4.00 Clause #40 (by superposition #[39, 31]): Eq False True % 3.85/4.00 Clause #41 (by clausification #[40]): False % 3.85/4.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------