%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET926+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %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 : 300s % DateTime : Fri Oct 3 08:00:42 PM UTC 2025 % Result : Theorem 3.62s 3.77s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET926+1 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.14 % Command : duper %s % 0.15/0.35 % Computer : n007.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Thu Oct 2 13:53:53 EDT 2025 % 0.15/0.35 % CPUTime : % 3.62/3.77 SZS status Theorem for theBenchmark.p % 3.62/3.77 SZS output start Proof for theBenchmark.p % 3.62/3.77 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) (singleton A)) (Not (in A B))) True % 3.62/3.77 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B)) True % 3.62/3.77 Clause #6 (by assumption #[]): Eq % 3.62/3.77 (Not % 3.62/3.77 (∀ (A B : Iota), % 3.62/3.77 Or (Eq (set_difference (singleton A) B) empty_set) (Eq (set_difference (singleton A) B) (singleton A)))) % 3.62/3.77 True % 3.62/3.77 Clause #15 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) empty_set) (in a B)) True % 3.62/3.77 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) empty_set) (in a a_1)) True % 3.62/3.77 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) empty_set) True) (Eq (in a a_1) False) % 3.62/3.77 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_difference (singleton a) a_1) empty_set) % 3.62/3.77 Clause #20 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) (singleton a)) (Not (in a B))) True % 3.62/3.77 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) (singleton a)) (Not (in a a_1))) True % 3.62/3.77 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) (singleton a)) True) (Eq (Not (in a a_1)) False) % 3.62/3.77 Clause #24 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (set_difference (singleton a) a_1) (singleton a)) % 3.62/3.77 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (set_difference (singleton a) a_1) (singleton a)) (Eq (in a a_1) True) % 3.62/3.77 Clause #32 (by clausification #[6]): Eq % 3.62/3.77 (∀ (A B : Iota), % 3.62/3.77 Or (Eq (set_difference (singleton A) B) empty_set) (Eq (set_difference (singleton A) B) (singleton A))) % 3.62/3.77 False % 3.62/3.77 Clause #33 (by clausification #[32]): ∀ (a : Iota), % 3.62/3.77 Eq % 3.62/3.77 (Not % 3.62/3.77 (∀ (B : Iota), % 3.62/3.77 Or (Eq (set_difference (singleton (skS.0 2 a)) B) empty_set) % 3.62/3.77 (Eq (set_difference (singleton (skS.0 2 a)) B) (singleton (skS.0 2 a))))) % 3.62/3.77 True % 3.62/3.77 Clause #34 (by clausification #[33]): ∀ (a : Iota), % 3.62/3.77 Eq % 3.62/3.77 (∀ (B : Iota), % 3.62/3.77 Or (Eq (set_difference (singleton (skS.0 2 a)) B) empty_set) % 3.62/3.77 (Eq (set_difference (singleton (skS.0 2 a)) B) (singleton (skS.0 2 a)))) % 3.62/3.77 False % 3.62/3.77 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 3.62/3.77 Eq % 3.62/3.77 (Not % 3.62/3.77 (Or (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) % 3.62/3.77 (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))))) % 3.62/3.77 True % 3.62/3.77 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.62/3.77 Eq % 3.62/3.77 (Or (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) % 3.62/3.77 (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a)))) % 3.62/3.77 False % 3.62/3.77 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) False % 3.62/3.77 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) False % 3.62/3.77 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Ne (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a)) % 3.62/3.77 Clause #40 (by superposition #[39, 25]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True) (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) % 3.62/3.77 Clause #41 (by clausification #[38]): ∀ (a a_1 : Iota), Ne (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set % 3.62/3.77 Clause #43 (by eliminate resolved literals #[40]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True % 3.62/3.77 Clause #45 (by superposition #[43, 19]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) % 3.62/3.77 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set % 3.62/3.77 Clause #48 (by forward contextual literal cutting #[47, 41]): False % 3.62/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------