%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET880+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:00:38 PM UTC 2025 % Result : Theorem 3.86s 4.03s % Output : Proof 3.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET880+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n003.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 13:59:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.86/4.03 SZS status Theorem for theBenchmark.p % 3.86/4.03 SZS output start Proof for theBenchmark.p % 3.86/4.03 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.86/4.03 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B)) True % 3.86/4.03 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_difference (singleton A) (singleton B)) empty_set → Eq A B)) True % 3.86/4.03 Clause #15 (by clausification #[6]): Eq (∀ (A B : Iota), Eq (set_difference (singleton A) (singleton B)) empty_set → Eq A B) False % 3.86/4.03 Clause #16 (by clausification #[15]): ∀ (a : Iota), % 3.86/4.03 Eq (Not (∀ (B : Iota), Eq (set_difference (singleton (skS.0 2 a)) (singleton B)) empty_set → Eq (skS.0 2 a) B)) True % 3.86/4.03 Clause #17 (by clausification #[16]): ∀ (a : Iota), % 3.86/4.03 Eq (∀ (B : Iota), Eq (set_difference (singleton (skS.0 2 a)) (singleton B)) empty_set → Eq (skS.0 2 a) B) False % 3.86/4.03 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 3.86/4.03 Eq % 3.86/4.03 (Not % 3.86/4.03 (Eq (set_difference (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) empty_set → % 3.86/4.03 Eq (skS.0 2 a) (skS.0 3 a a_1))) % 3.86/4.03 True % 3.86/4.03 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 3.86/4.03 Eq % 3.86/4.03 (Eq (set_difference (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) empty_set → Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.86/4.03 False % 3.86/4.03 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) empty_set) True % 3.86/4.03 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) False % 3.86/4.03 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (set_difference (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) empty_set % 3.86/4.03 Clause #23 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.86/4.03 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.86/4.03 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.86/4.03 Clause #33 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) empty_set) (in a B)) True % 3.86/4.03 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) empty_set) (in a a_1)) True % 3.86/4.03 Clause #36 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) empty_set) False) (Eq (in a a_1) True) % 3.86/4.03 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Ne (set_difference (singleton a) a_1) empty_set) % 3.86/4.03 Clause #39 (by superposition #[38, 22]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Ne empty_set empty_set) % 3.86/4.03 Clause #40 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.86/4.03 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.86/4.03 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True)) % 3.86/4.03 Clause #52 (by clausification #[21]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (skS.0 3 a a_1) % 3.86/4.03 Clause #53 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 3.86/4.03 Clause #54 (by destructive equality resolution #[53]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 3.86/4.03 Clause #57 (by eliminate resolved literals #[39]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True % 3.86/4.03 Clause #58 (by superposition #[57, 54]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.86/4.03 Clause #61 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1) % 3.86/4.03 Clause #62 (by forward contextual literal cutting #[61, 52]): False % 3.86/4.03 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------