%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET879+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 5.33s 5.50s % Output : Proof 5.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET879+1 : TPTP v9.2.0. Released v3.2.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n031.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 13:54:08 EDT 2025 % 0.14/0.34 % CPUTime : % 5.33/5.50 SZS status Theorem for theBenchmark.p % 5.33/5.50 SZS output start Proof for theBenchmark.p % 5.33/5.50 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 5.33/5.50 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) (singleton A)) (Not (in A B))) True % 5.33/5.50 Clause #5 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) (singleton B)) (singleton A)) (Ne A B))) True % 5.33/5.50 Clause #14 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) (singleton a)) (Not (in a B))) True % 5.33/5.50 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) (singleton a)) (Not (in a a_1))) True % 5.33/5.50 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) (singleton a)) True) (Eq (Not (in a a_1)) False) % 5.33/5.50 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) (singleton a)) False) (Eq (Not (in a a_1)) True) % 5.33/5.50 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (set_difference (singleton a) a_1) (singleton a)) % 5.33/5.50 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (set_difference (singleton a) a_1) (singleton a)) (Eq (in a a_1) True) % 5.33/5.50 Clause #20 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) True) (Ne (set_difference (singleton a) a_1) (singleton a)) % 5.33/5.50 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Ne (set_difference (singleton a) a_1) (singleton a)) (Eq (in a a_1) False) % 5.33/5.50 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 % 5.33/5.50 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 % 5.33/5.50 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) % 5.33/5.50 Clause #33 (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)) % 5.33/5.50 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 5.33/5.50 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False)) % 5.33/5.50 Clause #36 (by clausification #[34]): ∀ (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)) % 5.33/5.50 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 5.33/5.50 Clause #38 (by destructive equality resolution #[37]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 5.33/5.50 Clause #39 (by destructive equality resolution #[38]): ∀ (a : Iota), Eq (in a (singleton a)) True % 5.33/5.50 Clause #42 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 5.33/5.50 Clause #43 (by destructive equality resolution #[42]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 5.33/5.50 Clause #46 (by clausification #[5]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) (singleton B)) (singleton A)) (Ne A B)) False % 5.33/5.50 Clause #47 (by clausification #[46]): ∀ (a : Iota), % 5.33/5.50 Eq % 5.33/5.50 (Not % 5.33/5.50 (∀ (B : Iota), % 5.33/5.50 Iff (Eq (set_difference (singleton (skS.0 3 a)) (singleton B)) (singleton (skS.0 3 a))) (Ne (skS.0 3 a) B))) % 5.33/5.50 True % 5.33/5.50 Clause #48 (by clausification #[47]): ∀ (a : Iota), % 5.33/5.50 Eq % 5.33/5.50 (∀ (B : Iota), % 5.33/5.50 Iff (Eq (set_difference (singleton (skS.0 3 a)) (singleton B)) (singleton (skS.0 3 a))) (Ne (skS.0 3 a) B)) % 5.33/5.50 False % 5.33/5.50 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 5.33/5.50 Eq % 5.33/5.50 (Not % 5.33/5.50 (Iff (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) % 5.33/5.50 (Ne (skS.0 3 a) (skS.0 4 a a_1)))) % 5.33/5.50 True % 5.33/5.50 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 5.33/5.50 Eq % 5.33/5.50 (Iff (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) % 5.33/5.52 (Ne (skS.0 3 a) (skS.0 4 a a_1))) % 5.33/5.52 False % 5.33/5.52 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 5.33/5.52 Or (Eq (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) False) % 5.33/5.52 (Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) False) % 5.33/5.52 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota), % 5.33/5.52 Or (Eq (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) True) % 5.33/5.52 (Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) True) % 5.33/5.52 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), % 5.33/5.52 Or (Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) False) % 5.33/5.52 (Ne (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) % 5.33/5.52 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), % 5.33/5.52 Or (Ne (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) % 5.33/5.52 (Eq (skS.0 3 a) (skS.0 4 a a_1)) % 5.33/5.52 Clause #55 (by superposition #[54, 19]): ∀ (a a_1 : Iota), % 5.33/5.52 Or (Eq (in (skS.0 3 a) (singleton (skS.0 4 a a_1))) True) % 5.33/5.52 (Or (Ne (singleton (skS.0 3 a)) (singleton (skS.0 3 a))) (Eq (skS.0 3 a) (skS.0 4 a a_1))) % 5.33/5.52 Clause #82 (by clausification #[52]): ∀ (a a_1 : Iota), % 5.33/5.52 Or (Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) True) % 5.33/5.52 (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) % 5.33/5.52 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), % 5.33/5.52 Or (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) % 5.33/5.52 (Ne (skS.0 3 a) (skS.0 4 a a_1)) % 5.33/5.52 Clause #127 (by eliminate resolved literals #[55]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 3 a) (singleton (skS.0 4 a a_1))) True) (Eq (skS.0 3 a) (skS.0 4 a a_1)) % 5.33/5.52 Clause #128 (by superposition #[127, 43]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a) (skS.0 4 a a_1)) (Or (Eq True False) (Eq (skS.0 3 a) (skS.0 4 a a_1))) % 5.33/5.52 Clause #561 (by clausification #[128]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a) (skS.0 4 a a_1)) (Eq (skS.0 3 a) (skS.0 4 a a_1)) % 5.33/5.52 Clause #562 (by eliminate duplicate literals #[561]): ∀ (a a_1 : Iota), Eq (skS.0 3 a) (skS.0 4 a a_1) % 5.33/5.52 Clause #568 (by backward contextual literal cutting #[562, 83]): ∀ (a a_1 : Iota), Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a)) % 5.33/5.52 Clause #569 (by forward demodulation #[568, 562]): ∀ (a : Iota), Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 3 a))) (singleton (skS.0 3 a)) % 5.33/5.52 Clause #570 (by superposition #[569, 21]): ∀ (a : Iota), % 5.33/5.52 Or (Ne (singleton (skS.0 3 a)) (singleton (skS.0 3 a))) (Eq (in (skS.0 3 a) (singleton (skS.0 3 a))) False) % 5.33/5.52 Clause #582 (by eliminate resolved literals #[570]): ∀ (a : Iota), Eq (in (skS.0 3 a) (singleton (skS.0 3 a))) False % 5.33/5.52 Clause #583 (by superposition #[582, 39]): Eq False True % 5.33/5.52 Clause #640 (by clausification #[583]): False % 5.33/5.52 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------