%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET874+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:00:37 PM UTC 2025 % Result : Theorem 5.82s 6.07s % Output : Proof 5.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET874+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.12 % Command : duper %s % 0.12/0.33 % Computer : n004.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 13:35:38 EDT 2025 % 0.12/0.33 % CPUTime : % 5.82/6.07 SZS status Theorem for theBenchmark.p % 5.82/6.07 SZS output start Proof for theBenchmark.p % 5.82/6.07 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 5.82/6.07 Clause #3 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (unordered_pair A B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D A) (Eq D B)))) True % 5.82/6.07 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), in A B → Eq (set_union2 (singleton A) B) B) True % 5.82/6.07 Clause #10 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_union2 (singleton A) (unordered_pair A B)) (unordered_pair A B))) True % 5.82/6.07 Clause #28 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 5.82/6.07 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 5.82/6.07 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 5.82/6.07 Clause #36 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → Eq (set_union2 (singleton a) B) B) True % 5.82/6.07 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (in a a_1 → Eq (set_union2 (singleton a) a_1) a_1) True % 5.82/6.07 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (Eq (set_union2 (singleton a) a_1) a_1) True) % 5.82/6.07 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_union2 (singleton a) a_1) a_1) % 5.82/6.07 Clause #43 (by clausification #[10]): Eq (∀ (A B : Iota), Eq (set_union2 (singleton A) (unordered_pair A B)) (unordered_pair A B)) False % 5.82/6.07 Clause #44 (by clausification #[43]): ∀ (a : Iota), % 5.82/6.07 Eq % 5.82/6.07 (Not % 5.82/6.07 (∀ (B : Iota), % 5.82/6.07 Eq (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B)) (unordered_pair (skS.0 2 a) B))) % 5.82/6.07 True % 5.82/6.07 Clause #45 (by clausification #[44]): ∀ (a : Iota), % 5.82/6.07 Eq % 5.82/6.07 (∀ (B : Iota), % 5.82/6.07 Eq (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B)) (unordered_pair (skS.0 2 a) B)) % 5.82/6.07 False % 5.82/6.07 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), % 5.82/6.07 Eq % 5.82/6.07 (Not % 5.82/6.07 (Eq (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 5.82/6.07 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))) % 5.82/6.07 True % 5.82/6.07 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), % 5.82/6.07 Eq % 5.82/6.07 (Eq (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 5.82/6.07 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 5.82/6.07 False % 5.82/6.07 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 5.82/6.07 Ne (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 5.82/6.07 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) % 5.82/6.07 Clause #49 (by clausification #[3]): ∀ (a : Iota), % 5.82/6.07 Eq (∀ (B C : Iota), Iff (Eq C (unordered_pair a B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D B)))) True % 5.82/6.07 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 5.82/6.07 Eq (∀ (C : Iota), Iff (Eq C (unordered_pair a a_1)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D a_1)))) True % 5.82/6.07 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 5.82/6.07 Eq (Iff (Eq a (unordered_pair a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2)))) True % 5.82/6.07 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 5.82/6.07 Or (Eq (Eq a (unordered_pair a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) % 5.82/6.07 Clause #62 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 5.82/6.07 Or (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) (Ne a (unordered_pair a_1 a_2)) % 5.82/6.07 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Eq (Iff (in a_3 a) (Or (Eq a_3 a_1) (Eq a_3 a_2))) True) % 5.82/6.07 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota), % 5.82/6.07 Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (Eq a_3 a_1) (Eq a_3 a_2)) False)) % 5.82/6.07 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Eq a_3 a_2) False)) % 5.82/6.07 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Ne a_3 a_2)) % 5.82/6.07 Clause #69 (by destructive equality resolution #[68]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 5.82/6.07 Clause #70 (by destructive equality resolution #[69]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 5.82/6.07 Clause #72 (by superposition #[70, 39]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_union2 (singleton a) (unordered_pair a_1 a)) (unordered_pair a_1 a)) % 5.82/6.07 Clause #96 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton a) (unordered_pair a_1 a)) (unordered_pair a_1 a) % 5.82/6.07 Clause #99 (by superposition #[96, 30]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton a) (unordered_pair a a_1)) (unordered_pair a a_1) % 5.82/6.07 Clause #102 (by backward contextual literal cutting #[99, 48]): False % 5.82/6.07 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------