%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET886+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 3.63s 3.79s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET886+1 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.14 % Command : duper %s % 0.13/0.35 % Computer : n031.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 14:30:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.63/3.79 SZS status Theorem for theBenchmark.p % 3.63/3.79 SZS output start Proof for theBenchmark.p % 3.63/3.79 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 3.63/3.79 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), subset (unordered_pair A B) (singleton C) → Eq A C) True % 3.63/3.79 Clause #5 (by assumption #[]): Eq (Not (∀ (A B C : Iota), subset (unordered_pair A B) (singleton C) → Eq (unordered_pair A B) (singleton C))) True % 3.63/3.79 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Eq (unordered_pair A A) (singleton A)) True % 3.63/3.79 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset (unordered_pair a B) (singleton C) → Eq a C) True % 3.63/3.79 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), subset (unordered_pair a a_1) (singleton C) → Eq a C) True % 3.63/3.79 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair a a_1) (singleton a_2) → Eq a a_2) True % 3.63/3.79 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) (singleton a_2)) False) (Eq (Eq a a_2) True) % 3.63/3.79 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) (singleton a_2)) False) (Eq a a_2) % 3.63/3.79 Clause #18 (by clausification #[6]): ∀ (a : Iota), Eq (Eq (unordered_pair a a) (singleton a)) True % 3.63/3.79 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (unordered_pair a a) (singleton a) % 3.63/3.79 Clause #21 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 3.63/3.79 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 3.63/3.79 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 3.63/3.79 Clause #24 (by superposition #[23, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) (singleton a_2)) False) (Eq a_1 a_2) % 3.63/3.79 Clause #27 (by clausification #[5]): Eq (∀ (A B C : Iota), subset (unordered_pair A B) (singleton C) → Eq (unordered_pair A B) (singleton C)) False % 3.63/3.79 Clause #28 (by clausification #[27]): ∀ (a : Iota), % 3.63/3.79 Eq % 3.63/3.79 (Not % 3.63/3.79 (∀ (B C : Iota), % 3.63/3.79 subset (unordered_pair (skS.0 2 a) B) (singleton C) → Eq (unordered_pair (skS.0 2 a) B) (singleton C))) % 3.63/3.79 True % 3.63/3.79 Clause #29 (by clausification #[28]): ∀ (a : Iota), % 3.63/3.79 Eq % 3.63/3.79 (∀ (B C : Iota), % 3.63/3.79 subset (unordered_pair (skS.0 2 a) B) (singleton C) → Eq (unordered_pair (skS.0 2 a) B) (singleton C)) % 3.63/3.79 False % 3.63/3.79 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 3.63/3.79 Eq % 3.63/3.79 (Not % 3.63/3.79 (∀ (C : Iota), % 3.63/3.79 subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton C) → % 3.63/3.79 Eq (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton C))) % 3.63/3.79 True % 3.63/3.79 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 3.63/3.79 Eq % 3.63/3.79 (∀ (C : Iota), % 3.63/3.79 subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton C) → % 3.63/3.79 Eq (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton C)) % 3.63/3.79 False % 3.63/3.79 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 3.63/3.79 Eq % 3.63/3.79 (Not % 3.63/3.79 (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2)) → % 3.63/3.79 Eq (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2)))) % 3.63/3.79 True % 3.63/3.79 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 3.63/3.79 Eq % 3.63/3.79 (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2)) → % 3.63/3.79 Eq (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2))) % 3.63/3.79 False % 3.63/3.79 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2))) True % 3.63/3.79 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (Eq (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2))) False % 3.63/3.79 Clause #36 (by superposition #[34, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 3.63/3.79 Clause #37 (by superposition #[34, 24]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 3.63/3.79 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 2 a) (skS.0 4 a a_1 a_2) % 3.63/3.80 Clause #40 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Ne (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2)) % 3.63/3.80 Clause #41 (by forward demodulation #[40, 38]): ∀ (a a_1 : Iota), Ne (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 2 a)) % 3.63/3.80 Clause #42 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2) % 3.63/3.80 Clause #43 (by superposition #[42, 38]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1) % 3.63/3.80 Clause #44 (by backward demodulation #[43, 41]): ∀ (a : Iota), Ne (unordered_pair (skS.0 2 a) (skS.0 2 a)) (singleton (skS.0 2 a)) % 3.63/3.80 Clause #45 (by forward demodulation #[44, 19]): ∀ (a : Iota), Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a)) % 3.63/3.80 Clause #46 (by eliminate resolved literals #[45]): False % 3.63/3.80 SZS output end Proof for theBenchmark.p 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