%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU150+3 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:00:58 PM UTC 2025 % Result : Theorem 3.56s 3.80s % Output : Proof 3.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU150+3 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n016.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 05:54:38 EDT 2025 % 0.14/0.36 % CPUTime : % 3.56/3.80 SZS status Theorem for theBenchmark.p % 3.56/3.80 SZS output start Proof for theBenchmark.p % 3.56/3.80 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 3.56/3.80 Clause #3 (by assumption #[]): Eq (∀ (A B C : Iota), Eq (singleton A) (unordered_pair B C) → Eq A B) True % 3.56/3.80 Clause #4 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Eq (singleton A) (unordered_pair B C) → Eq B C)) True % 3.56/3.80 Clause #9 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B C : Iota), Eq (singleton a) (unordered_pair B C) → Eq a B) True % 3.56/3.80 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Eq (singleton a) (unordered_pair a_1 C) → Eq a a_1) True % 3.56/3.80 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (Eq (singleton a) (unordered_pair a_1 a_2) → Eq a a_1) True % 3.56/3.80 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq (singleton a) (unordered_pair a_1 a_2)) False) (Eq (Eq a a_1) True) % 3.56/3.80 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Ne (singleton a) (unordered_pair a_1 a_2)) % 3.56/3.80 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (unordered_pair a_1 a_2)) (Eq a a_1) % 3.56/3.80 Clause #15 (by clausification #[4]): Eq (∀ (A B C : Iota), Eq (singleton A) (unordered_pair B C) → Eq B C) False % 3.56/3.80 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), Eq (singleton (skS.0 2 a)) (unordered_pair B C) → Eq B C)) True % 3.56/3.80 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (B C : Iota), Eq (singleton (skS.0 2 a)) (unordered_pair B C) → Eq B C) False % 3.56/3.80 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 3.56/3.80 Eq (Not (∀ (C : Iota), Eq (singleton (skS.0 2 a)) (unordered_pair (skS.0 3 a a_1) C) → Eq (skS.0 3 a a_1) C)) True % 3.56/3.80 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 3.56/3.80 Eq (∀ (C : Iota), Eq (singleton (skS.0 2 a)) (unordered_pair (skS.0 3 a a_1) C) → Eq (skS.0 3 a a_1) C) False % 3.56/3.80 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.56/3.80 Eq % 3.56/3.80 (Not % 3.56/3.80 (Eq (singleton (skS.0 2 a)) (unordered_pair (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) → % 3.56/3.80 Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 3.56/3.80 True % 3.56/3.80 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 3.56/3.80 Eq % 3.56/3.80 (Eq (singleton (skS.0 2 a)) (unordered_pair (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) → % 3.56/3.80 Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 3.56/3.80 False % 3.56/3.80 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Eq (Eq (singleton (skS.0 2 a)) (unordered_pair (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True % 3.56/3.80 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False % 3.56/3.80 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (singleton (skS.0 2 a)) (unordered_pair (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 3.56/3.80 Clause #25 (by superposition #[24, 14]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (singleton (skS.0 2 a_1))) (Eq a (skS.0 3 a_1 a_2)) % 3.56/3.80 Clause #26 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 3.56/3.80 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 3.56/3.80 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 3.56/3.80 Clause #29 (by superposition #[28, 14]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (unordered_pair a_1 a_2)) (Eq a a_2) % 3.56/3.80 Clause #30 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2) % 3.56/3.80 Clause #31 (by superposition #[29, 24]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (singleton a) (singleton (skS.0 2 a_1))) (Eq a (skS.0 4 a_1 a_2 a_3)) % 3.56/3.80 Clause #32 (by equality resolution #[25]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1) % 3.56/3.80 Clause #34 (by backward demodulation #[32, 30]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 2 a) (skS.0 4 a a_1 a_2) % 3.56/3.80 Clause #37 (by equality resolution #[31]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 2 a) (skS.0 4 a a_1 a_2) % 3.56/3.80 Clause #38 (by forward demodulation #[34, 37]): ∀ (a : Iota), Ne (skS.0 2 a) (skS.0 2 a) % 3.56/3.80 Clause #39 (by eliminate resolved literals #[38]): False % 3.56/3.80 SZS output end Proof for theBenchmark.p 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