%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU150+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 3.51s 3.69s % Output : Proof 3.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU150+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.14 % Command : duper %s % 0.13/0.35 % Computer : n002.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 : Fri Oct 3 04:29:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.51/3.69 SZS status Theorem for theBenchmark.p % 3.51/3.69 SZS output start Proof for theBenchmark.p % 3.51/3.69 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 3.51/3.69 Clause #2 (by assumption #[]): Eq (∀ (A B C : Iota), Eq (singleton A) (unordered_pair B C) → Eq A B) True % 3.51/3.69 Clause #3 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Eq (singleton A) (unordered_pair B C) → Eq B C)) True % 3.51/3.69 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B C : Iota), Eq (singleton a) (unordered_pair B C) → Eq a B) True % 3.51/3.69 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Eq (singleton a) (unordered_pair a_1 C) → Eq a a_1) True % 3.51/3.69 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (Eq (singleton a) (unordered_pair a_1 a_2) → Eq a a_1) True % 3.51/3.69 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq (singleton a) (unordered_pair a_1 a_2)) False) (Eq (Eq a a_1) True) % 3.51/3.69 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Ne (singleton a) (unordered_pair a_1 a_2)) % 3.51/3.69 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (unordered_pair a_1 a_2)) (Eq a a_1) % 3.51/3.69 Clause #10 (by clausification #[3]): Eq (∀ (A B C : Iota), Eq (singleton A) (unordered_pair B C) → Eq B C) False % 3.51/3.69 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair B C) → Eq B C)) True % 3.51/3.69 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (B C : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair B C) → Eq B C) False % 3.51/3.69 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 3.51/3.69 Eq (Not (∀ (C : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) C) → Eq (skS.0 1 a a_1) C)) True % 3.51/3.69 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 3.51/3.69 Eq (∀ (C : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) C) → Eq (skS.0 1 a a_1) C) False % 3.51/3.69 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 3.51/3.69 Eq % 3.51/3.69 (Not % 3.51/3.69 (Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 3.51/3.69 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.51/3.69 True % 3.51/3.69 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 3.51/3.69 Eq % 3.51/3.69 (Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 3.51/3.69 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.51/3.69 False % 3.51/3.69 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 3.51/3.69 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False % 3.51/3.69 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.51/3.69 Clause #20 (by superposition #[19, 9]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (singleton (skS.0 0 a_1))) (Eq a (skS.0 1 a_1 a_2)) % 3.51/3.69 Clause #21 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 3.51/3.69 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 3.51/3.69 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 3.51/3.69 Clause #24 (by superposition #[23, 9]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (unordered_pair a_1 a_2)) (Eq a a_2) % 3.51/3.69 Clause #25 (by superposition #[24, 19]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (singleton a) (singleton (skS.0 0 a_1))) (Eq a (skS.0 2 a_1 a_2 a_3)) % 3.51/3.69 Clause #26 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) % 3.51/3.69 Clause #27 (by equality resolution #[20]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 1 a a_1) % 3.51/3.69 Clause #29 (by backward demodulation #[27, 26]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 0 a) (skS.0 2 a a_1 a_2) % 3.51/3.69 Clause #32 (by equality resolution #[25]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 0 a) (skS.0 2 a a_1 a_2) % 3.51/3.69 Clause #33 (by forward contextual literal cutting #[32, 29]): False % 3.51/3.69 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------