%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU505^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:01:46 PM UTC 2025 % Result : Theorem 4.07s 4.26s % Output : Proof 4.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU505^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 05:44:53 EDT 2025 % 0.13/0.34 % CPUTime : % 4.07/4.26 SZS status Theorem for theBenchmark.p % 4.07/4.26 SZS output start Proof for theBenchmark.p % 4.07/4.26 Clause #0 (by assumption #[]): Eq (Eq setextAx (∀ (A B : Iota), (∀ (Xx : Iota), Iff (in Xx A) (in Xx B)) → Eq A B)) True % 4.07/4.26 Clause #1 (by assumption #[]): Eq (Not (setextAx → ∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B)) % 4.07/4.26 True % 4.07/4.26 Clause #2 (by clausification #[1]): Eq (setextAx → ∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) False % 4.07/4.26 Clause #3 (by clausification #[2]): Eq setextAx True % 4.07/4.26 Clause #4 (by clausification #[2]): Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) False % 4.07/4.26 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 4.07/4.26 Eq % 4.07/4.26 (Not % 4.07/4.26 (∀ (B : Iota), % 4.07/4.26 (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx (skS.0 0 a)) → Eq (skS.0 0 a) B)) % 4.07/4.26 True % 4.07/4.26 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 4.07/4.26 Eq % 4.07/4.26 (∀ (B : Iota), % 4.07/4.26 (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx (skS.0 0 a)) → Eq (skS.0 0 a) B) % 4.07/4.26 False % 4.07/4.26 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.07/4.26 Eq % 4.07/4.26 (Not % 4.07/4.26 ((∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) → % 4.07/4.26 (∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a)) → Eq (skS.0 0 a) (skS.0 1 a a_1))) % 4.07/4.26 True % 4.07/4.26 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.07/4.26 Eq % 4.07/4.26 ((∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) → % 4.07/4.26 (∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a)) → Eq (skS.0 0 a) (skS.0 1 a a_1)) % 4.07/4.26 False % 4.07/4.26 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) True % 4.07/4.26 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a)) → Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 4.07/4.26 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Eq (in a (skS.0 0 a_1) → in a (skS.0 1 a_1 a_2)) True % 4.07/4.26 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Eq (in a (skS.0 1 a_1 a_2)) True) % 4.07/4.26 Clause #13 (by clausification #[0]): Eq setextAx (∀ (A B : Iota), (∀ (Xx : Iota), Iff (in Xx A) (in Xx B)) → Eq A B) % 4.07/4.26 Clause #14 (by forward demodulation #[13, 3]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), Iff (in Xx A) (in Xx B)) → Eq A B) % 4.07/4.26 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), Iff (in Xx a) (in Xx B)) → Eq a B) True % 4.07/4.26 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), Iff (in Xx a) (in Xx a_1)) → Eq a a_1) True % 4.07/4.26 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), Iff (in Xx a) (in Xx a_1)) False) (Eq (Eq a a_1) True) % 4.07/4.26 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 4.07/4.26 Or (Eq (Eq a a_1) True) (Eq (Not (Iff (in (skS.0 2 a a_1 a_2) a) (in (skS.0 2 a a_1 a_2) a_1))) True) % 4.07/4.26 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (Iff (in (skS.0 2 a a_1 a_2) a) (in (skS.0 2 a a_1 a_2) a_1))) True) (Eq a a_1) % 4.07/4.26 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq a a_1) (Eq (Iff (in (skS.0 2 a a_1 a_2) a) (in (skS.0 2 a a_1 a_2) a_1)) False) % 4.07/4.26 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq a a_1) (Or (Eq (in (skS.0 2 a a_1 a_2) a) False) (Eq (in (skS.0 2 a a_1 a_2) a_1) False)) % 4.07/4.26 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq a a_1) (Or (Eq (in (skS.0 2 a a_1 a_2) a) True) (Eq (in (skS.0 2 a a_1 a_2) a_1) True)) % 4.07/4.26 Clause #23 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a)) True % 4.07/4.26 Clause #24 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 4.07/4.26 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (in a (skS.0 1 a_1 a_2) → in a (skS.0 0 a_1)) True % 4.07/4.26 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 1 a_1 a_2)) False) (Eq (in a (skS.0 0 a_1)) True) % 4.07/4.27 Clause #27 (by clausification #[24]): ∀ (a a_1 : Iota), Ne (skS.0 0 a) (skS.0 1 a a_1) % 4.07/4.27 Clause #40 (by superposition #[22, 12]): ∀ (a a_1 a_2 a_3 : Iota), % 4.07/4.27 Or (Eq a (skS.0 0 a_1)) % 4.07/4.27 (Or (Eq (in (skS.0 2 a (skS.0 0 a_1) a_2) a) True) % 4.07/4.27 (Or (Eq True False) (Eq (in (skS.0 2 a (skS.0 0 a_1) a_2) (skS.0 1 a_1 a_3)) True))) % 4.07/4.27 Clause #49 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.07/4.27 Or (Eq a (skS.0 0 a_1)) % 4.07/4.27 (Or (Eq (in (skS.0 2 a (skS.0 0 a_1) a_2) a) True) (Eq (in (skS.0 2 a (skS.0 0 a_1) a_2) (skS.0 1 a_1 a_3)) True)) % 4.07/4.27 Clause #62 (by equality factoring #[49]): ∀ (a a_1 a_2 : Iota), % 4.07/4.27 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 4.07/4.27 (Or (Ne True True) (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True)) % 4.07/4.27 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 4.07/4.27 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 4.07/4.27 (Or (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) (Or (Eq True False) (Eq True False))) % 4.07/4.27 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 4.07/4.27 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 4.07/4.27 (Or (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) (Eq True False)) % 4.07/4.27 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 4.07/4.27 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) % 4.07/4.27 Clause #67 (by forward contextual literal cutting #[66, 27]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True % 4.07/4.27 Clause #68 (by superposition #[67, 26]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True) % 4.07/4.27 Clause #69 (by superposition #[67, 21]): ∀ (a a_1 a_2 : Iota), % 4.07/4.27 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 4.07/4.27 (Or (Eq True False) (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False)) % 4.07/4.27 Clause #82 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True % 4.07/4.27 Clause #103 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 4.07/4.27 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False) % 4.07/4.27 Clause #104 (by forward contextual literal cutting #[103, 27]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False % 4.07/4.27 Clause #105 (by superposition #[104, 82]): Eq False True % 4.07/4.27 Clause #113 (by clausification #[105]): False % 4.07/4.27 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------