%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU894^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:02:36 PM UTC 2025 % Result : Theorem 3.58s 3.74s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU894^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n008.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 06:11:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.58/3.74 SZS status Theorem for theBenchmark.p % 3.58/3.74 SZS output start Proof for theBenchmark.p % 3.58/3.74 Clause #0 (by assumption #[]): Eq % 3.58/3.74 (Not % 3.58/3.74 (∀ (F : Iota → Iota), % 3.58/3.74 Exists fun G => % 3.58/3.74 And (∀ (P : (Iota → Iota) → Prop), And (P F) (∀ (H : Iota → Iota), P H → P fun T => F (H T)) → P G) % 3.58/3.74 (Exists fun X => And (Eq (G X) X) (∀ (Y : Iota), Eq (G Y) Y → Eq X Y)) → % 3.58/3.74 Exists fun Y => Eq (F Y) Y)) % 3.58/3.74 True % 3.58/3.74 Clause #1 (by clausification #[0]): Eq % 3.58/3.74 (∀ (F : Iota → Iota), % 3.58/3.74 Exists fun G => % 3.58/3.74 And (∀ (P : (Iota → Iota) → Prop), And (P F) (∀ (H : Iota → Iota), P H → P fun T => F (H T)) → P G) % 3.58/3.74 (Exists fun X => And (Eq (G X) X) (∀ (Y : Iota), Eq (G Y) Y → Eq X Y)) → % 3.58/3.74 Exists fun Y => Eq (F Y) Y) % 3.58/3.74 False % 3.58/3.74 Clause #2 (by clausification #[1]): ∀ (a : Iota → Iota), % 3.58/3.74 Eq % 3.58/3.74 (Not % 3.58/3.74 (Exists fun G => % 3.58/3.74 And % 3.58/3.74 (∀ (P : (Iota → Iota) → Prop), % 3.58/3.74 And (P (skS.0 0 a)) (∀ (H : Iota → Iota), P H → P fun T => skS.0 0 a (H T)) → P G) % 3.58/3.74 (Exists fun X => And (Eq (G X) X) (∀ (Y : Iota), Eq (G Y) Y → Eq X Y)) → % 3.58/3.74 Exists fun Y => Eq (skS.0 0 a Y) Y)) % 3.58/3.74 True % 3.58/3.74 Clause #3 (by clausification #[2]): ∀ (a : Iota → Iota), % 3.58/3.74 Eq % 3.58/3.74 (Exists fun G => % 3.58/3.74 And % 3.58/3.74 (∀ (P : (Iota → Iota) → Prop), % 3.58/3.74 And (P (skS.0 0 a)) (∀ (H : Iota → Iota), P H → P fun T => skS.0 0 a (H T)) → P G) % 3.58/3.74 (Exists fun X => And (Eq (G X) X) (∀ (Y : Iota), Eq (G Y) Y → Eq X Y)) → % 3.58/3.74 Exists fun Y => Eq (skS.0 0 a Y) Y) % 3.58/3.74 False % 3.58/3.74 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota → Iota), % 3.58/3.74 Eq % 3.58/3.74 (And % 3.58/3.74 (∀ (P : (Iota → Iota) → Prop), % 3.58/3.74 And (P (skS.0 0 a)) (∀ (H : Iota → Iota), P H → P fun T => skS.0 0 a (H T)) → P a_1) % 3.58/3.74 (Exists fun X => And (Eq (a_1 X) X) (∀ (Y : Iota), Eq (a_1 Y) Y → Eq X Y)) → % 3.58/3.74 Exists fun Y => Eq (skS.0 0 a Y) Y) % 3.58/3.74 False % 3.58/3.74 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota → Iota), % 3.58/3.74 Eq % 3.58/3.74 (And % 3.58/3.74 (∀ (P : (Iota → Iota) → Prop), % 3.58/3.74 And (P (skS.0 0 a)) (∀ (H : Iota → Iota), P H → P fun T => skS.0 0 a (H T)) → P a_1) % 3.58/3.74 (Exists fun X => And (Eq (a_1 X) X) (∀ (Y : Iota), Eq (a_1 Y) Y → Eq X Y))) % 3.58/3.74 True % 3.58/3.74 Clause #6 (by clausification #[4]): ∀ (a : Iota → Iota), Eq (Exists fun Y => Eq (skS.0 0 a Y) Y) False % 3.58/3.74 Clause #7 (by clausification #[5]): ∀ (a : Iota → Iota), Eq (Exists fun X => And (Eq (a X) X) (∀ (Y : Iota), Eq (a Y) Y → Eq X Y)) True % 3.58/3.74 Clause #9 (by clausification #[7]): ∀ (a : Iota → Iota) (a_1 : Iota), % 3.58/3.74 Eq (And (Eq (a (skS.0 1 a a_1)) (skS.0 1 a a_1)) (∀ (Y : Iota), Eq (a Y) Y → Eq (skS.0 1 a a_1) Y)) True % 3.58/3.74 Clause #10 (by clausification #[9]): ∀ (a : Iota → Iota) (a_1 : Iota), Eq (∀ (Y : Iota), Eq (a Y) Y → Eq (skS.0 1 a a_1) Y) True % 3.58/3.74 Clause #12 (by clausification #[10]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Eq (Eq (a a_1) a_1 → Eq (skS.0 1 a a_2) a_1) True % 3.58/3.74 Clause #13 (by clausification #[12]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Or (Eq (Eq (a a_1) a_1) False) (Eq (Eq (skS.0 1 a a_2) a_1) True) % 3.58/3.74 Clause #14 (by clausification #[13]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Or (Eq (Eq (skS.0 1 a a_1) a_2) True) (Ne (a a_2) a_2) % 3.58/3.74 Clause #15 (by clausification #[14]): ∀ (a : Iota → Iota) (a_1 a_2 : Iota), Or (Ne (a a_1) a_1) (Eq (skS.0 1 a a_2) a_1) % 3.58/3.74 Clause #16 (by equality resolution #[15]): ∀ (a a_1 : Iota), Eq (skS.0 1 (fun x => x) a) a_1 % 3.58/3.74 Clause #46 (by superposition #[16, 16]): ∀ (a a_1 : Iota), Eq a a_1 % 3.58/3.74 Clause #59 (by clausification #[6]): ∀ (a : Iota → Iota) (a_1 : Iota), Eq (Eq (skS.0 0 a a_1) a_1) False % 3.58/3.74 Clause #60 (by clausification #[59]): ∀ (a : Iota → Iota) (a_1 : Iota), Ne (skS.0 0 a a_1) a_1 % 3.58/3.74 Clause #61 (by forward contextual literal cutting #[60, 46]): False % 3.58/3.74 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------