%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PHI011+1 : TPTP v9.2.0. Released v7.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:57:56 PM UTC 2025 % Result : Theorem 4.20s 4.38s % Output : Proof 4.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : PHI011+1 : TPTP v9.2.0. Released v7.2.0. % 0.07/0.14 % Command : duper %s % 0.15/0.35 % Computer : n024.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 09:06:23 EDT 2025 % 0.15/0.35 % CPUTime : % 4.20/4.38 SZS status Theorem for theBenchmark.p % 4.20/4.38 SZS output start Proof for theBenchmark.p % 4.20/4.38 Clause #3 (by assumption #[]): Eq % 4.20/4.38 (∀ (X F Y : Iota), % 4.20/4.38 And (And (object X) (property F)) (object Y) → And (is_the X F) (Eq X Y) → exemplifies_property F Y) % 4.20/4.38 True % 4.20/4.38 Clause #4 (by assumption #[]): Eq % 4.20/4.38 (Not % 4.20/4.38 (∀ (F : Iota), % 4.20/4.38 property F → % 4.20/4.38 (Exists fun Y => And (object Y) (is_the Y F)) → ∀ (Z : Iota), object Z → is_the Z F → exemplifies_property F Z)) % 4.20/4.38 True % 4.20/4.38 Clause #8 (by clausification #[3]): ∀ (a : Iota), % 4.20/4.38 Eq % 4.20/4.38 (∀ (F Y : Iota), % 4.20/4.38 And (And (object a) (property F)) (object Y) → And (is_the a F) (Eq a Y) → exemplifies_property F Y) % 4.20/4.38 True % 4.20/4.38 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (∀ (Y : Iota), % 4.20/4.38 And (And (object a) (property a_1)) (object Y) → And (is_the a a_1) (Eq a Y) → exemplifies_property a_1 Y) % 4.20/4.38 True % 4.20/4.38 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq (And (And (object a) (property a_1)) (object a_2) → And (is_the a a_1) (Eq a a_2) → exemplifies_property a_1 a_2) % 4.20/4.38 True % 4.20/4.38 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Or (Eq (And (And (object a) (property a_1)) (object a_2)) False) % 4.20/4.38 (Eq (And (is_the a a_1) (Eq a a_2) → exemplifies_property a_1 a_2) True) % 4.20/4.38 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Or (Eq (And (is_the a a_1) (Eq a a_2) → exemplifies_property a_1 a_2) True) % 4.20/4.38 (Or (Eq (And (object a) (property a_1)) False) (Eq (object a_2) False)) % 4.20/4.38 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Or (Eq (And (object a) (property a_1)) False) % 4.20/4.38 (Or (Eq (object a_2) False) % 4.20/4.38 (Or (Eq (And (is_the a a_1) (Eq a a_2)) False) (Eq (exemplifies_property a_1 a_2) True))) % 4.20/4.38 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Or (Eq (object a) False) % 4.20/4.38 (Or (Eq (And (is_the a_1 a_2) (Eq a_1 a)) False) % 4.20/4.38 (Or (Eq (exemplifies_property a_2 a) True) (Or (Eq (object a_1) False) (Eq (property a_2) False)))) % 4.20/4.38 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Or (Eq (object a) False) % 4.20/4.38 (Or (Eq (exemplifies_property a_1 a) True) % 4.20/4.38 (Or (Eq (object a_2) False) % 4.20/4.38 (Or (Eq (property a_1) False) (Or (Eq (is_the a_2 a_1) False) (Eq (Eq a_2 a) False))))) % 4.20/4.38 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Or (Eq (object a) False) % 4.20/4.38 (Or (Eq (exemplifies_property a_1 a) True) % 4.20/4.38 (Or (Eq (object a_2) False) (Or (Eq (property a_1) False) (Or (Eq (is_the a_2 a_1) False) (Ne a_2 a))))) % 4.20/4.38 Clause #17 (by destructive equality resolution #[16]): ∀ (a a_1 : Iota), % 4.20/4.38 Or (Eq (object a) False) % 4.20/4.38 (Or (Eq (exemplifies_property a_1 a) True) % 4.20/4.38 (Or (Eq (object a) False) (Or (Eq (property a_1) False) (Eq (is_the a a_1) False)))) % 4.20/4.38 Clause #18 (by eliminate duplicate literals #[17]): ∀ (a a_1 : Iota), % 4.20/4.38 Or (Eq (object a) False) % 4.20/4.38 (Or (Eq (exemplifies_property a_1 a) True) (Or (Eq (property a_1) False) (Eq (is_the a a_1) False))) % 4.20/4.38 Clause #29 (by clausification #[4]): Eq % 4.20/4.38 (∀ (F : Iota), % 4.20/4.38 property F → % 4.20/4.38 (Exists fun Y => And (object Y) (is_the Y F)) → ∀ (Z : Iota), object Z → is_the Z F → exemplifies_property F Z) % 4.20/4.38 False % 4.20/4.38 Clause #30 (by clausification #[29]): ∀ (a : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (property (skS.0 0 a) → % 4.20/4.38 (Exists fun Y => And (object Y) (is_the Y (skS.0 0 a))) → % 4.20/4.38 ∀ (Z : Iota), object Z → is_the Z (skS.0 0 a) → exemplifies_property (skS.0 0 a) Z)) % 4.20/4.38 True % 4.20/4.38 Clause #31 (by clausification #[30]): ∀ (a : Iota), % 4.20/4.38 Eq % 4.20/4.38 (property (skS.0 0 a) → % 4.20/4.38 (Exists fun Y => And (object Y) (is_the Y (skS.0 0 a))) → % 4.20/4.38 ∀ (Z : Iota), object Z → is_the Z (skS.0 0 a) → exemplifies_property (skS.0 0 a) Z) % 4.20/4.38 False % 4.20/4.38 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (property (skS.0 0 a)) True % 4.20/4.38 Clause #33 (by clausification #[31]): ∀ (a : Iota), % 4.20/4.38 Eq % 4.20/4.38 ((Exists fun Y => And (object Y) (is_the Y (skS.0 0 a))) → % 4.20/4.38 ∀ (Z : Iota), object Z → is_the Z (skS.0 0 a) → exemplifies_property (skS.0 0 a) Z) % 4.20/4.38 False % 4.20/4.38 Clause #35 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Z : Iota), object Z → is_the Z (skS.0 0 a) → exemplifies_property (skS.0 0 a) Z) False % 4.20/4.40 Clause #43 (by clausification #[35]): ∀ (a a_1 : Iota), % 4.20/4.40 Eq % 4.20/4.40 (Not % 4.20/4.40 (object (skS.0 2 a a_1) → is_the (skS.0 2 a a_1) (skS.0 0 a) → exemplifies_property (skS.0 0 a) (skS.0 2 a a_1))) % 4.20/4.40 True % 4.20/4.40 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), % 4.20/4.40 Eq (object (skS.0 2 a a_1) → is_the (skS.0 2 a a_1) (skS.0 0 a) → exemplifies_property (skS.0 0 a) (skS.0 2 a a_1)) % 4.20/4.40 False % 4.20/4.40 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (object (skS.0 2 a a_1)) True % 4.20/4.40 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (is_the (skS.0 2 a a_1) (skS.0 0 a) → exemplifies_property (skS.0 0 a) (skS.0 2 a a_1)) False % 4.20/4.40 Clause #48 (by superposition #[45, 18]): ∀ (a a_1 a_2 : Iota), % 4.20/4.40 Or (Eq True False) % 4.20/4.40 (Or (Eq (exemplifies_property a (skS.0 2 a_1 a_2)) True) % 4.20/4.40 (Or (Eq (property a) False) (Eq (is_the (skS.0 2 a_1 a_2) a) False))) % 4.20/4.40 Clause #51 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (is_the (skS.0 2 a a_1) (skS.0 0 a)) True % 4.20/4.40 Clause #52 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (exemplifies_property (skS.0 0 a) (skS.0 2 a a_1)) False % 4.20/4.40 Clause #56 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), % 4.20/4.40 Or (Eq (exemplifies_property a (skS.0 2 a_1 a_2)) True) % 4.20/4.40 (Or (Eq (property a) False) (Eq (is_the (skS.0 2 a_1 a_2) a) False)) % 4.20/4.40 Clause #57 (by superposition #[56, 32]): ∀ (a a_1 a_2 : Iota), % 4.20/4.40 Or (Eq (exemplifies_property (skS.0 0 a) (skS.0 2 a_1 a_2)) True) % 4.20/4.40 (Or (Eq (is_the (skS.0 2 a_1 a_2) (skS.0 0 a)) False) (Eq False True)) % 4.20/4.40 Clause #61 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 4.20/4.40 Or (Eq (exemplifies_property (skS.0 0 a) (skS.0 2 a_1 a_2)) True) (Eq (is_the (skS.0 2 a_1 a_2) (skS.0 0 a)) False) % 4.20/4.40 Clause #62 (by superposition #[61, 51]): ∀ (a a_1 : Iota), Or (Eq (exemplifies_property (skS.0 0 a) (skS.0 2 a a_1)) True) (Eq False True) % 4.20/4.40 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Eq (exemplifies_property (skS.0 0 a) (skS.0 2 a a_1)) True % 4.20/4.40 Clause #64 (by superposition #[63, 52]): Eq True False % 4.20/4.40 Clause #65 (by clausification #[64]): False % 4.20/4.40 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------