%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PHI009+1 : TPTP v9.2.0. Released v7.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 7.28s 7.53s % Output : Proof 7.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : PHI009+1 : TPTP v9.2.0. Released v7.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.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 09:08:53 EDT 2025 % 0.13/0.34 % CPUTime : % 7.28/7.53 SZS status Theorem for theBenchmark.p % 7.28/7.53 SZS output start Proof for theBenchmark.p % 7.28/7.53 Clause #0 (by assumption #[]): Eq % 7.28/7.53 (∀ (F G X : Iota), % 7.28/7.53 And (And (property F) (property G)) (object X) → % 7.28/7.53 Iff (And (is_the X F) (exemplifies_property G X)) % 7.28/7.53 (Exists fun Y => % 7.28/7.53 And % 7.28/7.53 (And (And (object Y) (exemplifies_property F Y)) % 7.28/7.53 (∀ (Z : Iota), object Z → exemplifies_property F Z → Eq Z Y)) % 7.28/7.53 (exemplifies_property G Y))) % 7.28/7.53 True % 7.28/7.53 Clause #1 (by assumption #[]): Eq % 7.28/7.53 (Not % 7.28/7.53 (∀ (F : Iota), % 7.28/7.53 property F → % 7.28/7.53 (Exists fun Y => % 7.28/7.53 And (And (object Y) (exemplifies_property F Y)) % 7.28/7.53 (∀ (Z : Iota), object Z → exemplifies_property F Z → Eq Z Y)) → % 7.28/7.53 Exists fun U => And (object U) (is_the U F))) % 7.28/7.53 True % 7.28/7.53 Clause #2 (by clausification #[1]): Eq % 7.28/7.53 (∀ (F : Iota), % 7.28/7.53 property F → % 7.28/7.53 (Exists fun Y => % 7.28/7.53 And (And (object Y) (exemplifies_property F Y)) % 7.28/7.53 (∀ (Z : Iota), object Z → exemplifies_property F Z → Eq Z Y)) → % 7.28/7.53 Exists fun U => And (object U) (is_the U F)) % 7.28/7.53 False % 7.28/7.53 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 7.28/7.53 Eq % 7.28/7.53 (Not % 7.28/7.53 (property (skS.0 0 a) → % 7.28/7.53 (Exists fun Y => % 7.28/7.53 And (And (object Y) (exemplifies_property (skS.0 0 a) Y)) % 7.28/7.53 (∀ (Z : Iota), object Z → exemplifies_property (skS.0 0 a) Z → Eq Z Y)) → % 7.28/7.53 Exists fun U => And (object U) (is_the U (skS.0 0 a)))) % 7.28/7.53 True % 7.28/7.53 Clause #4 (by clausification #[3]): ∀ (a : Iota), % 7.28/7.53 Eq % 7.28/7.53 (property (skS.0 0 a) → % 7.28/7.53 (Exists fun Y => % 7.28/7.53 And (And (object Y) (exemplifies_property (skS.0 0 a) Y)) % 7.28/7.53 (∀ (Z : Iota), object Z → exemplifies_property (skS.0 0 a) Z → Eq Z Y)) → % 7.28/7.53 Exists fun U => And (object U) (is_the U (skS.0 0 a))) % 7.28/7.53 False % 7.28/7.53 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (property (skS.0 0 a)) True % 7.28/7.53 Clause #6 (by clausification #[4]): ∀ (a : Iota), % 7.28/7.53 Eq % 7.28/7.53 ((Exists fun Y => % 7.28/7.53 And (And (object Y) (exemplifies_property (skS.0 0 a) Y)) % 7.28/7.53 (∀ (Z : Iota), object Z → exemplifies_property (skS.0 0 a) Z → Eq Z Y)) → % 7.28/7.53 Exists fun U => And (object U) (is_the U (skS.0 0 a))) % 7.28/7.53 False % 7.28/7.53 Clause #7 (by clausification #[6]): ∀ (a : Iota), % 7.28/7.53 Eq % 7.28/7.53 (Exists fun Y => % 7.28/7.53 And (And (object Y) (exemplifies_property (skS.0 0 a) Y)) % 7.28/7.53 (∀ (Z : Iota), object Z → exemplifies_property (skS.0 0 a) Z → Eq Z Y)) % 7.28/7.53 True % 7.28/7.53 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (Exists fun U => And (object U) (is_the U (skS.0 0 a))) False % 7.28/7.53 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota), % 7.28/7.53 Eq % 7.28/7.53 (And (And (object (skS.0 1 a a_1)) (exemplifies_property (skS.0 0 a) (skS.0 1 a a_1))) % 7.28/7.53 (∀ (Z : Iota), object Z → exemplifies_property (skS.0 0 a) Z → Eq Z (skS.0 1 a a_1))) % 7.28/7.53 True % 7.28/7.53 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), object Z → exemplifies_property (skS.0 0 a) Z → Eq Z (skS.0 1 a a_1)) True % 7.28/7.53 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (And (object (skS.0 1 a a_1)) (exemplifies_property (skS.0 0 a) (skS.0 1 a a_1))) True % 7.28/7.53 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (object a → exemplifies_property (skS.0 0 a_1) a → Eq a (skS.0 1 a_1 a_2)) True % 7.28/7.53 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (object a) False) (Eq (exemplifies_property (skS.0 0 a_1) a → Eq a (skS.0 1 a_1 a_2)) True) % 7.28/7.53 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 7.28/7.53 Or (Eq (object a) False) (Or (Eq (exemplifies_property (skS.0 0 a_1) a) False) (Eq (Eq a (skS.0 1 a_1 a_2)) True)) % 7.28/7.53 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 7.28/7.53 Or (Eq (object a) False) (Or (Eq (exemplifies_property (skS.0 0 a_1) a) False) (Eq a (skS.0 1 a_1 a_2))) % 7.28/7.53 Clause #16 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (And (object a) (is_the a (skS.0 0 a_1))) False % 7.28/7.53 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (object a) False) (Eq (is_the a (skS.0 0 a_1)) False) % 7.28/7.53 Clause #18 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (exemplifies_property (skS.0 0 a) (skS.0 1 a a_1)) True % 7.38/7.57 Clause #19 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (object (skS.0 1 a a_1)) True % 7.38/7.57 Clause #21 (by superposition #[19, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) False) % 7.38/7.57 Clause #22 (by clausification #[0]): ∀ (a : Iota), % 7.38/7.57 Eq % 7.38/7.57 (∀ (G X : Iota), % 7.38/7.57 And (And (property a) (property G)) (object X) → % 7.38/7.57 Iff (And (is_the X a) (exemplifies_property G X)) % 7.38/7.57 (Exists fun Y => % 7.38/7.57 And % 7.38/7.57 (And (And (object Y) (exemplifies_property a Y)) % 7.38/7.57 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 7.38/7.57 (exemplifies_property G Y))) % 7.38/7.57 True % 7.38/7.57 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 7.38/7.57 Eq % 7.38/7.57 (∀ (X : Iota), % 7.38/7.57 And (And (property a) (property a_1)) (object X) → % 7.38/7.57 Iff (And (is_the X a) (exemplifies_property a_1 X)) % 7.38/7.57 (Exists fun Y => % 7.38/7.57 And % 7.38/7.57 (And (And (object Y) (exemplifies_property a Y)) % 7.38/7.57 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 7.38/7.57 (exemplifies_property a_1 Y))) % 7.38/7.57 True % 7.38/7.57 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 7.38/7.57 Eq % 7.38/7.57 (And (And (property a) (property a_1)) (object a_2) → % 7.38/7.57 Iff (And (is_the a_2 a) (exemplifies_property a_1 a_2)) % 7.38/7.57 (Exists fun Y => % 7.38/7.57 And % 7.38/7.57 (And (And (object Y) (exemplifies_property a Y)) % 7.38/7.57 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 7.38/7.57 (exemplifies_property a_1 Y))) % 7.38/7.57 True % 7.38/7.57 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 7.38/7.57 Or (Eq (And (And (property a) (property a_1)) (object a_2)) False) % 7.38/7.57 (Eq % 7.38/7.57 (Iff (And (is_the a_2 a) (exemplifies_property a_1 a_2)) % 7.38/7.57 (Exists fun Y => % 7.38/7.57 And % 7.38/7.57 (And (And (object Y) (exemplifies_property a Y)) % 7.38/7.57 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 7.38/7.57 (exemplifies_property a_1 Y))) % 7.38/7.57 True) % 7.38/7.57 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 7.38/7.57 Or % 7.38/7.57 (Eq % 7.38/7.57 (Iff (And (is_the a a_1) (exemplifies_property a_2 a)) % 7.38/7.57 (Exists fun Y => % 7.38/7.57 And % 7.38/7.57 (And (And (object Y) (exemplifies_property a_1 Y)) % 7.38/7.57 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z Y)) % 7.38/7.57 (exemplifies_property a_2 Y))) % 7.38/7.57 True) % 7.38/7.57 (Or (Eq (And (property a_1) (property a_2)) False) (Eq (object a) False)) % 7.38/7.57 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 7.38/7.57 Or (Eq (And (property a) (property a_1)) False) % 7.38/7.57 (Or (Eq (object a_2) False) % 7.38/7.57 (Or (Eq (And (is_the a_2 a) (exemplifies_property a_1 a_2)) True) % 7.38/7.57 (Eq % 7.38/7.57 (Exists fun Y => % 7.38/7.57 And % 7.38/7.57 (And (And (object Y) (exemplifies_property a Y)) % 7.38/7.57 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 7.38/7.57 (exemplifies_property a_1 Y)) % 7.38/7.57 False))) % 7.38/7.57 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 7.38/7.57 Or (Eq (object a) False) % 7.38/7.57 (Or (Eq (And (is_the a a_1) (exemplifies_property a_2 a)) True) % 7.38/7.57 (Or % 7.38/7.57 (Eq % 7.38/7.57 (Exists fun Y => % 7.38/7.57 And % 7.38/7.57 (And (And (object Y) (exemplifies_property a_1 Y)) % 7.38/7.57 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z Y)) % 7.38/7.57 (exemplifies_property a_2 Y)) % 7.38/7.57 False) % 7.38/7.57 (Or (Eq (property a_1) False) (Eq (property a_2) False)))) % 7.38/7.57 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 7.38/7.57 Or (Eq (object a) False) % 7.38/7.57 (Or % 7.38/7.57 (Eq % 7.38/7.57 (Exists fun Y => % 7.38/7.57 And % 7.38/7.57 (And (And (object Y) (exemplifies_property a_1 Y)) % 7.38/7.57 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z Y)) % 7.38/7.57 (exemplifies_property a_2 Y)) % 7.38/7.57 False) % 7.38/7.57 (Or (Eq (property a_1) False) (Or (Eq (property a_2) False) (Eq (is_the a a_1) True)))) % 7.38/7.57 Clause #41 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) False % 7.38/7.57 Clause #45 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 7.38/7.57 Or (Eq (object a) False) % 7.38/7.57 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (property a_2) False) % 7.44/7.62 (Or (Eq (is_the a a_1) True) % 7.44/7.62 (Eq % 7.44/7.62 (And % 7.44/7.62 (And (And (object a_3) (exemplifies_property a_1 a_3)) % 7.44/7.62 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z a_3)) % 7.44/7.62 (exemplifies_property a_2 a_3)) % 7.44/7.62 False)))) % 7.44/7.62 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 7.44/7.62 Or (Eq (object a) False) % 7.44/7.62 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (property a_2) False) % 7.44/7.62 (Or (Eq (is_the a a_1) True) % 7.44/7.62 (Or % 7.44/7.62 (Eq % 7.44/7.62 (And (And (object a_3) (exemplifies_property a_1 a_3)) % 7.44/7.62 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z a_3)) % 7.44/7.62 False) % 7.44/7.62 (Eq (exemplifies_property a_2 a_3) False))))) % 7.44/7.62 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), % 7.44/7.62 Or (Eq (object a) False) % 7.44/7.62 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (property a_2) False) % 7.44/7.62 (Or (Eq (is_the a a_1) True) % 7.44/7.62 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.44/7.62 (Or (Eq (And (object a_3) (exemplifies_property a_1 a_3)) False) % 7.44/7.62 (Eq (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z a_3) False)))))) % 7.44/7.62 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 7.44/7.62 Or (Eq (object a) False) % 7.44/7.62 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (property a_2) False) % 7.44/7.62 (Or (Eq (is_the a a_1) True) % 7.44/7.62 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.44/7.62 (Or (Eq (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z a_3) False) % 7.44/7.62 (Or (Eq (object a_3) False) (Eq (exemplifies_property a_1 a_3) False))))))) % 7.44/7.62 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.44/7.62 Or (Eq (object a) False) % 7.44/7.62 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (property a_2) False) % 7.44/7.62 (Or (Eq (is_the a a_1) True) % 7.44/7.62 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.44/7.62 (Or (Eq (object a_3) False) % 7.44/7.62 (Or (Eq (exemplifies_property a_1 a_3) False) % 7.44/7.62 (Eq % 7.44/7.62 (Not % 7.44/7.62 (object (skS.0 3 a_1 a_3 a_4) → % 7.44/7.62 exemplifies_property a_1 (skS.0 3 a_1 a_3 a_4) → Eq (skS.0 3 a_1 a_3 a_4) a_3)) % 7.44/7.62 True))))))) % 7.44/7.62 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.44/7.62 Or (Eq (object a) False) % 7.44/7.62 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (property a_2) False) % 7.44/7.62 (Or (Eq (is_the a a_1) True) % 7.44/7.62 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.44/7.62 (Or (Eq (object a_3) False) % 7.44/7.62 (Or (Eq (exemplifies_property a_1 a_3) False) % 7.44/7.62 (Eq % 7.44/7.62 (object (skS.0 3 a_1 a_3 a_4) → % 7.44/7.62 exemplifies_property a_1 (skS.0 3 a_1 a_3 a_4) → Eq (skS.0 3 a_1 a_3 a_4) a_3) % 7.44/7.62 False))))))) % 7.44/7.62 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.44/7.62 Or (Eq (object a) False) % 7.44/7.62 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (property a_2) False) % 7.44/7.62 (Or (Eq (is_the a a_1) True) % 7.44/7.62 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.44/7.62 (Or (Eq (object a_3) False) % 7.44/7.62 (Or (Eq (exemplifies_property a_1 a_3) False) (Eq (object (skS.0 3 a_1 a_3 a_4)) True))))))) % 7.44/7.62 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.44/7.62 Or (Eq (object a) False) % 7.44/7.62 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (property a_2) False) % 7.44/7.62 (Or (Eq (is_the a a_1) True) % 7.44/7.62 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.44/7.62 (Or (Eq (object a_3) False) % 7.44/7.62 (Or (Eq (exemplifies_property a_1 a_3) False) % 7.44/7.62 (Eq (exemplifies_property a_1 (skS.0 3 a_1 a_3 a_4) → Eq (skS.0 3 a_1 a_3 a_4) a_3) False))))))) % 7.44/7.62 Clause #53 (by superposition #[51, 19]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.44/7.62 Or (Eq (property a) False) % 7.44/7.62 (Or (Eq (property a_1) False) % 7.44/7.62 (Or (Eq (is_the (skS.0 1 a_2 a_3) a) True) % 7.44/7.62 (Or (Eq (exemplifies_property a_1 a_4) False) % 7.44/7.62 (Or (Eq (object a_4) False) % 7.44/7.62 (Or (Eq (exemplifies_property a a_4) False) (Or (Eq (object (skS.0 3 a a_4 a_5)) True) (Eq False True))))))) % 7.50/7.67 Clause #65 (by clausification #[52]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.50/7.67 Or (Eq (object a) False) % 7.50/7.67 (Or (Eq (property a_1) False) % 7.50/7.67 (Or (Eq (property a_2) False) % 7.50/7.67 (Or (Eq (is_the a a_1) True) % 7.50/7.67 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.50/7.67 (Or (Eq (object a_3) False) % 7.50/7.67 (Or (Eq (exemplifies_property a_1 a_3) False) % 7.50/7.67 (Eq (exemplifies_property a_1 (skS.0 3 a_1 a_3 a_4)) True))))))) % 7.50/7.67 Clause #66 (by clausification #[52]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.50/7.67 Or (Eq (object a) False) % 7.50/7.67 (Or (Eq (property a_1) False) % 7.50/7.67 (Or (Eq (property a_2) False) % 7.50/7.67 (Or (Eq (is_the a a_1) True) % 7.50/7.67 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.50/7.67 (Or (Eq (object a_3) False) % 7.50/7.67 (Or (Eq (exemplifies_property a_1 a_3) False) (Eq (Eq (skS.0 3 a_1 a_3 a_4) a_3) False))))))) % 7.50/7.67 Clause #67 (by superposition #[65, 19]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.50/7.67 Or (Eq (property a) False) % 7.50/7.67 (Or (Eq (property a_1) False) % 7.50/7.67 (Or (Eq (is_the (skS.0 1 a_2 a_3) a) True) % 7.50/7.67 (Or (Eq (exemplifies_property a_1 a_4) False) % 7.50/7.67 (Or (Eq (object a_4) False) % 7.50/7.67 (Or (Eq (exemplifies_property a a_4) False) % 7.50/7.67 (Or (Eq (exemplifies_property a (skS.0 3 a a_4 a_5)) True) (Eq False True))))))) % 7.50/7.67 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.50/7.67 Or (Eq (object a) False) % 7.50/7.67 (Or (Eq (property a_1) False) % 7.50/7.67 (Or (Eq (property a_2) False) % 7.50/7.67 (Or (Eq (is_the a a_1) True) % 7.50/7.67 (Or (Eq (exemplifies_property a_2 a_3) False) % 7.50/7.67 (Or (Eq (object a_3) False) % 7.50/7.67 (Or (Eq (exemplifies_property a_1 a_3) False) (Ne (skS.0 3 a_1 a_3 a_4) a_3))))))) % 7.50/7.67 Clause #69 (by superposition #[68, 19]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.50/7.67 Or (Eq (property a) False) % 7.50/7.67 (Or (Eq (property a_1) False) % 7.50/7.67 (Or (Eq (is_the (skS.0 1 a_2 a_3) a) True) % 7.50/7.67 (Or (Eq (exemplifies_property a_1 a_4) False) % 7.50/7.67 (Or (Eq (object a_4) False) % 7.50/7.67 (Or (Eq (exemplifies_property a a_4) False) (Or (Ne (skS.0 3 a a_4 a_5) a_4) (Eq False True))))))) % 7.50/7.67 Clause #72 (by clausification #[69]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.50/7.67 Or (Eq (property a) False) % 7.50/7.67 (Or (Eq (property a_1) False) % 7.50/7.67 (Or (Eq (is_the (skS.0 1 a_2 a_3) a) True) % 7.50/7.67 (Or (Eq (exemplifies_property a_1 a_4) False) % 7.50/7.67 (Or (Eq (object a_4) False) (Or (Eq (exemplifies_property a a_4) False) (Ne (skS.0 3 a a_4 a_5) a_4)))))) % 7.50/7.67 Clause #73 (by superposition #[72, 5]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.50/7.67 Or (Eq (property a) False) % 7.50/7.67 (Or (Eq (is_the (skS.0 1 a_1 a_2) (skS.0 0 a_3)) True) % 7.50/7.67 (Or (Eq (exemplifies_property a a_4) False) % 7.50/7.67 (Or (Eq (object a_4) False) % 7.50/7.67 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.50/7.67 (Or (Ne (skS.0 3 (skS.0 0 a_3) a_4 a_5) a_4) (Eq False True)))))) % 7.50/7.67 Clause #76 (by clausification #[53]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.50/7.67 Or (Eq (property a) False) % 7.50/7.67 (Or (Eq (property a_1) False) % 7.50/7.67 (Or (Eq (is_the (skS.0 1 a_2 a_3) a) True) % 7.50/7.67 (Or (Eq (exemplifies_property a_1 a_4) False) % 7.50/7.67 (Or (Eq (object a_4) False) % 7.50/7.67 (Or (Eq (exemplifies_property a a_4) False) (Eq (object (skS.0 3 a a_4 a_5)) True)))))) % 7.50/7.67 Clause #77 (by superposition #[76, 5]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.50/7.67 Or (Eq (property a) False) % 7.50/7.67 (Or (Eq (is_the (skS.0 1 a_1 a_2) (skS.0 0 a_3)) True) % 7.50/7.67 (Or (Eq (exemplifies_property a a_4) False) % 7.50/7.67 (Or (Eq (object a_4) False) % 7.50/7.67 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.50/7.67 (Or (Eq (object (skS.0 3 (skS.0 0 a_3) a_4 a_5)) True) (Eq False True)))))) % 7.50/7.67 Clause #80 (by clausification #[67]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.50/7.67 Or (Eq (property a) False) % 7.50/7.67 (Or (Eq (property a_1) False) % 7.50/7.67 (Or (Eq (is_the (skS.0 1 a_2 a_3) a) True) % 7.50/7.67 (Or (Eq (exemplifies_property a_1 a_4) False) % 7.50/7.67 (Or (Eq (object a_4) False) % 7.50/7.67 (Or (Eq (exemplifies_property a a_4) False) (Eq (exemplifies_property a (skS.0 3 a a_4 a_5)) True)))))) % 7.50/7.67 Clause #81 (by superposition #[80, 5]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (property a) False) % 7.56/7.73 (Or (Eq (is_the (skS.0 1 a_1 a_2) (skS.0 0 a_3)) True) % 7.56/7.73 (Or (Eq (exemplifies_property a a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) (skS.0 3 (skS.0 0 a_3) a_4 a_5)) True) (Eq False True)))))) % 7.56/7.73 Clause #103 (by clausification #[73]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (property a) False) % 7.56/7.73 (Or (Eq (is_the (skS.0 1 a_1 a_2) (skS.0 0 a_3)) True) % 7.56/7.73 (Or (Eq (exemplifies_property a a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) (Ne (skS.0 3 (skS.0 0 a_3) a_4 a_5) a_4))))) % 7.56/7.73 Clause #104 (by superposition #[103, 5]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_2) a_4) False) % 7.56/7.73 (Or (Ne (skS.0 3 (skS.0 0 a_2) a_4 a_5) a_4) (Eq False True))))) % 7.56/7.73 Clause #109 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (property a) False) % 7.56/7.73 (Or (Eq (is_the (skS.0 1 a_1 a_2) (skS.0 0 a_3)) True) % 7.56/7.73 (Or (Eq (exemplifies_property a a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) (Eq (object (skS.0 3 (skS.0 0 a_3) a_4 a_5)) True))))) % 7.56/7.73 Clause #110 (by superposition #[109, 5]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_2) a_4) False) % 7.56/7.73 (Or (Eq (object (skS.0 3 (skS.0 0 a_2) a_4 a_5)) True) (Eq False True))))) % 7.56/7.73 Clause #113 (by clausification #[81]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (property a) False) % 7.56/7.73 (Or (Eq (is_the (skS.0 1 a_1 a_2) (skS.0 0 a_3)) True) % 7.56/7.73 (Or (Eq (exemplifies_property a a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.56/7.73 (Eq (exemplifies_property (skS.0 0 a_3) (skS.0 3 (skS.0 0 a_3) a_4 a_5)) True))))) % 7.56/7.73 Clause #114 (by superposition #[113, 5]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_2) a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 3 (skS.0 0 a_2) a_4 a_5)) True) (Eq False True))))) % 7.56/7.73 Clause #118 (by clausification #[104]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_2) a_4) False) (Ne (skS.0 3 (skS.0 0 a_2) a_4 a_5) a_4)))) % 7.56/7.73 Clause #119 (by superposition #[118, 18]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.56/7.73 (Or (Eq (object (skS.0 1 a_3 a_4)) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.56/7.73 (Or (Ne (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5) (skS.0 1 a_3 a_4)) (Eq False True)))) % 7.56/7.73 Clause #120 (by clausification #[110]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.56/7.73 (Or (Eq (object a_4) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_2) a_4) False) (Eq (object (skS.0 3 (skS.0 0 a_2) a_4 a_5)) True)))) % 7.56/7.73 Clause #121 (by superposition #[120, 18]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.56/7.73 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.56/7.73 (Or (Eq (object (skS.0 1 a_3 a_4)) False) % 7.56/7.73 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.56/7.73 (Or (Eq (object (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5)) True) (Eq False True)))) % 7.56/7.73 Clause #127 (by clausification #[114]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_3) a_4) False) % 7.59/7.78 (Or (Eq (object a_4) False) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) a_4) False) % 7.59/7.78 (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 3 (skS.0 0 a_2) a_4 a_5)) True)))) % 7.59/7.78 Clause #128 (by superposition #[127, 18]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq (object (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5)) True) % 7.59/7.78 (Eq False True)))) % 7.59/7.78 Clause #212 (by clausification #[119]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq (object (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Ne (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5) (skS.0 1 a_3 a_4)))) % 7.59/7.78 Clause #213 (by forward demodulation #[212, 19]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq True False) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Ne (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5) (skS.0 1 a_3 a_4)))) % 7.59/7.78 Clause #214 (by clausification #[213]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Ne (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5) (skS.0 1 a_3 a_4))) % 7.59/7.78 Clause #215 (by superposition #[214, 18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Ne (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) a_4) (skS.0 1 a_2 a_3)) (Eq False True)) % 7.59/7.78 Clause #240 (by clausification #[215]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Ne (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) a_4) (skS.0 1 a_2 a_3)) % 7.59/7.78 Clause #241 (by clausification #[121]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq (object (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Eq (object (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5)) True))) % 7.59/7.78 Clause #242 (by forward demodulation #[241, 19]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq True False) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Eq (object (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5)) True))) % 7.59/7.78 Clause #243 (by clausification #[242]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.78 (Eq (object (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5)) True)) % 7.59/7.78 Clause #244 (by superposition #[243, 18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq (object (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) a_4)) True) (Eq False True)) % 7.59/7.78 Clause #247 (by clausification #[244]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) (Eq (object (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) a_4)) True) % 7.59/7.78 Clause #248 (by superposition #[247, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq (object (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2)) True) (Eq True False) % 7.59/7.78 Clause #261 (by clausification #[248]): ∀ (a a_1 a_2 : Iota), Eq (object (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2)) True % 7.59/7.78 Clause #262 (by superposition #[261, 15]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.59/7.78 Or (Eq True False) % 7.59/7.78 (Or (Eq (exemplifies_property (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) (skS.0 1 a_1 a_2) a_3)) False) % 7.59/7.78 (Eq (skS.0 3 (skS.0 0 a_1) (skS.0 1 a_1 a_2) a_3) (skS.0 1 a a_4))) % 7.59/7.78 Clause #374 (by clausification #[128]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.78 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.78 (Or (Eq (object (skS.0 1 a_3 a_4)) False) % 7.59/7.82 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.82 (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5)) True))) % 7.59/7.82 Clause #375 (by forward demodulation #[374, 19]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.82 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.82 (Or (Eq True False) % 7.59/7.82 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.82 (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5)) True))) % 7.59/7.82 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.59/7.82 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.82 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 1 a_3 a_4)) False) % 7.59/7.82 (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_3 a_4) a_5)) True)) % 7.59/7.82 Clause #377 (by superposition #[376, 18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.59/7.82 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.82 (Or (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) a_4)) True) (Eq False True)) % 7.59/7.82 Clause #399 (by clausification #[377]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.59/7.82 Or (Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.59/7.82 (Eq (exemplifies_property (skS.0 0 a_2) (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) a_4)) True) % 7.59/7.82 Clause #400 (by superposition #[399, 41]): ∀ (a a_1 a_2 : Iota), % 7.59/7.82 Or (Eq (exemplifies_property (skS.0 0 a) (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2)) True) (Eq True False) % 7.59/7.82 Clause #446 (by clausification #[400]): ∀ (a a_1 a_2 : Iota), Eq (exemplifies_property (skS.0 0 a) (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2)) True % 7.59/7.82 Clause #519 (by clausification #[262]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.59/7.82 Or (Eq (exemplifies_property (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) (skS.0 1 a_1 a_2) a_3)) False) % 7.59/7.82 (Eq (skS.0 3 (skS.0 0 a_1) (skS.0 1 a_1 a_2) a_3) (skS.0 1 a a_4)) % 7.59/7.82 Clause #520 (by superposition #[519, 446]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_3)) (Eq False True) % 7.59/7.82 Clause #524 (by clausification #[520]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_3) % 7.59/7.82 Clause #525 (by backward contextual literal cutting #[524, 240]): ∀ (a a_1 a_2 : Iota), Eq (is_the (skS.0 1 a a_1) (skS.0 0 a_2)) True % 7.59/7.82 Clause #561 (by superposition #[525, 41]): Eq True False % 7.59/7.82 Clause #562 (by clausification #[561]): False % 7.59/7.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------