%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PHI015+1 : TPTP v9.2.0. Released v7.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 11.23s 11.41s % Output : Proof 11.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : PHI015+1 : TPTP v9.2.0. Released v7.2.0. % 0.12/0.14 % Command : duper %s % 0.14/0.35 % Computer : n027.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.20/0.35 % WCLimit : 300 % 0.20/0.35 % DateTime : Fri Oct 3 09:06:53 EDT 2025 % 0.20/0.35 % CPUTime : % 11.23/11.41 SZS status Theorem for theBenchmark.p % 11.23/11.41 SZS output start Proof for theBenchmark.p % 11.23/11.41 Clause #1 (by assumption #[]): Eq (∀ (X F : Iota), exemplifies_property F X → And (property F) (object X)) True % 11.23/11.41 Clause #2 (by assumption #[]): Eq (∀ (X F : Iota), is_the X F → And (property F) (object X)) True % 11.23/11.41 Clause #4 (by assumption #[]): Eq % 11.23/11.41 (∀ (F X W : Iota), % 11.23/11.41 And (And (property F) (object X)) (object W) → % 11.23/11.41 Iff (And (is_the X F) (Eq X W)) % 11.23/11.41 (Exists fun Y => % 11.23/11.41 And % 11.23/11.41 (And (And (object Y) (exemplifies_property F Y)) % 11.23/11.41 (∀ (Z : Iota), object Z → exemplifies_property F Z → Eq Z Y)) % 11.23/11.41 (Eq Y W))) % 11.23/11.41 True % 11.23/11.41 Clause #6 (by assumption #[]): Eq % 11.23/11.41 (∀ (X : Iota), % 11.23/11.41 object X → % 11.23/11.41 Iff (exemplifies_property none_greater X) % 11.23/11.41 (And (exemplifies_property conceivable X) % 11.23/11.41 (Not % 11.23/11.41 (Exists fun Y => % 11.23/11.41 And (And (object Y) (exemplifies_relation greater_than Y X)) (exemplifies_property conceivable Y))))) % 11.23/11.41 True % 11.23/11.41 Clause #7 (by assumption #[]): Eq (Exists fun X => And (object X) (exemplifies_property none_greater X)) True % 11.23/11.41 Clause #8 (by assumption #[]): Eq % 11.23/11.41 (∀ (X : Iota), % 11.23/11.41 object X → % 11.23/11.41 And (is_the X none_greater) (Not (exemplifies_property existence X)) → % 11.23/11.41 Exists fun Y => % 11.23/11.41 And (And (object Y) (exemplifies_relation greater_than Y X)) (exemplifies_property conceivable Y)) % 11.23/11.41 True % 11.23/11.41 Clause #9 (by assumption #[]): Eq (is_the god none_greater) True % 11.23/11.41 Clause #10 (by assumption #[]): Eq (Not (exemplifies_property existence god)) True % 11.23/11.41 Clause #11 (by clausification #[10]): Eq (exemplifies_property existence god) False % 11.23/11.41 Clause #15 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (F : Iota), is_the a F → And (property F) (object a)) True % 11.23/11.41 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (is_the a a_1 → And (property a_1) (object a)) True % 11.23/11.41 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (is_the a a_1) False) (Eq (And (property a_1) (object a)) True) % 11.23/11.41 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (is_the a a_1) False) (Eq (object a) True) % 11.23/11.41 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (is_the a a_1) False) (Eq (property a_1) True) % 11.23/11.41 Clause #20 (by superposition #[18, 9]): Or (Eq (object god) True) (Eq False True) % 11.23/11.41 Clause #21 (by clausification #[20]): Eq (object god) True % 11.23/11.41 Clause #23 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (F : Iota), exemplifies_property F a → And (property F) (object a)) True % 11.23/11.41 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (exemplifies_property a a_1 → And (property a) (object a_1)) True % 11.23/11.41 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (exemplifies_property a a_1) False) (Eq (And (property a) (object a_1)) True) % 11.23/11.41 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (exemplifies_property a a_1) False) (Eq (object a_1) True) % 11.23/11.41 Clause #29 (by superposition #[19, 9]): Or (Eq (property none_greater) True) (Eq False True) % 11.23/11.41 Clause #30 (by clausification #[29]): Eq (property none_greater) True % 11.23/11.41 Clause #31 (by clausification #[7]): ∀ (a : Iota), Eq (And (object (skS.0 0 a)) (exemplifies_property none_greater (skS.0 0 a))) True % 11.23/11.41 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (exemplifies_property none_greater (skS.0 0 a)) True % 11.23/11.41 Clause #33 (by clausification #[31]): ∀ (a : Iota), Eq (object (skS.0 0 a)) True % 11.23/11.41 Clause #67 (by clausification #[4]): ∀ (a : Iota), % 11.23/11.41 Eq % 11.23/11.41 (∀ (X W : Iota), % 11.23/11.41 And (And (property a) (object X)) (object W) → % 11.23/11.41 Iff (And (is_the X a) (Eq X W)) % 11.23/11.41 (Exists fun Y => % 11.23/11.41 And % 11.23/11.41 (And (And (object Y) (exemplifies_property a Y)) % 11.23/11.41 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 11.23/11.41 (Eq Y W))) % 11.23/11.41 True % 11.23/11.41 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), % 11.23/11.41 Eq % 11.23/11.41 (∀ (W : Iota), % 11.23/11.41 And (And (property a) (object a_1)) (object W) → % 11.23/11.41 Iff (And (is_the a_1 a) (Eq a_1 W)) % 11.23/11.41 (Exists fun Y => % 11.23/11.41 And % 11.23/11.41 (And (And (object Y) (exemplifies_property a Y)) % 11.23/11.41 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 11.27/11.43 (Eq Y W))) % 11.27/11.43 True % 11.27/11.43 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), % 11.27/11.43 Eq % 11.27/11.43 (And (And (property a) (object a_1)) (object a_2) → % 11.27/11.43 Iff (And (is_the a_1 a) (Eq a_1 a_2)) % 11.27/11.43 (Exists fun Y => % 11.27/11.43 And % 11.27/11.43 (And (And (object Y) (exemplifies_property a Y)) % 11.27/11.43 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 11.27/11.43 (Eq Y a_2))) % 11.27/11.43 True % 11.27/11.43 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 11.27/11.43 Or (Eq (And (And (property a) (object a_1)) (object a_2)) False) % 11.27/11.43 (Eq % 11.27/11.43 (Iff (And (is_the a_1 a) (Eq a_1 a_2)) % 11.27/11.43 (Exists fun Y => % 11.27/11.43 And % 11.27/11.43 (And (And (object Y) (exemplifies_property a Y)) % 11.27/11.43 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 11.27/11.43 (Eq Y a_2))) % 11.27/11.43 True) % 11.27/11.43 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), % 11.27/11.43 Or % 11.27/11.43 (Eq % 11.27/11.43 (Iff (And (is_the a a_1) (Eq a a_2)) % 11.27/11.43 (Exists fun Y => % 11.27/11.43 And % 11.27/11.43 (And (And (object Y) (exemplifies_property a_1 Y)) % 11.27/11.43 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z Y)) % 11.27/11.43 (Eq Y a_2))) % 11.27/11.43 True) % 11.27/11.43 (Or (Eq (And (property a_1) (object a)) False) (Eq (object a_2) False)) % 11.27/11.43 Clause #73 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 11.27/11.43 Or (Eq (And (property a) (object a_1)) False) % 11.27/11.43 (Or (Eq (object a_2) False) % 11.27/11.43 (Or (Eq (And (is_the a_1 a) (Eq a_1 a_2)) False) % 11.27/11.43 (Eq % 11.27/11.43 (Exists fun Y => % 11.27/11.43 And % 11.27/11.43 (And (And (object Y) (exemplifies_property a Y)) % 11.27/11.43 (∀ (Z : Iota), object Z → exemplifies_property a Z → Eq Z Y)) % 11.27/11.43 (Eq Y a_2)) % 11.27/11.43 True))) % 11.27/11.43 Clause #95 (by clausification #[8]): ∀ (a : Iota), % 11.27/11.43 Eq % 11.27/11.43 (object a → % 11.27/11.43 And (is_the a none_greater) (Not (exemplifies_property existence a)) → % 11.27/11.43 Exists fun Y => % 11.27/11.43 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y)) % 11.27/11.43 True % 11.27/11.43 Clause #96 (by clausification #[95]): ∀ (a : Iota), % 11.27/11.43 Or (Eq (object a) False) % 11.27/11.43 (Eq % 11.27/11.43 (And (is_the a none_greater) (Not (exemplifies_property existence a)) → % 11.27/11.43 Exists fun Y => % 11.27/11.43 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y)) % 11.27/11.43 True) % 11.27/11.43 Clause #97 (by clausification #[96]): ∀ (a : Iota), % 11.27/11.43 Or (Eq (object a) False) % 11.27/11.43 (Or (Eq (And (is_the a none_greater) (Not (exemplifies_property existence a))) False) % 11.27/11.43 (Eq % 11.27/11.43 (Exists fun Y => % 11.27/11.43 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y)) % 11.27/11.43 True)) % 11.27/11.43 Clause #98 (by clausification #[97]): ∀ (a : Iota), % 11.27/11.43 Or (Eq (object a) False) % 11.27/11.43 (Or % 11.27/11.43 (Eq % 11.27/11.43 (Exists fun Y => % 11.27/11.43 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y)) % 11.27/11.43 True) % 11.27/11.43 (Or (Eq (is_the a none_greater) False) (Eq (Not (exemplifies_property existence a)) False))) % 11.27/11.43 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), % 11.27/11.43 Or (Eq (object a) False) % 11.27/11.43 (Or (Eq (is_the a none_greater) False) % 11.27/11.43 (Or (Eq (Not (exemplifies_property existence a)) False) % 11.27/11.43 (Eq % 11.27/11.43 (And (And (object (skS.0 3 a a_1)) (exemplifies_relation greater_than (skS.0 3 a a_1) a)) % 11.27/11.43 (exemplifies_property conceivable (skS.0 3 a a_1))) % 11.27/11.43 True))) % 11.27/11.43 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota), % 11.27/11.43 Or (Eq (object a) False) % 11.27/11.43 (Or (Eq (is_the a none_greater) False) % 11.27/11.43 (Or % 11.27/11.43 (Eq % 11.27/11.43 (And (And (object (skS.0 3 a a_1)) (exemplifies_relation greater_than (skS.0 3 a a_1) a)) % 11.27/11.43 (exemplifies_property conceivable (skS.0 3 a a_1))) % 11.27/11.43 True) % 11.27/11.43 (Eq (exemplifies_property existence a) True))) % 11.27/11.43 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), % 11.27/11.43 Or (Eq (object a) False) % 11.27/11.43 (Or (Eq (is_the a none_greater) False) % 11.27/11.43 (Or (Eq (exemplifies_property existence a) True) (Eq (exemplifies_property conceivable (skS.0 3 a a_1)) True))) % 11.27/11.43 Clause #102 (by clausification #[100]): ∀ (a a_1 : Iota), % 11.27/11.45 Or (Eq (object a) False) % 11.27/11.45 (Or (Eq (is_the a none_greater) False) % 11.27/11.45 (Or (Eq (exemplifies_property existence a) True) % 11.27/11.45 (Eq (And (object (skS.0 3 a a_1)) (exemplifies_relation greater_than (skS.0 3 a a_1) a)) True))) % 11.27/11.45 Clause #103 (by superposition #[101, 21]): ∀ (a : Iota), % 11.27/11.45 Or (Eq (is_the god none_greater) False) % 11.27/11.45 (Or (Eq (exemplifies_property existence god) True) % 11.27/11.45 (Or (Eq (exemplifies_property conceivable (skS.0 3 god a)) True) (Eq False True))) % 11.27/11.45 Clause #105 (by clausification #[103]): ∀ (a : Iota), % 11.27/11.45 Or (Eq (is_the god none_greater) False) % 11.27/11.45 (Or (Eq (exemplifies_property existence god) True) (Eq (exemplifies_property conceivable (skS.0 3 god a)) True)) % 11.27/11.45 Clause #106 (by forward demodulation #[105, 9]): ∀ (a : Iota), % 11.27/11.45 Or (Eq True False) % 11.27/11.45 (Or (Eq (exemplifies_property existence god) True) (Eq (exemplifies_property conceivable (skS.0 3 god a)) True)) % 11.27/11.45 Clause #107 (by clausification #[106]): ∀ (a : Iota), % 11.27/11.45 Or (Eq (exemplifies_property existence god) True) (Eq (exemplifies_property conceivable (skS.0 3 god a)) True) % 11.27/11.45 Clause #108 (by forward demodulation #[107, 11]): ∀ (a : Iota), Or (Eq False True) (Eq (exemplifies_property conceivable (skS.0 3 god a)) True) % 11.27/11.45 Clause #109 (by clausification #[108]): ∀ (a : Iota), Eq (exemplifies_property conceivable (skS.0 3 god a)) True % 11.27/11.45 Clause #110 (by superposition #[109, 26]): ∀ (a : Iota), Or (Eq True False) (Eq (object (skS.0 3 god a)) True) % 11.27/11.45 Clause #113 (by clausification #[6]): ∀ (a : Iota), % 11.27/11.45 Eq % 11.27/11.45 (object a → % 11.27/11.45 Iff (exemplifies_property none_greater a) % 11.27/11.45 (And (exemplifies_property conceivable a) % 11.27/11.45 (Not % 11.27/11.45 (Exists fun Y => % 11.27/11.45 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y))))) % 11.27/11.45 True % 11.27/11.45 Clause #114 (by clausification #[113]): ∀ (a : Iota), % 11.27/11.45 Or (Eq (object a) False) % 11.27/11.45 (Eq % 11.27/11.45 (Iff (exemplifies_property none_greater a) % 11.27/11.45 (And (exemplifies_property conceivable a) % 11.27/11.45 (Not % 11.27/11.45 (Exists fun Y => % 11.27/11.45 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y))))) % 11.27/11.45 True) % 11.27/11.45 Clause #116 (by clausification #[114]): ∀ (a : Iota), % 11.27/11.45 Or (Eq (object a) False) % 11.27/11.45 (Or (Eq (exemplifies_property none_greater a) False) % 11.27/11.45 (Eq % 11.27/11.45 (And (exemplifies_property conceivable a) % 11.27/11.45 (Not % 11.27/11.45 (Exists fun Y => % 11.27/11.45 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y)))) % 11.27/11.45 True)) % 11.27/11.45 Clause #124 (by clausification #[110]): ∀ (a : Iota), Eq (object (skS.0 3 god a)) True % 11.27/11.45 Clause #168 (by clausification #[116]): ∀ (a : Iota), % 11.27/11.45 Or (Eq (object a) False) % 11.27/11.45 (Or (Eq (exemplifies_property none_greater a) False) % 11.27/11.45 (Eq % 11.27/11.45 (Not % 11.27/11.45 (Exists fun Y => % 11.27/11.45 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y))) % 11.27/11.45 True)) % 11.27/11.45 Clause #170 (by clausification #[168]): ∀ (a : Iota), % 11.27/11.45 Or (Eq (object a) False) % 11.27/11.45 (Or (Eq (exemplifies_property none_greater a) False) % 11.27/11.45 (Eq % 11.27/11.45 (Exists fun Y => % 11.27/11.45 And (And (object Y) (exemplifies_relation greater_than Y a)) (exemplifies_property conceivable Y)) % 11.27/11.45 False)) % 11.27/11.45 Clause #171 (by clausification #[170]): ∀ (a a_1 : Iota), % 11.27/11.45 Or (Eq (object a) False) % 11.27/11.45 (Or (Eq (exemplifies_property none_greater a) False) % 11.27/11.45 (Eq (And (And (object a_1) (exemplifies_relation greater_than a_1 a)) (exemplifies_property conceivable a_1)) % 11.27/11.45 False)) % 11.27/11.45 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), % 11.27/11.45 Or (Eq (object a) False) % 11.27/11.45 (Or (Eq (exemplifies_property none_greater a) False) % 11.27/11.45 (Or (Eq (And (object a_1) (exemplifies_relation greater_than a_1 a)) False) % 11.27/11.45 (Eq (exemplifies_property conceivable a_1) False))) % 11.27/11.45 Clause #173 (by clausification #[172]): ∀ (a a_1 : Iota), % 11.27/11.45 Or (Eq (object a) False) % 11.27/11.45 (Or (Eq (exemplifies_property none_greater a) False) % 11.27/11.45 (Or (Eq (exemplifies_property conceivable a_1) False) % 11.27/11.45 (Or (Eq (object a_1) False) (Eq (exemplifies_relation greater_than a_1 a) False)))) % 11.27/11.45 Clause #175 (by superposition #[173, 33]): ∀ (a a_1 : Iota), % 11.27/11.47 Or (Eq (exemplifies_property none_greater (skS.0 0 a)) False) % 11.27/11.47 (Or (Eq (exemplifies_property conceivable a_1) False) % 11.27/11.47 (Or (Eq (object a_1) False) (Or (Eq (exemplifies_relation greater_than a_1 (skS.0 0 a)) False) (Eq False True)))) % 11.27/11.47 Clause #193 (by clausification #[175]): ∀ (a a_1 : Iota), % 11.27/11.47 Or (Eq (exemplifies_property none_greater (skS.0 0 a)) False) % 11.27/11.47 (Or (Eq (exemplifies_property conceivable a_1) False) % 11.27/11.47 (Or (Eq (object a_1) False) (Eq (exemplifies_relation greater_than a_1 (skS.0 0 a)) False))) % 11.27/11.47 Clause #194 (by forward demodulation #[193, 32]): ∀ (a a_1 : Iota), % 11.27/11.47 Or (Eq True False) % 11.27/11.47 (Or (Eq (exemplifies_property conceivable a) False) % 11.27/11.47 (Or (Eq (object a) False) (Eq (exemplifies_relation greater_than a (skS.0 0 a_1)) False))) % 11.27/11.47 Clause #195 (by clausification #[194]): ∀ (a a_1 : Iota), % 11.27/11.47 Or (Eq (exemplifies_property conceivable a) False) % 11.27/11.47 (Or (Eq (object a) False) (Eq (exemplifies_relation greater_than a (skS.0 0 a_1)) False)) % 11.27/11.47 Clause #196 (by superposition #[195, 109]): ∀ (a a_1 : Iota), % 11.27/11.47 Or (Eq (object (skS.0 3 god a)) False) % 11.27/11.47 (Or (Eq (exemplifies_relation greater_than (skS.0 3 god a) (skS.0 0 a_1)) False) (Eq False True)) % 11.27/11.47 Clause #223 (by clausification #[196]): ∀ (a a_1 : Iota), % 11.27/11.47 Or (Eq (object (skS.0 3 god a)) False) (Eq (exemplifies_relation greater_than (skS.0 3 god a) (skS.0 0 a_1)) False) % 11.27/11.47 Clause #224 (by forward demodulation #[223, 124]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (exemplifies_relation greater_than (skS.0 3 god a) (skS.0 0 a_1)) False) % 11.27/11.47 Clause #225 (by clausification #[224]): ∀ (a a_1 : Iota), Eq (exemplifies_relation greater_than (skS.0 3 god a) (skS.0 0 a_1)) False % 11.27/11.47 Clause #259 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 11.27/11.47 Or (Eq (object a) False) % 11.27/11.47 (Or (Eq (And (is_the a_1 a_2) (Eq a_1 a)) False) % 11.27/11.47 (Or % 11.27/11.47 (Eq % 11.27/11.47 (Exists fun Y => % 11.27/11.47 And % 11.27/11.47 (And (And (object Y) (exemplifies_property a_2 Y)) % 11.27/11.47 (∀ (Z : Iota), object Z → exemplifies_property a_2 Z → Eq Z Y)) % 11.27/11.47 (Eq Y a)) % 11.27/11.47 True) % 11.27/11.47 (Or (Eq (property a_2) False) (Eq (object a_1) False)))) % 11.27/11.47 Clause #260 (by clausification #[259]): ∀ (a a_1 a_2 : Iota), % 11.27/11.47 Or (Eq (object a) False) % 11.27/11.47 (Or % 11.27/11.47 (Eq % 11.27/11.47 (Exists fun Y => % 11.27/11.47 And % 11.27/11.47 (And (And (object Y) (exemplifies_property a_1 Y)) % 11.27/11.47 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z Y)) % 11.27/11.47 (Eq Y a)) % 11.27/11.47 True) % 11.27/11.47 (Or (Eq (property a_1) False) % 11.27/11.47 (Or (Eq (object a_2) False) (Or (Eq (is_the a_2 a_1) False) (Eq (Eq a_2 a) False))))) % 11.27/11.47 Clause #261 (by clausification #[260]): ∀ (a a_1 a_2 a_3 : Iota), % 11.27/11.47 Or (Eq (object a) False) % 11.27/11.47 (Or (Eq (property a_1) False) % 11.27/11.47 (Or (Eq (object a_2) False) % 11.27/11.47 (Or (Eq (is_the a_2 a_1) False) % 11.27/11.47 (Or (Eq (Eq a_2 a) False) % 11.27/11.47 (Eq % 11.27/11.47 (And % 11.27/11.47 (And (And (object (skS.0 7 a_1 a a_3)) (exemplifies_property a_1 (skS.0 7 a_1 a a_3))) % 11.27/11.47 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z (skS.0 7 a_1 a a_3))) % 11.27/11.47 (Eq (skS.0 7 a_1 a a_3) a)) % 11.27/11.47 True))))) % 11.27/11.47 Clause #262 (by clausification #[261]): ∀ (a a_1 a_2 a_3 : Iota), % 11.27/11.47 Or (Eq (object a) False) % 11.27/11.47 (Or (Eq (property a_1) False) % 11.27/11.47 (Or (Eq (object a_2) False) % 11.27/11.47 (Or (Eq (is_the a_2 a_1) False) % 11.27/11.47 (Or % 11.27/11.47 (Eq % 11.27/11.47 (And % 11.27/11.47 (And (And (object (skS.0 7 a_1 a a_3)) (exemplifies_property a_1 (skS.0 7 a_1 a a_3))) % 11.27/11.47 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z (skS.0 7 a_1 a a_3))) % 11.27/11.47 (Eq (skS.0 7 a_1 a a_3) a)) % 11.27/11.47 True) % 11.27/11.47 (Ne a_2 a))))) % 11.27/11.47 Clause #263 (by clausification #[262]): ∀ (a a_1 a_2 a_3 : Iota), % 11.27/11.47 Or (Eq (object a) False) % 11.27/11.47 (Or (Eq (property a_1) False) % 11.27/11.47 (Or (Eq (object a_2) False) % 11.27/11.47 (Or (Eq (is_the a_2 a_1) False) (Or (Ne a_2 a) (Eq (Eq (skS.0 7 a_1 a a_3) a) True))))) % 11.27/11.47 Clause #264 (by clausification #[262]): ∀ (a a_1 a_2 a_3 : Iota), % 11.27/11.47 Or (Eq (object a) False) % 11.27/11.47 (Or (Eq (property a_1) False) % 11.27/11.49 (Or (Eq (object a_2) False) % 11.27/11.49 (Or (Eq (is_the a_2 a_1) False) % 11.27/11.49 (Or (Ne a_2 a) % 11.27/11.49 (Eq % 11.27/11.49 (And (And (object (skS.0 7 a_1 a a_3)) (exemplifies_property a_1 (skS.0 7 a_1 a a_3))) % 11.27/11.49 (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z (skS.0 7 a_1 a a_3))) % 11.27/11.49 True))))) % 11.27/11.49 Clause #265 (by clausification #[263]): ∀ (a a_1 a_2 a_3 : Iota), % 11.27/11.49 Or (Eq (object a) False) % 11.27/11.49 (Or (Eq (property a_1) False) % 11.27/11.49 (Or (Eq (object a_2) False) (Or (Eq (is_the a_2 a_1) False) (Or (Ne a_2 a) (Eq (skS.0 7 a_1 a a_3) a))))) % 11.27/11.49 Clause #266 (by destructive equality resolution #[265]): ∀ (a a_1 a_2 : Iota), % 11.27/11.49 Or (Eq (object a) False) % 11.27/11.49 (Or (Eq (property a_1) False) (Or (Eq (object a) False) (Or (Eq (is_the a a_1) False) (Eq (skS.0 7 a_1 a a_2) a)))) % 11.27/11.49 Clause #267 (by eliminate duplicate literals #[266]): ∀ (a a_1 a_2 : Iota), % 11.27/11.49 Or (Eq (object a) False) (Or (Eq (property a_1) False) (Or (Eq (is_the a a_1) False) (Eq (skS.0 7 a_1 a a_2) a))) % 11.27/11.49 Clause #268 (by superposition #[267, 21]): ∀ (a a_1 : Iota), % 11.27/11.49 Or (Eq (property a) False) (Or (Eq (is_the god a) False) (Or (Eq (skS.0 7 a god a_1) god) (Eq False True))) % 11.27/11.49 Clause #272 (by clausification #[268]): ∀ (a a_1 : Iota), Or (Eq (property a) False) (Or (Eq (is_the god a) False) (Eq (skS.0 7 a god a_1) god)) % 11.27/11.49 Clause #273 (by superposition #[272, 30]): ∀ (a : Iota), Or (Eq (is_the god none_greater) False) (Or (Eq (skS.0 7 none_greater god a) god) (Eq False True)) % 11.27/11.49 Clause #276 (by clausification #[273]): ∀ (a : Iota), Or (Eq (is_the god none_greater) False) (Eq (skS.0 7 none_greater god a) god) % 11.27/11.49 Clause #277 (by forward demodulation #[276, 9]): ∀ (a : Iota), Or (Eq True False) (Eq (skS.0 7 none_greater god a) god) % 11.27/11.49 Clause #278 (by clausification #[277]): ∀ (a : Iota), Eq (skS.0 7 none_greater god a) god % 11.27/11.49 Clause #348 (by clausification #[102]): ∀ (a a_1 : Iota), % 11.27/11.49 Or (Eq (object a) False) % 11.27/11.49 (Or (Eq (is_the a none_greater) False) % 11.27/11.49 (Or (Eq (exemplifies_property existence a) True) (Eq (exemplifies_relation greater_than (skS.0 3 a a_1) a) True))) % 11.27/11.49 Clause #350 (by superposition #[348, 21]): ∀ (a : Iota), % 11.27/11.49 Or (Eq (is_the god none_greater) False) % 11.27/11.49 (Or (Eq (exemplifies_property existence god) True) % 11.27/11.49 (Or (Eq (exemplifies_relation greater_than (skS.0 3 god a) god) True) (Eq False True))) % 11.27/11.49 Clause #362 (by clausification #[350]): ∀ (a : Iota), % 11.27/11.49 Or (Eq (is_the god none_greater) False) % 11.27/11.49 (Or (Eq (exemplifies_property existence god) True) % 11.27/11.49 (Eq (exemplifies_relation greater_than (skS.0 3 god a) god) True)) % 11.27/11.49 Clause #363 (by forward demodulation #[362, 9]): ∀ (a : Iota), % 11.27/11.49 Or (Eq True False) % 11.27/11.49 (Or (Eq (exemplifies_property existence god) True) % 11.27/11.49 (Eq (exemplifies_relation greater_than (skS.0 3 god a) god) True)) % 11.27/11.49 Clause #364 (by clausification #[363]): ∀ (a : Iota), % 11.27/11.49 Or (Eq (exemplifies_property existence god) True) (Eq (exemplifies_relation greater_than (skS.0 3 god a) god) True) % 11.27/11.49 Clause #365 (by forward demodulation #[364, 11]): ∀ (a : Iota), Or (Eq False True) (Eq (exemplifies_relation greater_than (skS.0 3 god a) god) True) % 11.27/11.49 Clause #366 (by clausification #[365]): ∀ (a : Iota), Eq (exemplifies_relation greater_than (skS.0 3 god a) god) True % 11.27/11.49 Clause #1990 (by clausification #[264]): ∀ (a a_1 a_2 a_3 : Iota), % 11.27/11.49 Or (Eq (object a) False) % 11.27/11.49 (Or (Eq (property a_1) False) % 11.27/11.49 (Or (Eq (object a_2) False) % 11.27/11.49 (Or (Eq (is_the a_2 a_1) False) % 11.27/11.49 (Or (Ne a_2 a) (Eq (∀ (Z : Iota), object Z → exemplifies_property a_1 Z → Eq Z (skS.0 7 a_1 a a_3)) True))))) % 11.27/11.49 Clause #1992 (by clausification #[1990]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 11.27/11.49 Or (Eq (object a) False) % 11.27/11.49 (Or (Eq (property a_1) False) % 11.27/11.49 (Or (Eq (object a_2) False) % 11.27/11.49 (Or (Eq (is_the a_2 a_1) False) % 11.27/11.49 (Or (Ne a_2 a) (Eq (object a_3 → exemplifies_property a_1 a_3 → Eq a_3 (skS.0 7 a_1 a a_4)) True))))) % 11.27/11.49 Clause #1993 (by clausification #[1992]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 11.27/11.49 Or (Eq (object a) False) % 11.27/11.49 (Or (Eq (property a_1) False) % 11.27/11.49 (Or (Eq (object a_2) False) % 11.27/11.49 (Or (Eq (is_the a_2 a_1) False) % 11.35/11.52 (Or (Ne a_2 a) % 11.35/11.52 (Or (Eq (object a_3) False) (Eq (exemplifies_property a_1 a_3 → Eq a_3 (skS.0 7 a_1 a a_4)) True)))))) % 11.35/11.52 Clause #1994 (by clausification #[1993]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 11.35/11.52 Or (Eq (object a) False) % 11.35/11.52 (Or (Eq (property a_1) False) % 11.35/11.52 (Or (Eq (object a_2) False) % 11.35/11.52 (Or (Eq (is_the a_2 a_1) False) % 11.35/11.52 (Or (Ne a_2 a) % 11.35/11.52 (Or (Eq (object a_3) False) % 11.35/11.52 (Or (Eq (exemplifies_property a_1 a_3) False) (Eq (Eq a_3 (skS.0 7 a_1 a a_4)) True))))))) % 11.35/11.52 Clause #1995 (by clausification #[1994]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 11.35/11.52 Or (Eq (object a) False) % 11.35/11.52 (Or (Eq (property a_1) False) % 11.35/11.52 (Or (Eq (object a_2) False) % 11.35/11.52 (Or (Eq (is_the a_2 a_1) False) % 11.35/11.52 (Or (Ne a_2 a) % 11.35/11.52 (Or (Eq (object a_3) False) (Or (Eq (exemplifies_property a_1 a_3) False) (Eq a_3 (skS.0 7 a_1 a a_4)))))))) % 11.35/11.52 Clause #1996 (by destructive equality resolution #[1995]): ∀ (a a_1 a_2 a_3 : Iota), % 11.35/11.52 Or (Eq (object a) False) % 11.35/11.52 (Or (Eq (property a_1) False) % 11.35/11.52 (Or (Eq (object a) False) % 11.35/11.52 (Or (Eq (is_the a a_1) False) % 11.35/11.52 (Or (Eq (object a_2) False) (Or (Eq (exemplifies_property a_1 a_2) False) (Eq a_2 (skS.0 7 a_1 a a_3))))))) % 11.35/11.52 Clause #1997 (by eliminate duplicate literals #[1996]): ∀ (a a_1 a_2 a_3 : Iota), % 11.35/11.52 Or (Eq (object a) False) % 11.35/11.52 (Or (Eq (property a_1) False) % 11.35/11.52 (Or (Eq (is_the a a_1) False) % 11.35/11.52 (Or (Eq (object a_2) False) (Or (Eq (exemplifies_property a_1 a_2) False) (Eq a_2 (skS.0 7 a_1 a a_3)))))) % 11.35/11.52 Clause #1998 (by superposition #[1997, 21]): ∀ (a a_1 a_2 : Iota), % 11.35/11.52 Or (Eq (property a) False) % 11.35/11.52 (Or (Eq (is_the god a) False) % 11.35/11.52 (Or (Eq (object a_1) False) % 11.35/11.52 (Or (Eq (exemplifies_property a a_1) False) (Or (Eq a_1 (skS.0 7 a god a_2)) (Eq False True))))) % 11.35/11.52 Clause #2025 (by clausification #[1998]): ∀ (a a_1 a_2 : Iota), % 11.35/11.52 Or (Eq (property a) False) % 11.35/11.52 (Or (Eq (is_the god a) False) % 11.35/11.52 (Or (Eq (object a_1) False) (Or (Eq (exemplifies_property a a_1) False) (Eq a_1 (skS.0 7 a god a_2))))) % 11.35/11.52 Clause #2026 (by superposition #[2025, 30]): ∀ (a a_1 : Iota), % 11.35/11.52 Or (Eq (is_the god none_greater) False) % 11.35/11.52 (Or (Eq (object a) False) % 11.35/11.52 (Or (Eq (exemplifies_property none_greater a) False) (Or (Eq a (skS.0 7 none_greater god a_1)) (Eq False True)))) % 11.35/11.52 Clause #2029 (by clausification #[2026]): ∀ (a a_1 : Iota), % 11.35/11.52 Or (Eq (is_the god none_greater) False) % 11.35/11.52 (Or (Eq (object a) False) % 11.35/11.52 (Or (Eq (exemplifies_property none_greater a) False) (Eq a (skS.0 7 none_greater god a_1)))) % 11.35/11.52 Clause #2030 (by forward demodulation #[2029, 278]): ∀ (a : Iota), % 11.35/11.52 Or (Eq (is_the god none_greater) False) % 11.35/11.52 (Or (Eq (object a) False) (Or (Eq (exemplifies_property none_greater a) False) (Eq a god))) % 11.35/11.52 Clause #2031 (by superposition #[2030, 9]): ∀ (a : Iota), % 11.35/11.52 Or (Eq (object a) False) (Or (Eq (exemplifies_property none_greater a) False) (Or (Eq a god) (Eq False True))) % 11.35/11.52 Clause #2032 (by clausification #[2031]): ∀ (a : Iota), Or (Eq (object a) False) (Or (Eq (exemplifies_property none_greater a) False) (Eq a god)) % 11.35/11.52 Clause #2034 (by superposition #[2032, 33]): ∀ (a : Iota), Or (Eq (exemplifies_property none_greater (skS.0 0 a)) False) (Or (Eq (skS.0 0 a) god) (Eq False True)) % 11.35/11.52 Clause #2064 (by clausification #[2034]): ∀ (a : Iota), Or (Eq (exemplifies_property none_greater (skS.0 0 a)) False) (Eq (skS.0 0 a) god) % 11.35/11.52 Clause #2065 (by superposition #[2064, 32]): ∀ (a : Iota), Or (Eq (skS.0 0 a) god) (Eq False True) % 11.35/11.52 Clause #2066 (by clausification #[2065]): ∀ (a : Iota), Eq (skS.0 0 a) god % 11.35/11.52 Clause #2072 (by backward demodulation #[2066, 225]): ∀ (a : Iota), Eq (exemplifies_relation greater_than (skS.0 3 god a) god) False % 11.35/11.52 Clause #2211 (by superposition #[2072, 366]): Eq False True % 11.35/11.52 Clause #2212 (by clausification #[2211]): False % 11.35/11.52 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------