%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET664+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:00:21 PM UTC 2025 % Result : Theorem 9.01s 9.19s % Output : Proof 9.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET664+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n031.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 : Thu Oct 2 14:23:08 EDT 2025 % 0.13/0.35 % CPUTime : % 9.01/9.19 SZS status Theorem for theBenchmark.p % 9.01/9.19 SZS output start Proof for theBenchmark.p % 9.01/9.19 Clause #0 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → subset B empty_set → Eq B empty_set) True % 9.01/9.19 Clause #1 (by assumption #[]): Eq % 9.01/9.19 (∀ (B : Iota), % 9.01/9.19 ilf_type B binary_relation_type → Or (Eq (domain_of B) empty_set) (Eq (range_of B) empty_set) → Eq B empty_set) % 9.01/9.19 True % 9.01/9.19 Clause #2 (by assumption #[]): Eq % 9.01/9.19 (∀ (B : Iota), % 9.01/9.19 ilf_type B set_type → % 9.01/9.19 ∀ (C : Iota), % 9.01/9.19 ilf_type C set_type → % 9.01/9.19 ∀ (D : Iota), ilf_type D (relation_type B C) → And (subset (domain_of D) B) (subset (range_of D) C)) % 9.01/9.19 True % 9.01/9.19 Clause #6 (by assumption #[]): Eq % 9.01/9.19 (∀ (B : Iota), % 9.01/9.19 ilf_type B set_type → % 9.01/9.19 ∀ (C : Iota), % 9.01/9.19 ilf_type C set_type → % 9.01/9.19 And (∀ (D : Iota), ilf_type D (subset_type (cross_product B C)) → ilf_type D (relation_type B C)) % 9.01/9.19 (∀ (E : Iota), ilf_type E (relation_type B C) → ilf_type E (subset_type (cross_product B C)))) % 9.01/9.19 True % 9.01/9.19 Clause #13 (by assumption #[]): Eq % 9.01/9.19 (∀ (B : Iota), % 9.01/9.19 ilf_type B set_type → Iff (ilf_type B binary_relation_type) (And (relation_like B) (ilf_type B set_type))) % 9.01/9.19 True % 9.01/9.19 Clause #28 (by assumption #[]): Eq % 9.01/9.19 (∀ (B : Iota), % 9.01/9.19 ilf_type B set_type → % 9.01/9.19 ∀ (C : Iota), ilf_type C set_type → ∀ (D : Iota), ilf_type D (subset_type (cross_product B C)) → relation_like D) % 9.01/9.19 True % 9.01/9.19 Clause #33 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True % 9.01/9.19 Clause #34 (by assumption #[]): Eq % 9.01/9.19 (Not % 9.01/9.19 (∀ (B : Iota), % 9.01/9.19 ilf_type B set_type → % 9.01/9.19 ∀ (C : Iota), % 9.01/9.19 ilf_type C set_type → % 9.01/9.19 ∀ (D : Iota), ilf_type D (relation_type C B) → ilf_type D (relation_type C empty_set) → Eq D empty_set)) % 9.01/9.19 True % 9.01/9.19 Clause #39 (by clausification #[33]): ∀ (a : Iota), Eq (ilf_type a set_type) True % 9.01/9.19 Clause #44 (by clausification #[0]): ∀ (a : Iota), Eq (ilf_type a set_type → subset a empty_set → Eq a empty_set) True % 9.01/9.19 Clause #45 (by clausification #[44]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (subset a empty_set → Eq a empty_set) True) % 9.01/9.19 Clause #46 (by clausification #[45]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Or (Eq (subset a empty_set) False) (Eq (Eq a empty_set) True)) % 9.01/9.19 Clause #47 (by clausification #[46]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Or (Eq (subset a empty_set) False) (Eq a empty_set)) % 9.01/9.19 Clause #48 (by forward demodulation #[47, 39]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (subset a empty_set) False) (Eq a empty_set)) % 9.01/9.19 Clause #49 (by clausification #[48]): ∀ (a : Iota), Or (Eq (subset a empty_set) False) (Eq a empty_set) % 9.01/9.19 Clause #60 (by clausification #[1]): ∀ (a : Iota), % 9.01/9.19 Eq (ilf_type a binary_relation_type → Or (Eq (domain_of a) empty_set) (Eq (range_of a) empty_set) → Eq a empty_set) % 9.01/9.19 True % 9.01/9.19 Clause #61 (by clausification #[60]): ∀ (a : Iota), % 9.01/9.19 Or (Eq (ilf_type a binary_relation_type) False) % 9.01/9.19 (Eq (Or (Eq (domain_of a) empty_set) (Eq (range_of a) empty_set) → Eq a empty_set) True) % 9.01/9.19 Clause #62 (by clausification #[61]): ∀ (a : Iota), % 9.01/9.19 Or (Eq (ilf_type a binary_relation_type) False) % 9.01/9.19 (Or (Eq (Or (Eq (domain_of a) empty_set) (Eq (range_of a) empty_set)) False) (Eq (Eq a empty_set) True)) % 9.01/9.19 Clause #63 (by clausification #[62]): ∀ (a : Iota), % 9.01/9.19 Or (Eq (ilf_type a binary_relation_type) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq (range_of a) empty_set) False)) % 9.01/9.19 Clause #65 (by clausification #[63]): ∀ (a : Iota), % 9.01/9.19 Or (Eq (ilf_type a binary_relation_type) False) (Or (Eq (Eq (range_of a) empty_set) False) (Eq a empty_set)) % 9.01/9.19 Clause #66 (by clausification #[65]): ∀ (a : Iota), Or (Eq (ilf_type a binary_relation_type) False) (Or (Eq a empty_set) (Ne (range_of a) empty_set)) % 9.01/9.19 Clause #73 (by clausification #[28]): ∀ (a : Iota), % 9.01/9.19 Eq % 9.01/9.19 (ilf_type a set_type → % 9.01/9.19 ∀ (C : Iota), ilf_type C set_type → ∀ (D : Iota), ilf_type D (subset_type (cross_product a C)) → relation_like D) % 9.01/9.19 True % 9.01/9.19 Clause #74 (by clausification #[73]): ∀ (a : Iota), % 9.01/9.19 Or (Eq (ilf_type a set_type) False) % 9.01/9.19 (Eq % 9.01/9.19 (∀ (C : Iota), ilf_type C set_type → ∀ (D : Iota), ilf_type D (subset_type (cross_product a C)) → relation_like D) % 9.04/9.21 True) % 9.04/9.21 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Eq (ilf_type a_1 set_type → ∀ (D : Iota), ilf_type D (subset_type (cross_product a a_1)) → relation_like D) True) % 9.04/9.21 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 set_type) False) % 9.04/9.21 (Eq (∀ (D : Iota), ilf_type D (subset_type (cross_product a a_1)) → relation_like D) True)) % 9.04/9.21 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 set_type) False) % 9.04/9.21 (Eq (ilf_type a_2 (subset_type (cross_product a a_1)) → relation_like a_2) True)) % 9.04/9.21 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_2 (subset_type (cross_product a a_1))) False) (Eq (relation_like a_2) True))) % 9.04/9.21 Clause #79 (by forward demodulation #[78, 39]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq True False) % 9.04/9.21 (Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 (subset_type (cross_product a_2 a))) False) (Eq (relation_like a_1) True))) % 9.04/9.21 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 (subset_type (cross_product a_2 a))) False) (Eq (relation_like a_1) True)) % 9.04/9.21 Clause #81 (by forward demodulation #[80, 39]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq True False) (Or (Eq (ilf_type a (subset_type (cross_product a_1 a_2))) False) (Eq (relation_like a) True)) % 9.04/9.21 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), Or (Eq (ilf_type a (subset_type (cross_product a_1 a_2))) False) (Eq (relation_like a) True) % 9.04/9.21 Clause #87 (by clausification #[2]): ∀ (a : Iota), % 9.04/9.21 Eq % 9.04/9.21 (ilf_type a set_type → % 9.04/9.21 ∀ (C : Iota), % 9.04/9.21 ilf_type C set_type → % 9.04/9.21 ∀ (D : Iota), ilf_type D (relation_type a C) → And (subset (domain_of D) a) (subset (range_of D) C)) % 9.04/9.21 True % 9.04/9.21 Clause #88 (by clausification #[87]): ∀ (a : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Eq % 9.04/9.21 (∀ (C : Iota), % 9.04/9.21 ilf_type C set_type → % 9.04/9.21 ∀ (D : Iota), ilf_type D (relation_type a C) → And (subset (domain_of D) a) (subset (range_of D) C)) % 9.04/9.21 True) % 9.04/9.21 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Eq % 9.04/9.21 (ilf_type a_1 set_type → % 9.04/9.21 ∀ (D : Iota), ilf_type D (relation_type a a_1) → And (subset (domain_of D) a) (subset (range_of D) a_1)) % 9.04/9.21 True) % 9.04/9.21 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 set_type) False) % 9.04/9.21 (Eq (∀ (D : Iota), ilf_type D (relation_type a a_1) → And (subset (domain_of D) a) (subset (range_of D) a_1)) % 9.04/9.21 True)) % 9.04/9.21 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 set_type) False) % 9.04/9.21 (Eq (ilf_type a_2 (relation_type a a_1) → And (subset (domain_of a_2) a) (subset (range_of a_2) a_1)) True)) % 9.04/9.21 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_2 (relation_type a a_1)) False) % 9.04/9.21 (Eq (And (subset (domain_of a_2) a) (subset (range_of a_2) a_1)) True))) % 9.04/9.21 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_2 (relation_type a a_1)) False) (Eq (subset (range_of a_2) a_1) True))) % 9.04/9.21 Clause #95 (by forward demodulation #[93, 39]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq True False) % 9.04/9.21 (Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 (relation_type a_2 a)) False) (Eq (subset (range_of a_1) a) True))) % 9.04/9.21 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), % 9.04/9.21 Or (Eq (ilf_type a set_type) False) % 9.04/9.21 (Or (Eq (ilf_type a_1 (relation_type a_2 a)) False) (Eq (subset (range_of a_1) a) True)) % 9.07/9.23 Clause #97 (by forward demodulation #[96, 39]): ∀ (a a_1 a_2 : Iota), % 9.07/9.23 Or (Eq True False) (Or (Eq (ilf_type a (relation_type a_1 a_2)) False) (Eq (subset (range_of a) a_2) True)) % 9.07/9.23 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 : Iota), Or (Eq (ilf_type a (relation_type a_1 a_2)) False) (Eq (subset (range_of a) a_2) True) % 9.07/9.23 Clause #135 (by clausification #[6]): ∀ (a : Iota), % 9.07/9.23 Eq % 9.07/9.23 (ilf_type a set_type → % 9.07/9.23 ∀ (C : Iota), % 9.07/9.23 ilf_type C set_type → % 9.07/9.23 And (∀ (D : Iota), ilf_type D (subset_type (cross_product a C)) → ilf_type D (relation_type a C)) % 9.07/9.23 (∀ (E : Iota), ilf_type E (relation_type a C) → ilf_type E (subset_type (cross_product a C)))) % 9.07/9.23 True % 9.07/9.23 Clause #136 (by clausification #[135]): ∀ (a : Iota), % 9.07/9.23 Or (Eq (ilf_type a set_type) False) % 9.07/9.23 (Eq % 9.07/9.23 (∀ (C : Iota), % 9.07/9.23 ilf_type C set_type → % 9.07/9.23 And (∀ (D : Iota), ilf_type D (subset_type (cross_product a C)) → ilf_type D (relation_type a C)) % 9.07/9.23 (∀ (E : Iota), ilf_type E (relation_type a C) → ilf_type E (subset_type (cross_product a C)))) % 9.07/9.23 True) % 9.07/9.23 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), % 9.07/9.23 Or (Eq (ilf_type a set_type) False) % 9.07/9.23 (Eq % 9.07/9.23 (ilf_type a_1 set_type → % 9.07/9.23 And (∀ (D : Iota), ilf_type D (subset_type (cross_product a a_1)) → ilf_type D (relation_type a a_1)) % 9.07/9.23 (∀ (E : Iota), ilf_type E (relation_type a a_1) → ilf_type E (subset_type (cross_product a a_1)))) % 9.07/9.23 True) % 9.07/9.23 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota), % 9.07/9.23 Or (Eq (ilf_type a set_type) False) % 9.07/9.23 (Or (Eq (ilf_type a_1 set_type) False) % 9.07/9.23 (Eq % 9.07/9.23 (And (∀ (D : Iota), ilf_type D (subset_type (cross_product a a_1)) → ilf_type D (relation_type a a_1)) % 9.07/9.23 (∀ (E : Iota), ilf_type E (relation_type a a_1) → ilf_type E (subset_type (cross_product a a_1)))) % 9.07/9.23 True)) % 9.07/9.23 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota), % 9.07/9.23 Or (Eq (ilf_type a set_type) False) % 9.07/9.23 (Or (Eq (ilf_type a_1 set_type) False) % 9.07/9.23 (Eq (∀ (E : Iota), ilf_type E (relation_type a a_1) → ilf_type E (subset_type (cross_product a a_1))) True)) % 9.07/9.23 Clause #141 (by clausification #[139]): ∀ (a a_1 a_2 : Iota), % 9.07/9.23 Or (Eq (ilf_type a set_type) False) % 9.07/9.23 (Or (Eq (ilf_type a_1 set_type) False) % 9.07/9.23 (Eq (ilf_type a_2 (relation_type a a_1) → ilf_type a_2 (subset_type (cross_product a a_1))) True)) % 9.07/9.23 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 : Iota), % 9.07/9.23 Or (Eq (ilf_type a set_type) False) % 9.07/9.23 (Or (Eq (ilf_type a_1 set_type) False) % 9.07/9.23 (Or (Eq (ilf_type a_2 (relation_type a a_1)) False) (Eq (ilf_type a_2 (subset_type (cross_product a a_1))) True))) % 9.07/9.23 Clause #143 (by forward demodulation #[142, 39]): ∀ (a a_1 a_2 : Iota), % 9.07/9.23 Or (Eq True False) % 9.07/9.23 (Or (Eq (ilf_type a set_type) False) % 9.07/9.23 (Or (Eq (ilf_type a_1 (relation_type a_2 a)) False) (Eq (ilf_type a_1 (subset_type (cross_product a_2 a))) True))) % 9.07/9.23 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 : Iota), % 9.07/9.23 Or (Eq (ilf_type a set_type) False) % 9.07/9.23 (Or (Eq (ilf_type a_1 (relation_type a_2 a)) False) (Eq (ilf_type a_1 (subset_type (cross_product a_2 a))) True)) % 9.07/9.23 Clause #145 (by forward demodulation #[144, 39]): ∀ (a a_1 a_2 : Iota), % 9.07/9.23 Or (Eq True False) % 9.07/9.23 (Or (Eq (ilf_type a (relation_type a_1 a_2)) False) (Eq (ilf_type a (subset_type (cross_product a_1 a_2))) True)) % 9.07/9.23 Clause #146 (by clausification #[145]): ∀ (a a_1 a_2 : Iota), % 9.07/9.23 Or (Eq (ilf_type a (relation_type a_1 a_2)) False) (Eq (ilf_type a (subset_type (cross_product a_1 a_2))) True) % 9.07/9.23 Clause #200 (by clausification #[34]): Eq % 9.07/9.23 (∀ (B : Iota), % 9.07/9.23 ilf_type B set_type → % 9.07/9.23 ∀ (C : Iota), % 9.07/9.23 ilf_type C set_type → % 9.07/9.23 ∀ (D : Iota), ilf_type D (relation_type C B) → ilf_type D (relation_type C empty_set) → Eq D empty_set) % 9.07/9.23 False % 9.07/9.23 Clause #201 (by clausification #[200]): ∀ (a : Iota), % 9.07/9.23 Eq % 9.07/9.23 (Not % 9.07/9.23 (ilf_type (skS.0 6 a) set_type → % 9.07/9.23 ∀ (C : Iota), % 9.07/9.23 ilf_type C set_type → % 9.07/9.23 ∀ (D : Iota), % 9.07/9.23 ilf_type D (relation_type C (skS.0 6 a)) → ilf_type D (relation_type C empty_set) → Eq D empty_set)) % 9.07/9.25 True % 9.07/9.25 Clause #202 (by clausification #[201]): ∀ (a : Iota), % 9.07/9.25 Eq % 9.07/9.25 (ilf_type (skS.0 6 a) set_type → % 9.07/9.25 ∀ (C : Iota), % 9.07/9.25 ilf_type C set_type → % 9.07/9.25 ∀ (D : Iota), % 9.07/9.25 ilf_type D (relation_type C (skS.0 6 a)) → ilf_type D (relation_type C empty_set) → Eq D empty_set) % 9.07/9.25 False % 9.07/9.25 Clause #204 (by clausification #[202]): ∀ (a : Iota), % 9.07/9.25 Eq % 9.07/9.25 (∀ (C : Iota), % 9.07/9.25 ilf_type C set_type → % 9.07/9.25 ∀ (D : Iota), % 9.07/9.25 ilf_type D (relation_type C (skS.0 6 a)) → ilf_type D (relation_type C empty_set) → Eq D empty_set) % 9.07/9.25 False % 9.07/9.25 Clause #205 (by clausification #[204]): ∀ (a a_1 : Iota), % 9.07/9.25 Eq % 9.07/9.25 (Not % 9.07/9.25 (ilf_type (skS.0 7 a a_1) set_type → % 9.07/9.25 ∀ (D : Iota), % 9.07/9.25 ilf_type D (relation_type (skS.0 7 a a_1) (skS.0 6 a)) → % 9.07/9.25 ilf_type D (relation_type (skS.0 7 a a_1) empty_set) → Eq D empty_set)) % 9.07/9.25 True % 9.07/9.25 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), % 9.07/9.25 Eq % 9.07/9.25 (ilf_type (skS.0 7 a a_1) set_type → % 9.07/9.25 ∀ (D : Iota), % 9.07/9.25 ilf_type D (relation_type (skS.0 7 a a_1) (skS.0 6 a)) → % 9.07/9.25 ilf_type D (relation_type (skS.0 7 a a_1) empty_set) → Eq D empty_set) % 9.07/9.25 False % 9.07/9.25 Clause #208 (by clausification #[206]): ∀ (a a_1 : Iota), % 9.07/9.25 Eq % 9.07/9.25 (∀ (D : Iota), % 9.07/9.25 ilf_type D (relation_type (skS.0 7 a a_1) (skS.0 6 a)) → % 9.07/9.25 ilf_type D (relation_type (skS.0 7 a a_1) empty_set) → Eq D empty_set) % 9.07/9.25 False % 9.07/9.25 Clause #209 (by clausification #[208]): ∀ (a a_1 a_2 : Iota), % 9.07/9.25 Eq % 9.07/9.25 (Not % 9.07/9.25 (ilf_type (skS.0 8 a a_1 a_2) (relation_type (skS.0 7 a a_1) (skS.0 6 a)) → % 9.07/9.25 ilf_type (skS.0 8 a a_1 a_2) (relation_type (skS.0 7 a a_1) empty_set) → Eq (skS.0 8 a a_1 a_2) empty_set)) % 9.07/9.25 True % 9.07/9.25 Clause #210 (by clausification #[209]): ∀ (a a_1 a_2 : Iota), % 9.07/9.25 Eq % 9.07/9.25 (ilf_type (skS.0 8 a a_1 a_2) (relation_type (skS.0 7 a a_1) (skS.0 6 a)) → % 9.07/9.25 ilf_type (skS.0 8 a a_1 a_2) (relation_type (skS.0 7 a a_1) empty_set) → Eq (skS.0 8 a a_1 a_2) empty_set) % 9.07/9.25 False % 9.07/9.25 Clause #211 (by clausification #[210]): ∀ (a a_1 a_2 : Iota), Eq (ilf_type (skS.0 8 a a_1 a_2) (relation_type (skS.0 7 a a_1) (skS.0 6 a))) True % 9.07/9.25 Clause #212 (by clausification #[210]): ∀ (a a_1 a_2 : Iota), % 9.07/9.25 Eq (ilf_type (skS.0 8 a a_1 a_2) (relation_type (skS.0 7 a a_1) empty_set) → Eq (skS.0 8 a a_1 a_2) empty_set) False % 9.07/9.25 Clause #214 (by superposition #[211, 146]): ∀ (a a_1 a_2 : Iota), % 9.07/9.25 Or (Eq True False) (Eq (ilf_type (skS.0 8 a a_1 a_2) (subset_type (cross_product (skS.0 7 a a_1) (skS.0 6 a)))) True) % 9.07/9.25 Clause #215 (by clausification #[13]): ∀ (a : Iota), % 9.07/9.25 Eq (ilf_type a set_type → Iff (ilf_type a binary_relation_type) (And (relation_like a) (ilf_type a set_type))) True % 9.07/9.25 Clause #216 (by clausification #[215]): ∀ (a : Iota), % 9.07/9.25 Or (Eq (ilf_type a set_type) False) % 9.07/9.25 (Eq (Iff (ilf_type a binary_relation_type) (And (relation_like a) (ilf_type a set_type))) True) % 9.07/9.25 Clause #217 (by clausification #[216]): ∀ (a : Iota), % 9.07/9.25 Or (Eq (ilf_type a set_type) False) % 9.07/9.25 (Or (Eq (ilf_type a binary_relation_type) True) (Eq (And (relation_like a) (ilf_type a set_type)) False)) % 9.07/9.25 Clause #219 (by clausification #[217]): ∀ (a : Iota), % 9.07/9.25 Or (Eq (ilf_type a set_type) False) % 9.07/9.25 (Or (Eq (ilf_type a binary_relation_type) True) (Or (Eq (relation_like a) False) (Eq (ilf_type a set_type) False))) % 9.07/9.25 Clause #220 (by eliminate duplicate literals #[219]): ∀ (a : Iota), % 9.07/9.25 Or (Eq (ilf_type a set_type) False) (Or (Eq (ilf_type a binary_relation_type) True) (Eq (relation_like a) False)) % 9.07/9.25 Clause #221 (by forward demodulation #[220, 39]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (ilf_type a binary_relation_type) True) (Eq (relation_like a) False)) % 9.07/9.25 Clause #222 (by clausification #[221]): ∀ (a : Iota), Or (Eq (ilf_type a binary_relation_type) True) (Eq (relation_like a) False) % 9.07/9.25 Clause #308 (by clausification #[212]): ∀ (a a_1 a_2 : Iota), Eq (ilf_type (skS.0 8 a a_1 a_2) (relation_type (skS.0 7 a a_1) empty_set)) True % 9.07/9.25 Clause #309 (by clausification #[212]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 8 a a_1 a_2) empty_set) False % 9.07/9.25 Clause #310 (by superposition #[308, 98]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (subset (range_of (skS.0 8 a a_1 a_2)) empty_set) True) % 9.07/9.27 Clause #314 (by clausification #[309]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 8 a a_1 a_2) empty_set % 9.07/9.27 Clause #371 (by clausification #[310]): ∀ (a a_1 a_2 : Iota), Eq (subset (range_of (skS.0 8 a a_1 a_2)) empty_set) True % 9.07/9.27 Clause #372 (by superposition #[371, 49]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (range_of (skS.0 8 a a_1 a_2)) empty_set) % 9.07/9.27 Clause #373 (by clausification #[372]): ∀ (a a_1 a_2 : Iota), Eq (range_of (skS.0 8 a a_1 a_2)) empty_set % 9.07/9.27 Clause #484 (by clausification #[214]): ∀ (a a_1 a_2 : Iota), Eq (ilf_type (skS.0 8 a a_1 a_2) (subset_type (cross_product (skS.0 7 a a_1) (skS.0 6 a)))) True % 9.07/9.27 Clause #485 (by superposition #[484, 82]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (relation_like (skS.0 8 a a_1 a_2)) True) % 9.07/9.27 Clause #488 (by clausification #[485]): ∀ (a a_1 a_2 : Iota), Eq (relation_like (skS.0 8 a a_1 a_2)) True % 9.07/9.27 Clause #489 (by superposition #[488, 222]): ∀ (a a_1 a_2 : Iota), Or (Eq (ilf_type (skS.0 8 a a_1 a_2) binary_relation_type) True) (Eq True False) % 9.07/9.27 Clause #490 (by clausification #[489]): ∀ (a a_1 a_2 : Iota), Eq (ilf_type (skS.0 8 a a_1 a_2) binary_relation_type) True % 9.07/9.27 Clause #491 (by superposition #[490, 66]): ∀ (a a_1 a_2 : Iota), % 9.07/9.27 Or (Eq True False) (Or (Eq (skS.0 8 a a_1 a_2) empty_set) (Ne (range_of (skS.0 8 a a_1 a_2)) empty_set)) % 9.07/9.27 Clause #1080 (by clausification #[491]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 8 a a_1 a_2) empty_set) (Ne (range_of (skS.0 8 a a_1 a_2)) empty_set) % 9.07/9.27 Clause #1081 (by forward demodulation #[1080, 373]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 8 a a_1 a_2) empty_set) (Ne empty_set empty_set) % 9.07/9.27 Clause #1082 (by eliminate resolved literals #[1081]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 8 a a_1 a_2) empty_set % 9.07/9.27 Clause #1083 (by forward contextual literal cutting #[1082, 314]): False % 9.07/9.27 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------