TSTP Solution File: SET642+3 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 : Thu Aug 31 14:47:14 EDT 2023
% Result : Theorem 111.39s 111.65s
% Output : Proof 111.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% 0.01/0.12 % Command : duper %s
% 0.08/0.30 % Computer : n002.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Sat Aug 26 11:52:18 EDT 2023
% 0.08/0.31 % CPUTime :
% 111.39/111.65 SZS status Theorem for theBenchmark.p
% 111.39/111.65 SZS output start Proof for theBenchmark.p
% 111.39/111.65 Clause #0 (by assumption #[]): Eq
% 111.39/111.65 (∀ (B : Iota),
% 111.39/111.65 ilf_type B set_type →
% 111.39/111.65 ∀ (C : Iota),
% 111.39/111.65 ilf_type C set_type →
% 111.39/111.65 ∀ (D : Iota),
% 111.39/111.65 ilf_type D set_type →
% 111.39/111.65 ∀ (E : Iota), ilf_type E (relation_type C D) → subset B E → subset B (cross_product C D))
% 111.39/111.65 True
% 111.39/111.65 Clause #1 (by assumption #[]): Eq
% 111.39/111.65 (∀ (B : Iota),
% 111.39/111.65 ilf_type B set_type →
% 111.39/111.65 ∀ (C : Iota),
% 111.39/111.65 ilf_type C set_type →
% 111.39/111.65 ∀ (D : Iota), ilf_type D set_type → subset B (cross_product C D) → ilf_type B (relation_type C D))
% 111.39/111.65 True
% 111.39/111.65 Clause #18 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True
% 111.39/111.65 Clause #19 (by assumption #[]): Eq
% 111.39/111.65 (Not
% 111.39/111.65 (∀ (B : Iota),
% 111.39/111.65 ilf_type B set_type →
% 111.39/111.65 ∀ (C : Iota),
% 111.39/111.65 ilf_type C set_type →
% 111.39/111.65 ∀ (D : Iota),
% 111.39/111.65 ilf_type D set_type →
% 111.39/111.65 ∀ (E : Iota), ilf_type E (relation_type C D) → subset B E → ilf_type B (relation_type C D)))
% 111.39/111.65 True
% 111.39/111.65 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (ilf_type a set_type) True
% 111.39/111.65 Clause #44 (by clausification #[0]): ∀ (a : Iota),
% 111.39/111.65 Eq
% 111.39/111.65 (ilf_type a set_type →
% 111.39/111.65 ∀ (C : Iota),
% 111.39/111.65 ilf_type C set_type →
% 111.39/111.65 ∀ (D : Iota),
% 111.39/111.65 ilf_type D set_type →
% 111.39/111.65 ∀ (E : Iota), ilf_type E (relation_type C D) → subset a E → subset a (cross_product C D))
% 111.39/111.65 True
% 111.39/111.65 Clause #45 (by clausification #[44]): ∀ (a : Iota),
% 111.39/111.65 Or (Eq (ilf_type a set_type) False)
% 111.39/111.65 (Eq
% 111.39/111.65 (∀ (C : Iota),
% 111.39/111.65 ilf_type C set_type →
% 111.39/111.65 ∀ (D : Iota),
% 111.39/111.65 ilf_type D set_type →
% 111.39/111.65 ∀ (E : Iota), ilf_type E (relation_type C D) → subset a E → subset a (cross_product C D))
% 111.39/111.65 True)
% 111.39/111.65 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota),
% 111.39/111.65 Or (Eq (ilf_type a set_type) False)
% 111.39/111.65 (Eq
% 111.39/111.65 (ilf_type a_1 set_type →
% 111.39/111.65 ∀ (D : Iota),
% 111.39/111.65 ilf_type D set_type →
% 111.39/111.65 ∀ (E : Iota), ilf_type E (relation_type a_1 D) → subset a E → subset a (cross_product a_1 D))
% 111.39/111.65 True)
% 111.39/111.65 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota),
% 111.39/111.65 Or (Eq (ilf_type a set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.65 (Eq
% 111.39/111.65 (∀ (D : Iota),
% 111.39/111.65 ilf_type D set_type →
% 111.39/111.65 ∀ (E : Iota), ilf_type E (relation_type a_1 D) → subset a E → subset a (cross_product a_1 D))
% 111.39/111.65 True))
% 111.39/111.65 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.65 Or (Eq (ilf_type a set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.65 (Eq
% 111.39/111.65 (ilf_type a_2 set_type →
% 111.39/111.65 ∀ (E : Iota), ilf_type E (relation_type a_1 a_2) → subset a E → subset a (cross_product a_1 a_2))
% 111.39/111.65 True))
% 111.39/111.65 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.65 Or (Eq (ilf_type a set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_2 set_type) False)
% 111.39/111.65 (Eq (∀ (E : Iota), ilf_type E (relation_type a_1 a_2) → subset a E → subset a (cross_product a_1 a_2)) True)))
% 111.39/111.65 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.65 Or (Eq (ilf_type a set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_2 set_type) False)
% 111.39/111.65 (Eq (ilf_type a_3 (relation_type a_1 a_2) → subset a a_3 → subset a (cross_product a_1 a_2)) True)))
% 111.39/111.65 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.65 Or (Eq (ilf_type a set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_2 set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_3 (relation_type a_1 a_2)) False)
% 111.39/111.65 (Eq (subset a a_3 → subset a (cross_product a_1 a_2)) True))))
% 111.39/111.65 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.65 Or (Eq (ilf_type a set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_2 set_type) False)
% 111.39/111.65 (Or (Eq (ilf_type a_3 (relation_type a_1 a_2)) False)
% 111.39/111.65 (Or (Eq (subset a a_3) False) (Eq (subset a (cross_product a_1 a_2)) True)))))
% 111.39/111.65 Clause #53 (by forward demodulation #[52, 20]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.67 Or (Eq True False)
% 111.39/111.67 (Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_2 (relation_type a a_1)) False)
% 111.39/111.67 (Or (Eq (subset a_3 a_2) False) (Eq (subset a_3 (cross_product a a_1)) True)))))
% 111.39/111.67 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_2 (relation_type a a_1)) False)
% 111.39/111.67 (Or (Eq (subset a_3 a_2) False) (Eq (subset a_3 (cross_product a a_1)) True))))
% 111.39/111.67 Clause #55 (by forward demodulation #[54, 20]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.67 Or (Eq True False)
% 111.39/111.67 (Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 (relation_type a_2 a)) False)
% 111.39/111.67 (Or (Eq (subset a_3 a_1) False) (Eq (subset a_3 (cross_product a_2 a)) True))))
% 111.39/111.67 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 (relation_type a_2 a)) False)
% 111.39/111.67 (Or (Eq (subset a_3 a_1) False) (Eq (subset a_3 (cross_product a_2 a)) True)))
% 111.39/111.67 Clause #57 (by forward demodulation #[56, 20]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.67 Or (Eq True False)
% 111.39/111.67 (Or (Eq (ilf_type a (relation_type a_1 a_2)) False)
% 111.39/111.67 (Or (Eq (subset a_3 a) False) (Eq (subset a_3 (cross_product a_1 a_2)) True)))
% 111.39/111.67 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a (relation_type a_1 a_2)) False)
% 111.39/111.67 (Or (Eq (subset a_3 a) False) (Eq (subset a_3 (cross_product a_1 a_2)) True))
% 111.39/111.67 Clause #98 (by clausification #[1]): ∀ (a : Iota),
% 111.39/111.67 Eq
% 111.39/111.67 (ilf_type a set_type →
% 111.39/111.67 ∀ (C : Iota),
% 111.39/111.67 ilf_type C set_type →
% 111.39/111.67 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product C D) → ilf_type a (relation_type C D))
% 111.39/111.67 True
% 111.39/111.67 Clause #99 (by clausification #[98]): ∀ (a : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Eq
% 111.39/111.67 (∀ (C : Iota),
% 111.39/111.67 ilf_type C set_type →
% 111.39/111.67 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product C D) → ilf_type a (relation_type C D))
% 111.39/111.67 True)
% 111.39/111.67 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Eq
% 111.39/111.67 (ilf_type a_1 set_type →
% 111.39/111.67 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product a_1 D) → ilf_type a (relation_type a_1 D))
% 111.39/111.67 True)
% 111.39/111.67 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.67 (Eq (∀ (D : Iota), ilf_type D set_type → subset a (cross_product a_1 D) → ilf_type a (relation_type a_1 D)) True))
% 111.39/111.67 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.67 (Eq (ilf_type a_2 set_type → subset a (cross_product a_1 a_2) → ilf_type a (relation_type a_1 a_2)) True))
% 111.39/111.67 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_2 set_type) False)
% 111.39/111.67 (Eq (subset a (cross_product a_1 a_2) → ilf_type a (relation_type a_1 a_2)) True)))
% 111.39/111.67 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_2 set_type) False)
% 111.39/111.67 (Or (Eq (subset a (cross_product a_1 a_2)) False) (Eq (ilf_type a (relation_type a_1 a_2)) True))))
% 111.39/111.67 Clause #105 (by forward demodulation #[104, 20]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.67 Or (Eq True False)
% 111.39/111.67 (Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.67 (Or (Eq (subset a_2 (cross_product a a_1)) False) (Eq (ilf_type a_2 (relation_type a a_1)) True))))
% 111.39/111.67 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.67 Or (Eq (ilf_type a set_type) False)
% 111.39/111.67 (Or (Eq (ilf_type a_1 set_type) False)
% 111.39/111.67 (Or (Eq (subset a_2 (cross_product a a_1)) False) (Eq (ilf_type a_2 (relation_type a a_1)) True)))
% 111.39/111.67 Clause #107 (by forward demodulation #[106, 20]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.69 Or (Eq True False)
% 111.39/111.69 (Or (Eq (ilf_type a set_type) False)
% 111.39/111.69 (Or (Eq (subset a_1 (cross_product a_2 a)) False) (Eq (ilf_type a_1 (relation_type a_2 a)) True)))
% 111.39/111.69 Clause #108 (by clausification #[107]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.69 Or (Eq (ilf_type a set_type) False)
% 111.39/111.69 (Or (Eq (subset a_1 (cross_product a_2 a)) False) (Eq (ilf_type a_1 (relation_type a_2 a)) True))
% 111.39/111.69 Clause #109 (by forward demodulation #[108, 20]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.69 Or (Eq True False) (Or (Eq (subset a (cross_product a_1 a_2)) False) (Eq (ilf_type a (relation_type a_1 a_2)) True))
% 111.39/111.69 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a (cross_product a_1 a_2)) False) (Eq (ilf_type a (relation_type a_1 a_2)) True)
% 111.39/111.69 Clause #197 (by clausification #[19]): Eq
% 111.39/111.69 (∀ (B : Iota),
% 111.39/111.69 ilf_type B set_type →
% 111.39/111.69 ∀ (C : Iota),
% 111.39/111.69 ilf_type C set_type →
% 111.39/111.69 ∀ (D : Iota),
% 111.39/111.69 ilf_type D set_type →
% 111.39/111.69 ∀ (E : Iota), ilf_type E (relation_type C D) → subset B E → ilf_type B (relation_type C D))
% 111.39/111.69 False
% 111.39/111.69 Clause #198 (by clausification #[197]): ∀ (a : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (Not
% 111.39/111.69 (ilf_type (skS.0 5 a) set_type →
% 111.39/111.69 ∀ (C : Iota),
% 111.39/111.69 ilf_type C set_type →
% 111.39/111.69 ∀ (D : Iota),
% 111.39/111.69 ilf_type D set_type →
% 111.39/111.69 ∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type C D) → subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type C D)))
% 111.39/111.69 True
% 111.39/111.69 Clause #199 (by clausification #[198]): ∀ (a : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (ilf_type (skS.0 5 a) set_type →
% 111.39/111.69 ∀ (C : Iota),
% 111.39/111.69 ilf_type C set_type →
% 111.39/111.69 ∀ (D : Iota),
% 111.39/111.69 ilf_type D set_type →
% 111.39/111.69 ∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type C D) → subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type C D))
% 111.39/111.69 False
% 111.39/111.69 Clause #201 (by clausification #[199]): ∀ (a : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (∀ (C : Iota),
% 111.39/111.69 ilf_type C set_type →
% 111.39/111.69 ∀ (D : Iota),
% 111.39/111.69 ilf_type D set_type →
% 111.39/111.69 ∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type C D) → subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type C D))
% 111.39/111.69 False
% 111.39/111.69 Clause #219 (by clausification #[201]): ∀ (a a_1 : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (Not
% 111.39/111.69 (ilf_type (skS.0 7 a a_1) set_type →
% 111.39/111.69 ∀ (D : Iota),
% 111.39/111.69 ilf_type D set_type →
% 111.39/111.69 ∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type (skS.0 7 a a_1) D) →
% 111.39/111.69 subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) D)))
% 111.39/111.69 True
% 111.39/111.69 Clause #220 (by clausification #[219]): ∀ (a a_1 : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (ilf_type (skS.0 7 a a_1) set_type →
% 111.39/111.69 ∀ (D : Iota),
% 111.39/111.69 ilf_type D set_type →
% 111.39/111.69 ∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type (skS.0 7 a a_1) D) →
% 111.39/111.69 subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) D))
% 111.39/111.69 False
% 111.39/111.69 Clause #222 (by clausification #[220]): ∀ (a a_1 : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (∀ (D : Iota),
% 111.39/111.69 ilf_type D set_type →
% 111.39/111.69 ∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type (skS.0 7 a a_1) D) →
% 111.39/111.69 subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) D))
% 111.39/111.69 False
% 111.39/111.69 Clause #368 (by clausification #[222]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (Not
% 111.39/111.69 (ilf_type (skS.0 9 a a_1 a_2) set_type →
% 111.39/111.69 ∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)) →
% 111.39/111.69 subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2))))
% 111.39/111.69 True
% 111.39/111.69 Clause #369 (by clausification #[368]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (ilf_type (skS.0 9 a a_1 a_2) set_type →
% 111.39/111.69 ∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)) →
% 111.39/111.69 subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)))
% 111.39/111.69 False
% 111.39/111.69 Clause #371 (by clausification #[369]): ∀ (a a_1 a_2 : Iota),
% 111.39/111.69 Eq
% 111.39/111.69 (∀ (E : Iota),
% 111.39/111.69 ilf_type E (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)) →
% 111.39/111.69 subset (skS.0 5 a) E → ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)))
% 111.50/111.78 False
% 111.50/111.78 Clause #700 (by clausification #[371]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.50/111.78 Eq
% 111.50/111.78 (Not
% 111.50/111.78 (ilf_type (skS.0 12 a a_1 a_2 a_3) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)) →
% 111.50/111.78 subset (skS.0 5 a) (skS.0 12 a a_1 a_2 a_3) →
% 111.50/111.78 ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2))))
% 111.50/111.78 True
% 111.50/111.78 Clause #701 (by clausification #[700]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.50/111.78 Eq
% 111.50/111.78 (ilf_type (skS.0 12 a a_1 a_2 a_3) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)) →
% 111.50/111.78 subset (skS.0 5 a) (skS.0 12 a a_1 a_2 a_3) →
% 111.50/111.78 ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)))
% 111.50/111.78 False
% 111.50/111.78 Clause #702 (by clausification #[701]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.50/111.78 Eq (ilf_type (skS.0 12 a a_1 a_2 a_3) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2))) True
% 111.50/111.78 Clause #703 (by clausification #[701]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.50/111.78 Eq
% 111.50/111.78 (subset (skS.0 5 a) (skS.0 12 a a_1 a_2 a_3) →
% 111.50/111.78 ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2)))
% 111.50/111.78 False
% 111.50/111.78 Clause #704 (by superposition #[702, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 111.50/111.78 Or (Eq True False)
% 111.50/111.78 (Or (Eq (subset a (skS.0 12 a_1 a_2 a_3 a_4)) False)
% 111.50/111.78 (Eq (subset a (cross_product (skS.0 7 a_1 a_2) (skS.0 9 a_1 a_2 a_3))) True))
% 111.50/111.78 Clause #923 (by clausification #[703]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 5 a) (skS.0 12 a a_1 a_2 a_3)) True
% 111.50/111.78 Clause #924 (by clausification #[703]): ∀ (a a_1 a_2 : Iota), Eq (ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2))) False
% 111.50/111.78 Clause #9095 (by clausification #[704]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 111.50/111.78 Or (Eq (subset a (skS.0 12 a_1 a_2 a_3 a_4)) False)
% 111.50/111.78 (Eq (subset a (cross_product (skS.0 7 a_1 a_2) (skS.0 9 a_1 a_2 a_3))) True)
% 111.50/111.78 Clause #9096 (by superposition #[9095, 923]): ∀ (a a_1 a_2 : Iota),
% 111.50/111.78 Or (Eq (subset (skS.0 5 a) (cross_product (skS.0 7 a a_1) (skS.0 9 a a_1 a_2))) True) (Eq False True)
% 111.50/111.78 Clause #9105 (by clausification #[9096]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a) (cross_product (skS.0 7 a a_1) (skS.0 9 a a_1 a_2))) True
% 111.50/111.78 Clause #9106 (by superposition #[9105, 110]): ∀ (a a_1 a_2 : Iota),
% 111.50/111.78 Or (Eq True False) (Eq (ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2))) True)
% 111.50/111.78 Clause #9108 (by clausification #[9106]): ∀ (a a_1 a_2 : Iota), Eq (ilf_type (skS.0 5 a) (relation_type (skS.0 7 a a_1) (skS.0 9 a a_1 a_2))) True
% 111.50/111.78 Clause #9109 (by superposition #[9108, 924]): Eq True False
% 111.50/111.78 Clause #9112 (by clausification #[9109]): False
% 111.50/111.78 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------