TSTP Solution File: SET643+3 by Duper---1.0
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% File : Duper---1.0
% Problem : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 5.28s 5.43s
% Output : Proof 5.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : duper %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 10:33:02 EDT 2023
% 0.15/0.36 % CPUTime :
% 5.28/5.43 SZS status Theorem for theBenchmark.p
% 5.28/5.43 SZS output start Proof for theBenchmark.p
% 5.28/5.43 Clause #0 (by assumption #[]): Eq
% 5.28/5.43 (∀ (B : Iota),
% 5.28/5.43 ilf_type B set_type →
% 5.28/5.43 ∀ (C : Iota),
% 5.28/5.43 ilf_type C set_type →
% 5.28/5.43 ∀ (D : Iota), ilf_type D set_type → subset B (cross_product C D) → ilf_type B (relation_type C D))
% 5.28/5.43 True
% 5.28/5.43 Clause #9 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → subset B B) True
% 5.28/5.43 Clause #18 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True
% 5.28/5.43 Clause #19 (by assumption #[]): Eq
% 5.28/5.43 (Not
% 5.28/5.43 (∀ (B : Iota),
% 5.28/5.43 ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product B C) (relation_type B C)))
% 5.28/5.43 True
% 5.28/5.43 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (ilf_type a set_type) True
% 5.28/5.43 Clause #24 (by clausification #[9]): ∀ (a : Iota), Eq (ilf_type a set_type → subset a a) True
% 5.28/5.43 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (subset a a) True)
% 5.28/5.43 Clause #26 (by forward demodulation #[25, 20]): ∀ (a : Iota), Or (Eq True False) (Eq (subset a a) True)
% 5.28/5.43 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (subset a a) True
% 5.28/5.43 Clause #44 (by clausification #[0]): ∀ (a : Iota),
% 5.28/5.43 Eq
% 5.28/5.43 (ilf_type a set_type →
% 5.28/5.43 ∀ (C : Iota),
% 5.28/5.43 ilf_type C set_type →
% 5.28/5.43 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product C D) → ilf_type a (relation_type C D))
% 5.28/5.43 True
% 5.28/5.43 Clause #45 (by clausification #[44]): ∀ (a : Iota),
% 5.28/5.43 Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Eq
% 5.28/5.43 (∀ (C : Iota),
% 5.28/5.43 ilf_type C set_type →
% 5.28/5.43 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product C D) → ilf_type a (relation_type C D))
% 5.28/5.43 True)
% 5.28/5.43 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota),
% 5.28/5.43 Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Eq
% 5.28/5.43 (ilf_type a_1 set_type →
% 5.28/5.43 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product a_1 D) → ilf_type a (relation_type a_1 D))
% 5.28/5.43 True)
% 5.28/5.43 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota),
% 5.28/5.43 Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Or (Eq (ilf_type a_1 set_type) False)
% 5.28/5.43 (Eq (∀ (D : Iota), ilf_type D set_type → subset a (cross_product a_1 D) → ilf_type a (relation_type a_1 D)) True))
% 5.28/5.43 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota),
% 5.28/5.43 Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Or (Eq (ilf_type a_1 set_type) False)
% 5.28/5.43 (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))
% 5.28/5.43 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota),
% 5.28/5.43 Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Or (Eq (ilf_type a_1 set_type) False)
% 5.28/5.43 (Or (Eq (ilf_type a_2 set_type) False)
% 5.28/5.43 (Eq (subset a (cross_product a_1 a_2) → ilf_type a (relation_type a_1 a_2)) True)))
% 5.28/5.43 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota),
% 5.28/5.43 Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Or (Eq (ilf_type a_1 set_type) False)
% 5.28/5.43 (Or (Eq (ilf_type a_2 set_type) False)
% 5.28/5.43 (Or (Eq (subset a (cross_product a_1 a_2)) False) (Eq (ilf_type a (relation_type a_1 a_2)) True))))
% 5.28/5.43 Clause #51 (by forward demodulation #[50, 20]): ∀ (a a_1 a_2 : Iota),
% 5.28/5.43 Or (Eq True False)
% 5.28/5.43 (Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Or (Eq (ilf_type a_1 set_type) False)
% 5.28/5.43 (Or (Eq (subset a_2 (cross_product a a_1)) False) (Eq (ilf_type a_2 (relation_type a a_1)) True))))
% 5.28/5.43 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 5.28/5.43 Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Or (Eq (ilf_type a_1 set_type) False)
% 5.28/5.43 (Or (Eq (subset a_2 (cross_product a a_1)) False) (Eq (ilf_type a_2 (relation_type a a_1)) True)))
% 5.28/5.43 Clause #53 (by forward demodulation #[52, 20]): ∀ (a a_1 a_2 : Iota),
% 5.28/5.43 Or (Eq True False)
% 5.28/5.43 (Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Or (Eq (subset a_1 (cross_product a_2 a)) False) (Eq (ilf_type a_1 (relation_type a_2 a)) True)))
% 5.28/5.43 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 5.28/5.43 Or (Eq (ilf_type a set_type) False)
% 5.28/5.43 (Or (Eq (subset a_1 (cross_product a_2 a)) False) (Eq (ilf_type a_1 (relation_type a_2 a)) True))
% 5.28/5.43 Clause #55 (by forward demodulation #[54, 20]): ∀ (a a_1 a_2 : Iota),
% 5.28/5.44 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))
% 5.28/5.44 Clause #56 (by clausification #[55]): ∀ (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)
% 5.28/5.44 Clause #57 (by superposition #[56, 27]): ∀ (a a_1 : Iota), Or (Eq (ilf_type (cross_product a a_1) (relation_type a a_1)) True) (Eq False True)
% 5.28/5.44 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (ilf_type (cross_product a a_1) (relation_type a a_1)) True
% 5.28/5.44 Clause #139 (by clausification #[19]): Eq
% 5.28/5.44 (∀ (B : Iota),
% 5.28/5.44 ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product B C) (relation_type B C))
% 5.28/5.44 False
% 5.28/5.44 Clause #140 (by clausification #[139]): ∀ (a : Iota),
% 5.28/5.44 Eq
% 5.28/5.44 (Not
% 5.28/5.44 (ilf_type (skS.0 3 a) set_type →
% 5.28/5.44 ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product (skS.0 3 a) C) (relation_type (skS.0 3 a) C)))
% 5.28/5.44 True
% 5.28/5.44 Clause #141 (by clausification #[140]): ∀ (a : Iota),
% 5.28/5.44 Eq
% 5.28/5.44 (ilf_type (skS.0 3 a) set_type →
% 5.28/5.44 ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product (skS.0 3 a) C) (relation_type (skS.0 3 a) C))
% 5.28/5.44 False
% 5.28/5.44 Clause #143 (by clausification #[141]): ∀ (a : Iota),
% 5.28/5.44 Eq (∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product (skS.0 3 a) C) (relation_type (skS.0 3 a) C)) False
% 5.28/5.44 Clause #302 (by clausification #[143]): ∀ (a a_1 : Iota),
% 5.28/5.44 Eq
% 5.28/5.44 (Not
% 5.28/5.44 (ilf_type (skS.0 10 a a_1) set_type →
% 5.28/5.44 ilf_type (cross_product (skS.0 3 a) (skS.0 10 a a_1)) (relation_type (skS.0 3 a) (skS.0 10 a a_1))))
% 5.28/5.44 True
% 5.28/5.44 Clause #303 (by clausification #[302]): ∀ (a a_1 : Iota),
% 5.28/5.44 Eq
% 5.28/5.44 (ilf_type (skS.0 10 a a_1) set_type →
% 5.28/5.44 ilf_type (cross_product (skS.0 3 a) (skS.0 10 a a_1)) (relation_type (skS.0 3 a) (skS.0 10 a a_1)))
% 5.28/5.44 False
% 5.28/5.44 Clause #305 (by clausification #[303]): ∀ (a a_1 : Iota),
% 5.28/5.44 Eq (ilf_type (cross_product (skS.0 3 a) (skS.0 10 a a_1)) (relation_type (skS.0 3 a) (skS.0 10 a a_1))) False
% 5.28/5.44 Clause #650 (by superposition #[305, 58]): Eq False True
% 5.28/5.44 Clause #651 (by clausification #[650]): False
% 5.28/5.44 SZS output end Proof for theBenchmark.p
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