TSTP Solution File: SET676+3 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n025.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 14:47:20 EDT 2023
% Result : Theorem 3.79s 3.97s
% Output : Proof 3.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n025.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 : Sat Aug 26 12:26:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.79/3.97 SZS status Theorem for theBenchmark.p
% 3.79/3.97 SZS output start Proof for theBenchmark.p
% 3.79/3.97 Clause #0 (by assumption #[]): Eq
% 3.79/3.97 (∀ (B : Iota),
% 3.79/3.97 ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product B C) (relation_type B C))
% 3.79/3.97 True
% 3.79/3.97 Clause #3 (by assumption #[]): Eq
% 3.79/3.97 (∀ (B : Iota),
% 3.79/3.97 ilf_type B set_type →
% 3.79/3.97 ∀ (C : Iota),
% 3.79/3.97 ilf_type C set_type → Iff (ilf_type C (identity_relation_of_type B)) (ilf_type C (relation_type B B)))
% 3.79/3.97 True
% 3.79/3.97 Clause #18 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True
% 3.79/3.97 Clause #19 (by assumption #[]): Eq (Not (∀ (B : Iota), ilf_type B set_type → ilf_type (cross_product B B) (identity_relation_of_type B))) True
% 3.79/3.97 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (ilf_type a set_type) True
% 3.79/3.97 Clause #34 (by clausification #[19]): Eq (∀ (B : Iota), ilf_type B set_type → ilf_type (cross_product B B) (identity_relation_of_type B)) False
% 3.79/3.97 Clause #35 (by clausification #[34]): ∀ (a : Iota),
% 3.79/3.97 Eq
% 3.79/3.97 (Not
% 3.79/3.97 (ilf_type (skS.0 0 a) set_type →
% 3.79/3.97 ilf_type (cross_product (skS.0 0 a) (skS.0 0 a)) (identity_relation_of_type (skS.0 0 a))))
% 3.79/3.97 True
% 3.79/3.97 Clause #36 (by clausification #[35]): ∀ (a : Iota),
% 3.79/3.97 Eq
% 3.79/3.97 (ilf_type (skS.0 0 a) set_type →
% 3.79/3.97 ilf_type (cross_product (skS.0 0 a) (skS.0 0 a)) (identity_relation_of_type (skS.0 0 a)))
% 3.79/3.97 False
% 3.79/3.97 Clause #38 (by clausification #[36]): ∀ (a : Iota), Eq (ilf_type (cross_product (skS.0 0 a) (skS.0 0 a)) (identity_relation_of_type (skS.0 0 a))) False
% 3.79/3.97 Clause #46 (by clausification #[0]): ∀ (a : Iota),
% 3.79/3.97 Eq (ilf_type a set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product a C) (relation_type a C)) True
% 3.79/3.97 Clause #47 (by clausification #[46]): ∀ (a : Iota),
% 3.79/3.97 Or (Eq (ilf_type a set_type) False)
% 3.79/3.97 (Eq (∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product a C) (relation_type a C)) True)
% 3.79/3.97 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota),
% 3.79/3.97 Or (Eq (ilf_type a set_type) False)
% 3.79/3.97 (Eq (ilf_type a_1 set_type → ilf_type (cross_product a a_1) (relation_type a a_1)) True)
% 3.79/3.97 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota),
% 3.79/3.97 Or (Eq (ilf_type a set_type) False)
% 3.79/3.97 (Or (Eq (ilf_type a_1 set_type) False) (Eq (ilf_type (cross_product a a_1) (relation_type a a_1)) True))
% 3.79/3.97 Clause #50 (by forward demodulation #[49, 20]): ∀ (a a_1 : Iota),
% 3.79/3.97 Or (Eq True False)
% 3.79/3.97 (Or (Eq (ilf_type a set_type) False) (Eq (ilf_type (cross_product a_1 a) (relation_type a_1 a)) True))
% 3.79/3.97 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (ilf_type a set_type) False) (Eq (ilf_type (cross_product a_1 a) (relation_type a_1 a)) True)
% 3.79/3.97 Clause #52 (by forward demodulation #[51, 20]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ilf_type (cross_product a a_1) (relation_type a a_1)) True)
% 3.79/3.97 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (ilf_type (cross_product a a_1) (relation_type a a_1)) True
% 3.79/3.97 Clause #154 (by clausification #[3]): ∀ (a : Iota),
% 3.79/3.97 Eq
% 3.79/3.97 (ilf_type a set_type →
% 3.79/3.97 ∀ (C : Iota),
% 3.79/3.97 ilf_type C set_type → Iff (ilf_type C (identity_relation_of_type a)) (ilf_type C (relation_type a a)))
% 3.79/3.97 True
% 3.79/3.97 Clause #155 (by clausification #[154]): ∀ (a : Iota),
% 3.79/3.97 Or (Eq (ilf_type a set_type) False)
% 3.79/3.97 (Eq
% 3.79/3.97 (∀ (C : Iota),
% 3.79/3.97 ilf_type C set_type → Iff (ilf_type C (identity_relation_of_type a)) (ilf_type C (relation_type a a)))
% 3.79/3.97 True)
% 3.79/3.97 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota),
% 3.79/3.97 Or (Eq (ilf_type a set_type) False)
% 3.79/3.97 (Eq (ilf_type a_1 set_type → Iff (ilf_type a_1 (identity_relation_of_type a)) (ilf_type a_1 (relation_type a a)))
% 3.79/3.97 True)
% 3.79/3.97 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota),
% 3.79/3.97 Or (Eq (ilf_type a set_type) False)
% 3.79/3.97 (Or (Eq (ilf_type a_1 set_type) False)
% 3.79/3.97 (Eq (Iff (ilf_type a_1 (identity_relation_of_type a)) (ilf_type a_1 (relation_type a a))) True))
% 3.79/3.97 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota),
% 3.79/3.97 Or (Eq (ilf_type a set_type) False)
% 3.79/3.97 (Or (Eq (ilf_type a_1 set_type) False)
% 3.79/3.97 (Or (Eq (ilf_type a_1 (identity_relation_of_type a)) True) (Eq (ilf_type a_1 (relation_type a a)) False)))
% 3.79/3.98 Clause #160 (by forward demodulation #[158, 20]): ∀ (a a_1 : Iota),
% 3.79/3.98 Or (Eq True False)
% 3.79/3.98 (Or (Eq (ilf_type a set_type) False)
% 3.79/3.98 (Or (Eq (ilf_type a (identity_relation_of_type a_1)) True) (Eq (ilf_type a (relation_type a_1 a_1)) False)))
% 3.79/3.98 Clause #161 (by clausification #[160]): ∀ (a a_1 : Iota),
% 3.79/3.98 Or (Eq (ilf_type a set_type) False)
% 3.79/3.98 (Or (Eq (ilf_type a (identity_relation_of_type a_1)) True) (Eq (ilf_type a (relation_type a_1 a_1)) False))
% 3.79/3.98 Clause #162 (by forward demodulation #[161, 20]): ∀ (a a_1 : Iota),
% 3.79/3.98 Or (Eq True False)
% 3.79/3.98 (Or (Eq (ilf_type a (identity_relation_of_type a_1)) True) (Eq (ilf_type a (relation_type a_1 a_1)) False))
% 3.79/3.98 Clause #163 (by clausification #[162]): ∀ (a a_1 : Iota),
% 3.79/3.98 Or (Eq (ilf_type a (identity_relation_of_type a_1)) True) (Eq (ilf_type a (relation_type a_1 a_1)) False)
% 3.79/3.98 Clause #164 (by superposition #[163, 53]): ∀ (a : Iota), Or (Eq (ilf_type (cross_product a a) (identity_relation_of_type a)) True) (Eq False True)
% 3.79/3.98 Clause #166 (by clausification #[164]): ∀ (a : Iota), Eq (ilf_type (cross_product a a) (identity_relation_of_type a)) True
% 3.79/3.98 Clause #245 (by superposition #[38, 166]): Eq True False
% 3.79/3.98 Clause #246 (by clausification #[245]): False
% 3.79/3.98 SZS output end Proof for theBenchmark.p
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