%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET676+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:00:23 PM UTC 2025 % Result : Theorem 6.12s 6.30s % Output : Proof 6.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SET676+3 : TPTP v9.2.0. Released v2.2.0. % 0.03/0.12 % Command : duper %s % 0.11/0.33 % Computer : n009.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Thu Oct 2 14:48:53 EDT 2025 % 0.11/0.33 % CPUTime : % 6.12/6.30 SZS status Theorem for theBenchmark.p % 6.12/6.30 SZS output start Proof for theBenchmark.p % 6.12/6.30 Clause #0 (by assumption #[]): Eq % 6.12/6.30 (∀ (B : Iota), % 6.12/6.30 ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product B C) (relation_type B C)) % 6.12/6.30 True % 6.12/6.30 Clause #3 (by assumption #[]): Eq % 6.12/6.30 (∀ (B : Iota), % 6.12/6.30 ilf_type B set_type → % 6.12/6.30 ∀ (C : Iota), % 6.12/6.30 ilf_type C set_type → Iff (ilf_type C (identity_relation_of_type B)) (ilf_type C (relation_type B B))) % 6.12/6.30 True % 6.12/6.30 Clause #18 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True % 6.12/6.30 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 % 6.12/6.30 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (ilf_type a set_type) True % 6.12/6.30 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 % 6.12/6.30 Clause #35 (by clausification #[34]): ∀ (a : Iota), % 6.12/6.30 Eq % 6.12/6.30 (Not % 6.12/6.30 (ilf_type (skS.0 0 a) set_type → % 6.12/6.30 ilf_type (cross_product (skS.0 0 a) (skS.0 0 a)) (identity_relation_of_type (skS.0 0 a)))) % 6.12/6.30 True % 6.12/6.30 Clause #36 (by clausification #[35]): ∀ (a : Iota), % 6.12/6.30 Eq % 6.12/6.30 (ilf_type (skS.0 0 a) set_type → % 6.12/6.30 ilf_type (cross_product (skS.0 0 a) (skS.0 0 a)) (identity_relation_of_type (skS.0 0 a))) % 6.12/6.30 False % 6.12/6.30 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 % 6.12/6.30 Clause #46 (by clausification #[0]): ∀ (a : Iota), % 6.12/6.30 Eq (ilf_type a set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product a C) (relation_type a C)) True % 6.12/6.30 Clause #47 (by clausification #[46]): ∀ (a : Iota), % 6.12/6.30 Or (Eq (ilf_type a set_type) False) % 6.12/6.30 (Eq (∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product a C) (relation_type a C)) True) % 6.12/6.30 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 6.12/6.30 Or (Eq (ilf_type a set_type) False) % 6.12/6.30 (Eq (ilf_type a_1 set_type → ilf_type (cross_product a a_1) (relation_type a a_1)) True) % 6.12/6.30 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 6.12/6.30 Or (Eq (ilf_type a set_type) False) % 6.12/6.30 (Or (Eq (ilf_type a_1 set_type) False) (Eq (ilf_type (cross_product a a_1) (relation_type a a_1)) True)) % 6.12/6.30 Clause #50 (by forward demodulation #[49, 20]): ∀ (a a_1 : Iota), % 6.12/6.30 Or (Eq True False) % 6.12/6.30 (Or (Eq (ilf_type a set_type) False) (Eq (ilf_type (cross_product a_1 a) (relation_type a_1 a)) True)) % 6.12/6.30 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) % 6.12/6.30 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) % 6.12/6.30 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (ilf_type (cross_product a a_1) (relation_type a a_1)) True % 6.12/6.30 Clause #154 (by clausification #[3]): ∀ (a : Iota), % 6.12/6.30 Eq % 6.12/6.30 (ilf_type a set_type → % 6.12/6.30 ∀ (C : Iota), % 6.12/6.30 ilf_type C set_type → Iff (ilf_type C (identity_relation_of_type a)) (ilf_type C (relation_type a a))) % 6.12/6.30 True % 6.12/6.30 Clause #155 (by clausification #[154]): ∀ (a : Iota), % 6.12/6.30 Or (Eq (ilf_type a set_type) False) % 6.12/6.30 (Eq % 6.12/6.30 (∀ (C : Iota), % 6.12/6.30 ilf_type C set_type → Iff (ilf_type C (identity_relation_of_type a)) (ilf_type C (relation_type a a))) % 6.12/6.30 True) % 6.12/6.30 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota), % 6.12/6.30 Or (Eq (ilf_type a set_type) False) % 6.12/6.30 (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))) % 6.12/6.30 True) % 6.12/6.30 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota), % 6.12/6.30 Or (Eq (ilf_type a set_type) False) % 6.12/6.30 (Or (Eq (ilf_type a_1 set_type) False) % 6.12/6.30 (Eq (Iff (ilf_type a_1 (identity_relation_of_type a)) (ilf_type a_1 (relation_type a a))) True)) % 6.12/6.30 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), % 6.12/6.30 Or (Eq (ilf_type a set_type) False) % 6.12/6.30 (Or (Eq (ilf_type a_1 set_type) False) % 6.12/6.30 (Or (Eq (ilf_type a_1 (identity_relation_of_type a)) True) (Eq (ilf_type a_1 (relation_type a a)) False))) % 6.12/6.31 Clause #160 (by forward demodulation #[158, 20]): ∀ (a a_1 : Iota), % 6.12/6.31 Or (Eq True False) % 6.12/6.31 (Or (Eq (ilf_type a set_type) False) % 6.12/6.31 (Or (Eq (ilf_type a (identity_relation_of_type a_1)) True) (Eq (ilf_type a (relation_type a_1 a_1)) False))) % 6.12/6.31 Clause #161 (by clausification #[160]): ∀ (a a_1 : Iota), % 6.12/6.31 Or (Eq (ilf_type a set_type) False) % 6.12/6.31 (Or (Eq (ilf_type a (identity_relation_of_type a_1)) True) (Eq (ilf_type a (relation_type a_1 a_1)) False)) % 6.12/6.31 Clause #162 (by forward demodulation #[161, 20]): ∀ (a a_1 : Iota), % 6.12/6.31 Or (Eq True False) % 6.12/6.31 (Or (Eq (ilf_type a (identity_relation_of_type a_1)) True) (Eq (ilf_type a (relation_type a_1 a_1)) False)) % 6.12/6.31 Clause #163 (by clausification #[162]): ∀ (a a_1 : Iota), % 6.12/6.31 Or (Eq (ilf_type a (identity_relation_of_type a_1)) True) (Eq (ilf_type a (relation_type a_1 a_1)) False) % 6.12/6.31 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) % 6.12/6.31 Clause #166 (by clausification #[164]): ∀ (a : Iota), Eq (ilf_type (cross_product a a) (identity_relation_of_type a)) True % 6.12/6.31 Clause #245 (by superposition #[38, 166]): Eq True False % 6.12/6.31 Clause #246 (by clausification #[245]): False % 6.12/6.31 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------