%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET643+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:00:20 PM UTC 2025 % Result : Theorem 5.73s 5.91s % Output : Proof 5.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SET643+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.12 % Command : duper %s % 0.13/0.33 % Computer : n008.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Oct 2 13:43:53 EDT 2025 % 0.13/0.33 % CPUTime : % 5.73/5.91 SZS status Theorem for theBenchmark.p % 5.73/5.91 SZS output start Proof for theBenchmark.p % 5.73/5.91 Clause #0 (by assumption #[]): Eq % 5.73/5.91 (∀ (B : Iota), % 5.73/5.91 ilf_type B set_type → % 5.73/5.91 ∀ (C : Iota), % 5.73/5.91 ilf_type C set_type → % 5.73/5.91 ∀ (D : Iota), ilf_type D set_type → subset B (cross_product C D) → ilf_type B (relation_type C D)) % 5.73/5.91 True % 5.73/5.91 Clause #9 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → subset B B) True % 5.73/5.91 Clause #18 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True % 5.73/5.91 Clause #19 (by assumption #[]): Eq % 5.73/5.91 (Not % 5.73/5.91 (∀ (B : Iota), % 5.73/5.91 ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product B C) (relation_type B C))) % 5.73/5.91 True % 5.73/5.91 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (ilf_type a set_type) True % 5.73/5.91 Clause #24 (by clausification #[9]): ∀ (a : Iota), Eq (ilf_type a set_type → subset a a) True % 5.73/5.91 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (subset a a) True) % 5.73/5.91 Clause #26 (by forward demodulation #[25, 20]): ∀ (a : Iota), Or (Eq True False) (Eq (subset a a) True) % 5.73/5.91 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (subset a a) True % 5.73/5.91 Clause #44 (by clausification #[0]): ∀ (a : Iota), % 5.73/5.91 Eq % 5.73/5.91 (ilf_type a set_type → % 5.73/5.91 ∀ (C : Iota), % 5.73/5.91 ilf_type C set_type → % 5.73/5.91 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product C D) → ilf_type a (relation_type C D)) % 5.73/5.91 True % 5.73/5.91 Clause #45 (by clausification #[44]): ∀ (a : Iota), % 5.73/5.91 Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Eq % 5.73/5.91 (∀ (C : Iota), % 5.73/5.91 ilf_type C set_type → % 5.73/5.91 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product C D) → ilf_type a (relation_type C D)) % 5.73/5.91 True) % 5.73/5.91 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), % 5.73/5.91 Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Eq % 5.73/5.91 (ilf_type a_1 set_type → % 5.73/5.91 ∀ (D : Iota), ilf_type D set_type → subset a (cross_product a_1 D) → ilf_type a (relation_type a_1 D)) % 5.73/5.91 True) % 5.73/5.91 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), % 5.73/5.91 Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Or (Eq (ilf_type a_1 set_type) False) % 5.73/5.91 (Eq (∀ (D : Iota), ilf_type D set_type → subset a (cross_product a_1 D) → ilf_type a (relation_type a_1 D)) True)) % 5.73/5.91 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 5.73/5.91 Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Or (Eq (ilf_type a_1 set_type) False) % 5.73/5.91 (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)) % 5.73/5.91 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), % 5.73/5.91 Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Or (Eq (ilf_type a_1 set_type) False) % 5.73/5.91 (Or (Eq (ilf_type a_2 set_type) False) % 5.73/5.91 (Eq (subset a (cross_product a_1 a_2) → ilf_type a (relation_type a_1 a_2)) True))) % 5.73/5.91 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 5.73/5.91 Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Or (Eq (ilf_type a_1 set_type) False) % 5.73/5.91 (Or (Eq (ilf_type a_2 set_type) False) % 5.73/5.91 (Or (Eq (subset a (cross_product a_1 a_2)) False) (Eq (ilf_type a (relation_type a_1 a_2)) True)))) % 5.73/5.91 Clause #51 (by forward demodulation #[50, 20]): ∀ (a a_1 a_2 : Iota), % 5.73/5.91 Or (Eq True False) % 5.73/5.91 (Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Or (Eq (ilf_type a_1 set_type) False) % 5.73/5.91 (Or (Eq (subset a_2 (cross_product a a_1)) False) (Eq (ilf_type a_2 (relation_type a a_1)) True)))) % 5.73/5.91 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 5.73/5.91 Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Or (Eq (ilf_type a_1 set_type) False) % 5.73/5.91 (Or (Eq (subset a_2 (cross_product a a_1)) False) (Eq (ilf_type a_2 (relation_type a a_1)) True))) % 5.73/5.91 Clause #53 (by forward demodulation #[52, 20]): ∀ (a a_1 a_2 : Iota), % 5.73/5.91 Or (Eq True False) % 5.73/5.91 (Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Or (Eq (subset a_1 (cross_product a_2 a)) False) (Eq (ilf_type a_1 (relation_type a_2 a)) True))) % 5.73/5.91 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 5.73/5.91 Or (Eq (ilf_type a set_type) False) % 5.73/5.91 (Or (Eq (subset a_1 (cross_product a_2 a)) False) (Eq (ilf_type a_1 (relation_type a_2 a)) True)) % 5.73/5.91 Clause #55 (by forward demodulation #[54, 20]): ∀ (a a_1 a_2 : Iota), % 5.73/5.92 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)) % 5.73/5.92 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) % 5.73/5.92 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) % 5.73/5.92 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (ilf_type (cross_product a a_1) (relation_type a a_1)) True % 5.73/5.92 Clause #139 (by clausification #[19]): Eq % 5.73/5.92 (∀ (B : Iota), % 5.73/5.92 ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product B C) (relation_type B C)) % 5.73/5.92 False % 5.73/5.92 Clause #140 (by clausification #[139]): ∀ (a : Iota), % 5.73/5.92 Eq % 5.73/5.92 (Not % 5.73/5.92 (ilf_type (skS.0 3 a) set_type → % 5.73/5.92 ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product (skS.0 3 a) C) (relation_type (skS.0 3 a) C))) % 5.73/5.92 True % 5.73/5.92 Clause #141 (by clausification #[140]): ∀ (a : Iota), % 5.73/5.92 Eq % 5.73/5.92 (ilf_type (skS.0 3 a) set_type → % 5.73/5.92 ∀ (C : Iota), ilf_type C set_type → ilf_type (cross_product (skS.0 3 a) C) (relation_type (skS.0 3 a) C)) % 5.73/5.92 False % 5.73/5.92 Clause #143 (by clausification #[141]): ∀ (a : Iota), % 5.73/5.92 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 % 5.73/5.92 Clause #302 (by clausification #[143]): ∀ (a a_1 : Iota), % 5.73/5.92 Eq % 5.73/5.92 (Not % 5.73/5.92 (ilf_type (skS.0 10 a a_1) set_type → % 5.73/5.92 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)))) % 5.73/5.92 True % 5.73/5.92 Clause #303 (by clausification #[302]): ∀ (a a_1 : Iota), % 5.73/5.92 Eq % 5.73/5.92 (ilf_type (skS.0 10 a a_1) set_type → % 5.73/5.92 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))) % 5.73/5.92 False % 5.73/5.92 Clause #305 (by clausification #[303]): ∀ (a a_1 : Iota), % 5.73/5.92 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 % 5.73/5.92 Clause #650 (by superposition #[305, 58]): Eq False True % 5.73/5.92 Clause #651 (by clausification #[650]): False % 5.73/5.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------