%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET662+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:00:21 PM UTC 2025 % Result : Theorem 4.18s 4.36s % Output : Proof 4.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET662+3 : TPTP v9.2.0. Released v2.2.0. % 0.06/0.13 % Command : duper %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 14:31:08 EDT 2025 % 0.12/0.34 % CPUTime : % 4.18/4.36 SZS status Theorem for theBenchmark.p % 4.18/4.36 SZS output start Proof for theBenchmark.p % 4.18/4.36 Clause #1 (by assumption #[]): Eq % 4.18/4.36 (∀ (B : Iota), % 4.18/4.36 ilf_type B set_type → % 4.18/4.36 ∀ (C : Iota), % 4.18/4.36 ilf_type C set_type → % 4.18/4.36 And (∀ (D : Iota), ilf_type D (subset_type (cross_product B C)) → ilf_type D (relation_type B C)) % 4.18/4.36 (∀ (E : Iota), ilf_type E (relation_type B C) → ilf_type E (subset_type (cross_product B C)))) % 4.18/4.36 True % 4.18/4.36 Clause #3 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → Not (member B empty_set)) True % 4.18/4.36 Clause #7 (by assumption #[]): Eq % 4.18/4.36 (∀ (B : Iota), % 4.18/4.36 ilf_type B set_type → % 4.18/4.36 ∀ (C : Iota), ilf_type C set_type → Iff (ilf_type C (subset_type B)) (ilf_type C (member_type (power_set B)))) % 4.18/4.36 True % 4.18/4.36 Clause #12 (by assumption #[]): Eq % 4.18/4.36 (∀ (B : Iota), % 4.18/4.36 ilf_type B set_type → % 4.18/4.36 ∀ (C : Iota), % 4.18/4.36 ilf_type C set_type → % 4.18/4.36 Iff (member B (power_set C)) (∀ (D : Iota), ilf_type D set_type → member D B → member D C)) % 4.18/4.36 True % 4.18/4.36 Clause #13 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → And (Not (empty (power_set B))) (ilf_type (power_set B) set_type)) True % 4.18/4.36 Clause #14 (by assumption #[]): Eq % 4.18/4.36 (∀ (B : Iota), % 4.18/4.36 ilf_type B set_type → % 4.18/4.36 ∀ (C : Iota), And (Not (empty C)) (ilf_type C set_type) → Iff (ilf_type B (member_type C)) (member B C)) % 4.18/4.36 True % 4.18/4.36 Clause #20 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True % 4.18/4.36 Clause #21 (by assumption #[]): Eq % 4.18/4.36 (Not (∀ (B : Iota), ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type empty_set (relation_type B C))) % 4.18/4.36 True % 4.18/4.36 Clause #22 (by clausification #[20]): ∀ (a : Iota), Eq (ilf_type a set_type) True % 4.18/4.36 Clause #39 (by clausification #[3]): ∀ (a : Iota), Eq (ilf_type a set_type → Not (member a empty_set)) True % 4.18/4.36 Clause #40 (by clausification #[39]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (Not (member a empty_set)) True) % 4.18/4.36 Clause #41 (by clausification #[40]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (member a empty_set) False) % 4.18/4.36 Clause #42 (by forward demodulation #[41, 22]): ∀ (a : Iota), Or (Eq True False) (Eq (member a empty_set) False) % 4.18/4.36 Clause #43 (by clausification #[42]): ∀ (a : Iota), Eq (member a empty_set) False % 4.18/4.36 Clause #58 (by clausification #[1]): ∀ (a : Iota), % 4.18/4.36 Eq % 4.18/4.36 (ilf_type a set_type → % 4.18/4.36 ∀ (C : Iota), % 4.18/4.36 ilf_type C set_type → % 4.18/4.36 And (∀ (D : Iota), ilf_type D (subset_type (cross_product a C)) → ilf_type D (relation_type a C)) % 4.18/4.36 (∀ (E : Iota), ilf_type E (relation_type a C) → ilf_type E (subset_type (cross_product a C)))) % 4.18/4.36 True % 4.18/4.36 Clause #59 (by clausification #[58]): ∀ (a : Iota), % 4.18/4.36 Or (Eq (ilf_type a set_type) False) % 4.18/4.36 (Eq % 4.18/4.36 (∀ (C : Iota), % 4.18/4.36 ilf_type C set_type → % 4.18/4.36 And (∀ (D : Iota), ilf_type D (subset_type (cross_product a C)) → ilf_type D (relation_type a C)) % 4.18/4.36 (∀ (E : Iota), ilf_type E (relation_type a C) → ilf_type E (subset_type (cross_product a C)))) % 4.18/4.36 True) % 4.18/4.36 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), % 4.18/4.36 Or (Eq (ilf_type a set_type) False) % 4.18/4.36 (Eq % 4.18/4.36 (ilf_type a_1 set_type → % 4.18/4.36 And (∀ (D : Iota), ilf_type D (subset_type (cross_product a a_1)) → ilf_type D (relation_type a a_1)) % 4.18/4.36 (∀ (E : Iota), ilf_type E (relation_type a a_1) → ilf_type E (subset_type (cross_product a a_1)))) % 4.18/4.36 True) % 4.18/4.36 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), % 4.18/4.36 Or (Eq (ilf_type a set_type) False) % 4.18/4.36 (Or (Eq (ilf_type a_1 set_type) False) % 4.18/4.36 (Eq % 4.18/4.36 (And (∀ (D : Iota), ilf_type D (subset_type (cross_product a a_1)) → ilf_type D (relation_type a a_1)) % 4.18/4.36 (∀ (E : Iota), ilf_type E (relation_type a a_1) → ilf_type E (subset_type (cross_product a a_1)))) % 4.18/4.36 True)) % 4.18/4.36 Clause #63 (by clausification #[61]): ∀ (a a_1 : Iota), % 4.18/4.36 Or (Eq (ilf_type a set_type) False) % 4.18/4.36 (Or (Eq (ilf_type a_1 set_type) False) % 4.18/4.36 (Eq (∀ (D : Iota), ilf_type D (subset_type (cross_product a a_1)) → ilf_type D (relation_type a a_1)) True)) % 4.18/4.36 Clause #99 (by clausification #[21]): Eq (∀ (B : Iota), ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → ilf_type empty_set (relation_type B C)) % 4.22/4.38 False % 4.22/4.38 Clause #100 (by clausification #[99]): ∀ (a : Iota), % 4.22/4.38 Eq % 4.22/4.38 (Not % 4.22/4.38 (ilf_type (skS.0 2 a) set_type → % 4.22/4.38 ∀ (C : Iota), ilf_type C set_type → ilf_type empty_set (relation_type (skS.0 2 a) C))) % 4.22/4.38 True % 4.22/4.38 Clause #101 (by clausification #[100]): ∀ (a : Iota), % 4.22/4.38 Eq % 4.22/4.38 (ilf_type (skS.0 2 a) set_type → % 4.22/4.38 ∀ (C : Iota), ilf_type C set_type → ilf_type empty_set (relation_type (skS.0 2 a) C)) % 4.22/4.38 False % 4.22/4.38 Clause #103 (by clausification #[101]): ∀ (a : Iota), Eq (∀ (C : Iota), ilf_type C set_type → ilf_type empty_set (relation_type (skS.0 2 a) C)) False % 4.22/4.38 Clause #114 (by clausification #[13]): ∀ (a : Iota), Eq (ilf_type a set_type → And (Not (empty (power_set a))) (ilf_type (power_set a) set_type)) True % 4.22/4.38 Clause #115 (by clausification #[114]): ∀ (a : Iota), % 4.22/4.38 Or (Eq (ilf_type a set_type) False) (Eq (And (Not (empty (power_set a))) (ilf_type (power_set a) set_type)) True) % 4.22/4.38 Clause #117 (by clausification #[115]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (Not (empty (power_set a))) True) % 4.22/4.38 Clause #120 (by clausification #[117]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (empty (power_set a)) False) % 4.22/4.38 Clause #121 (by forward demodulation #[120, 22]): ∀ (a : Iota), Or (Eq True False) (Eq (empty (power_set a)) False) % 4.22/4.38 Clause #122 (by clausification #[121]): ∀ (a : Iota), Eq (empty (power_set a)) False % 4.22/4.38 Clause #133 (by clausification #[103]): ∀ (a a_1 : Iota), % 4.22/4.38 Eq (Not (ilf_type (skS.0 5 a a_1) set_type → ilf_type empty_set (relation_type (skS.0 2 a) (skS.0 5 a a_1)))) True % 4.22/4.38 Clause #134 (by clausification #[133]): ∀ (a a_1 : Iota), % 4.22/4.38 Eq (ilf_type (skS.0 5 a a_1) set_type → ilf_type empty_set (relation_type (skS.0 2 a) (skS.0 5 a a_1))) False % 4.22/4.38 Clause #136 (by clausification #[134]): ∀ (a a_1 : Iota), Eq (ilf_type empty_set (relation_type (skS.0 2 a) (skS.0 5 a a_1))) False % 4.22/4.38 Clause #137 (by clausification #[14]): ∀ (a : Iota), % 4.22/4.38 Eq % 4.22/4.38 (ilf_type a set_type → % 4.22/4.38 ∀ (C : Iota), And (Not (empty C)) (ilf_type C set_type) → Iff (ilf_type a (member_type C)) (member a C)) % 4.22/4.38 True % 4.22/4.38 Clause #138 (by clausification #[137]): ∀ (a : Iota), % 4.22/4.38 Or (Eq (ilf_type a set_type) False) % 4.22/4.38 (Eq (∀ (C : Iota), And (Not (empty C)) (ilf_type C set_type) → Iff (ilf_type a (member_type C)) (member a C)) True) % 4.22/4.38 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota), % 4.22/4.38 Or (Eq (ilf_type a set_type) False) % 4.22/4.38 (Eq (And (Not (empty a_1)) (ilf_type a_1 set_type) → Iff (ilf_type a (member_type a_1)) (member a a_1)) True) % 4.22/4.38 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), % 4.22/4.38 Or (Eq (ilf_type a set_type) False) % 4.22/4.38 (Or (Eq (And (Not (empty a_1)) (ilf_type a_1 set_type)) False) % 4.22/4.38 (Eq (Iff (ilf_type a (member_type a_1)) (member a a_1)) True)) % 4.22/4.38 Clause #141 (by clausification #[140]): ∀ (a a_1 : Iota), % 4.22/4.38 Or (Eq (ilf_type a set_type) False) % 4.22/4.38 (Or (Eq (Iff (ilf_type a (member_type a_1)) (member a a_1)) True) % 4.22/4.38 (Or (Eq (Not (empty a_1)) False) (Eq (ilf_type a_1 set_type) False))) % 4.22/4.38 Clause #142 (by clausification #[141]): ∀ (a a_1 : Iota), % 4.22/4.38 Or (Eq (ilf_type a set_type) False) % 4.22/4.38 (Or (Eq (Not (empty a_1)) False) % 4.22/4.38 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (ilf_type a (member_type a_1)) True) (Eq (member a a_1) False)))) % 4.22/4.38 Clause #144 (by clausification #[142]): ∀ (a a_1 : Iota), % 4.22/4.38 Or (Eq (ilf_type a set_type) False) % 4.22/4.38 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.38 (Or (Eq (ilf_type a (member_type a_1)) True) (Or (Eq (member a a_1) False) (Eq (empty a_1) True)))) % 4.22/4.38 Clause #145 (by forward demodulation #[144, 22]): ∀ (a a_1 : Iota), % 4.22/4.38 Or (Eq True False) % 4.22/4.38 (Or (Eq (ilf_type a set_type) False) % 4.22/4.38 (Or (Eq (ilf_type a_1 (member_type a)) True) (Or (Eq (member a_1 a) False) (Eq (empty a) True)))) % 4.22/4.38 Clause #146 (by clausification #[145]): ∀ (a a_1 : Iota), % 4.22/4.38 Or (Eq (ilf_type a set_type) False) % 4.22/4.38 (Or (Eq (ilf_type a_1 (member_type a)) True) (Or (Eq (member a_1 a) False) (Eq (empty a) True))) % 4.22/4.38 Clause #147 (by forward demodulation #[146, 22]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq True False) (Or (Eq (ilf_type a (member_type a_1)) True) (Or (Eq (member a a_1) False) (Eq (empty a_1) True))) % 4.22/4.40 Clause #148 (by clausification #[147]): ∀ (a a_1 : Iota), Or (Eq (ilf_type a (member_type a_1)) True) (Or (Eq (member a a_1) False) (Eq (empty a_1) True)) % 4.22/4.40 Clause #149 (by clausification #[7]): ∀ (a : Iota), % 4.22/4.40 Eq % 4.22/4.40 (ilf_type a set_type → % 4.22/4.40 ∀ (C : Iota), ilf_type C set_type → Iff (ilf_type C (subset_type a)) (ilf_type C (member_type (power_set a)))) % 4.22/4.40 True % 4.22/4.40 Clause #150 (by clausification #[149]): ∀ (a : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Eq (∀ (C : Iota), ilf_type C set_type → Iff (ilf_type C (subset_type a)) (ilf_type C (member_type (power_set a)))) % 4.22/4.40 True) % 4.22/4.40 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Eq (ilf_type a_1 set_type → Iff (ilf_type a_1 (subset_type a)) (ilf_type a_1 (member_type (power_set a)))) True) % 4.22/4.40 Clause #152 (by clausification #[151]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.40 (Eq (Iff (ilf_type a_1 (subset_type a)) (ilf_type a_1 (member_type (power_set a)))) True)) % 4.22/4.40 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a_1 (subset_type a)) True) (Eq (ilf_type a_1 (member_type (power_set a))) False))) % 4.22/4.40 Clause #155 (by forward demodulation #[153, 22]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq True False) % 4.22/4.40 (Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a (subset_type a_1)) True) (Eq (ilf_type a (member_type (power_set a_1))) False))) % 4.22/4.40 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a (subset_type a_1)) True) (Eq (ilf_type a (member_type (power_set a_1))) False)) % 4.22/4.40 Clause #157 (by forward demodulation #[156, 22]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq True False) (Or (Eq (ilf_type a (subset_type a_1)) True) (Eq (ilf_type a (member_type (power_set a_1))) False)) % 4.22/4.40 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), Or (Eq (ilf_type a (subset_type a_1)) True) (Eq (ilf_type a (member_type (power_set a_1))) False) % 4.22/4.40 Clause #183 (by clausification #[12]): ∀ (a : Iota), % 4.22/4.40 Eq % 4.22/4.40 (ilf_type a set_type → % 4.22/4.40 ∀ (C : Iota), % 4.22/4.40 ilf_type C set_type → % 4.22/4.40 Iff (member a (power_set C)) (∀ (D : Iota), ilf_type D set_type → member D a → member D C)) % 4.22/4.40 True % 4.22/4.40 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Eq % 4.22/4.40 (∀ (C : Iota), % 4.22/4.40 ilf_type C set_type → % 4.22/4.40 Iff (member a (power_set C)) (∀ (D : Iota), ilf_type D set_type → member D a → member D C)) % 4.22/4.40 True) % 4.22/4.40 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Eq % 4.22/4.40 (ilf_type a_1 set_type → % 4.22/4.40 Iff (member a (power_set a_1)) (∀ (D : Iota), ilf_type D set_type → member D a → member D a_1)) % 4.22/4.40 True) % 4.22/4.40 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.40 (Eq (Iff (member a (power_set a_1)) (∀ (D : Iota), ilf_type D set_type → member D a → member D a_1)) True)) % 4.22/4.40 Clause #187 (by clausification #[186]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.40 (Or (Eq (member a (power_set a_1)) True) % 4.22/4.40 (Eq (∀ (D : Iota), ilf_type D set_type → member D a → member D a_1) False))) % 4.22/4.40 Clause #189 (by clausification #[187]): ∀ (a a_1 a_2 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.40 (Or (Eq (member a (power_set a_1)) True) % 4.22/4.40 (Eq % 4.22/4.40 (Not (ilf_type (skS.0 7 a a_1 a_2) set_type → member (skS.0 7 a a_1 a_2) a → member (skS.0 7 a a_1 a_2) a_1)) % 4.22/4.40 True))) % 4.22/4.40 Clause #190 (by clausification #[189]): ∀ (a a_1 a_2 : Iota), % 4.22/4.40 Or (Eq (ilf_type a set_type) False) % 4.22/4.40 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.40 (Or (Eq (member a (power_set a_1)) True) % 4.22/4.43 (Eq (ilf_type (skS.0 7 a a_1 a_2) set_type → member (skS.0 7 a a_1 a_2) a → member (skS.0 7 a a_1 a_2) a_1) % 4.22/4.43 False))) % 4.22/4.43 Clause #192 (by clausification #[190]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq (ilf_type a set_type) False) % 4.22/4.43 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.43 (Or (Eq (member a (power_set a_1)) True) % 4.22/4.43 (Eq (member (skS.0 7 a a_1 a_2) a → member (skS.0 7 a a_1 a_2) a_1) False))) % 4.22/4.43 Clause #207 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq (ilf_type a set_type) False) % 4.22/4.43 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.43 (Eq (ilf_type a_2 (subset_type (cross_product a a_1)) → ilf_type a_2 (relation_type a a_1)) True)) % 4.22/4.43 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq (ilf_type a set_type) False) % 4.22/4.43 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.43 (Or (Eq (ilf_type a_2 (subset_type (cross_product a a_1))) False) (Eq (ilf_type a_2 (relation_type a a_1)) True))) % 4.22/4.43 Clause #209 (by forward demodulation #[208, 22]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq True False) % 4.22/4.43 (Or (Eq (ilf_type a set_type) False) % 4.22/4.43 (Or (Eq (ilf_type a_1 (subset_type (cross_product a_2 a))) False) (Eq (ilf_type a_1 (relation_type a_2 a)) True))) % 4.22/4.43 Clause #210 (by clausification #[209]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq (ilf_type a set_type) False) % 4.22/4.43 (Or (Eq (ilf_type a_1 (subset_type (cross_product a_2 a))) False) (Eq (ilf_type a_1 (relation_type a_2 a)) True)) % 4.22/4.43 Clause #211 (by forward demodulation #[210, 22]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq True False) % 4.22/4.43 (Or (Eq (ilf_type a (subset_type (cross_product a_1 a_2))) False) (Eq (ilf_type a (relation_type a_1 a_2)) True)) % 4.22/4.43 Clause #212 (by clausification #[211]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq (ilf_type a (subset_type (cross_product a_1 a_2))) False) (Eq (ilf_type a (relation_type a_1 a_2)) True) % 4.22/4.43 Clause #320 (by clausification #[192]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq (ilf_type a set_type) False) % 4.22/4.43 (Or (Eq (ilf_type a_1 set_type) False) % 4.22/4.43 (Or (Eq (member a (power_set a_1)) True) (Eq (member (skS.0 7 a a_1 a_2) a) True))) % 4.22/4.43 Clause #322 (by forward demodulation #[320, 22]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq True False) % 4.22/4.43 (Or (Eq (ilf_type a set_type) False) % 4.22/4.43 (Or (Eq (member a_1 (power_set a)) True) (Eq (member (skS.0 7 a_1 a a_2) a_1) True))) % 4.22/4.43 Clause #323 (by clausification #[322]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq (ilf_type a set_type) False) % 4.22/4.43 (Or (Eq (member a_1 (power_set a)) True) (Eq (member (skS.0 7 a_1 a a_2) a_1) True)) % 4.22/4.43 Clause #324 (by forward demodulation #[323, 22]): ∀ (a a_1 a_2 : Iota), % 4.22/4.43 Or (Eq True False) (Or (Eq (member a (power_set a_1)) True) (Eq (member (skS.0 7 a a_1 a_2) a) True)) % 4.22/4.43 Clause #325 (by clausification #[324]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (power_set a_1)) True) (Eq (member (skS.0 7 a a_1 a_2) a) True) % 4.22/4.43 Clause #326 (by superposition #[325, 43]): ∀ (a : Iota), Or (Eq (member empty_set (power_set a)) True) (Eq True False) % 4.22/4.43 Clause #331 (by clausification #[326]): ∀ (a : Iota), Eq (member empty_set (power_set a)) True % 4.22/4.43 Clause #332 (by superposition #[331, 148]): ∀ (a : Iota), % 4.22/4.43 Or (Eq (ilf_type empty_set (member_type (power_set a))) True) (Or (Eq True False) (Eq (empty (power_set a)) True)) % 4.22/4.43 Clause #333 (by clausification #[332]): ∀ (a : Iota), Or (Eq (ilf_type empty_set (member_type (power_set a))) True) (Eq (empty (power_set a)) True) % 4.22/4.43 Clause #334 (by forward demodulation #[333, 122]): ∀ (a : Iota), Or (Eq (ilf_type empty_set (member_type (power_set a))) True) (Eq False True) % 4.22/4.43 Clause #335 (by clausification #[334]): ∀ (a : Iota), Eq (ilf_type empty_set (member_type (power_set a))) True % 4.22/4.43 Clause #336 (by superposition #[335, 158]): ∀ (a : Iota), Or (Eq (ilf_type empty_set (subset_type a)) True) (Eq True False) % 4.22/4.43 Clause #338 (by clausification #[336]): ∀ (a : Iota), Eq (ilf_type empty_set (subset_type a)) True % 4.22/4.43 Clause #340 (by superposition #[338, 212]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ilf_type empty_set (relation_type a a_1)) True) % 4.22/4.43 Clause #360 (by clausification #[340]): ∀ (a a_1 : Iota), Eq (ilf_type empty_set (relation_type a a_1)) True % 4.22/4.43 Clause #361 (by superposition #[360, 136]): Eq True False % 4.22/4.43 Clause #363 (by clausification #[361]): False % 4.22/4.43 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------