%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET679+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 08:00:23 PM UTC 2025 % Result : Theorem 22.90s 23.12s % Output : Proof 23.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET679+3 : TPTP v9.2.0. Released v2.2.0. % 0.11/0.14 % Command : duper %s % 0.13/0.35 % Computer : n021.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 14:30:38 EDT 2025 % 0.13/0.35 % CPUTime : % 22.90/23.12 SZS status Theorem for theBenchmark.p % 22.90/23.12 SZS output start Proof for theBenchmark.p % 22.90/23.12 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → Not (member B empty_set)) True % 22.90/23.12 Clause #4 (by assumption #[]): Eq % 22.90/23.12 (∀ (B : Iota), % 22.90/23.12 ilf_type B set_type → % 22.90/23.12 ∀ (C : Iota), % 22.90/23.12 ilf_type C set_type → % 22.90/23.12 ∀ (D : Iota), % 22.90/23.12 ilf_type D set_type → Iff (member (ordered_pair C D) (identity_relation_of B)) (And (member C B) (Eq C D))) % 22.90/23.12 True % 22.90/23.12 Clause #7 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → Iff (not_equal B C) (Ne B C)) True % 22.90/23.12 Clause #8 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → Iff (empty B) (∀ (C : Iota), ilf_type C set_type → Not (member C B))) True % 22.90/23.12 Clause #22 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True % 22.90/23.12 Clause #23 (by assumption #[]): Eq (Not (∀ (B : Iota), And (Not (empty B)) (ilf_type B set_type) → not_equal (identity_relation_of B) empty_set)) True % 22.90/23.12 Clause #28 (by clausification #[22]): ∀ (a : Iota), Eq (ilf_type a set_type) True % 22.90/23.12 Clause #40 (by clausification #[1]): ∀ (a : Iota), Eq (ilf_type a set_type → Not (member a empty_set)) True % 22.90/23.12 Clause #41 (by clausification #[40]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (Not (member a empty_set)) True) % 22.90/23.12 Clause #42 (by clausification #[41]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (member a empty_set) False) % 22.90/23.12 Clause #43 (by forward demodulation #[42, 28]): ∀ (a : Iota), Or (Eq True False) (Eq (member a empty_set) False) % 22.90/23.12 Clause #44 (by clausification #[43]): ∀ (a : Iota), Eq (member a empty_set) False % 22.90/23.12 Clause #49 (by clausification #[23]): Eq (∀ (B : Iota), And (Not (empty B)) (ilf_type B set_type) → not_equal (identity_relation_of B) empty_set) False % 22.90/23.12 Clause #50 (by clausification #[49]): ∀ (a : Iota), % 22.90/23.12 Eq % 22.90/23.12 (Not % 22.90/23.12 (And (Not (empty (skS.0 1 a))) (ilf_type (skS.0 1 a) set_type) → % 22.90/23.12 not_equal (identity_relation_of (skS.0 1 a)) empty_set)) % 22.90/23.12 True % 22.90/23.12 Clause #51 (by clausification #[50]): ∀ (a : Iota), % 22.90/23.12 Eq % 22.90/23.12 (And (Not (empty (skS.0 1 a))) (ilf_type (skS.0 1 a) set_type) → % 22.90/23.12 not_equal (identity_relation_of (skS.0 1 a)) empty_set) % 22.90/23.12 False % 22.90/23.12 Clause #52 (by clausification #[51]): ∀ (a : Iota), Eq (And (Not (empty (skS.0 1 a))) (ilf_type (skS.0 1 a) set_type)) True % 22.90/23.12 Clause #53 (by clausification #[51]): ∀ (a : Iota), Eq (not_equal (identity_relation_of (skS.0 1 a)) empty_set) False % 22.90/23.12 Clause #55 (by clausification #[52]): ∀ (a : Iota), Eq (Not (empty (skS.0 1 a))) True % 22.90/23.12 Clause #56 (by clausification #[55]): ∀ (a : Iota), Eq (empty (skS.0 1 a)) False % 22.90/23.12 Clause #59 (by clausification #[4]): ∀ (a : Iota), % 22.90/23.12 Eq % 22.90/23.12 (ilf_type a set_type → % 22.90/23.12 ∀ (C : Iota), % 22.90/23.12 ilf_type C set_type → % 22.90/23.12 ∀ (D : Iota), % 22.90/23.12 ilf_type D set_type → Iff (member (ordered_pair C D) (identity_relation_of a)) (And (member C a) (Eq C D))) % 22.90/23.12 True % 22.90/23.12 Clause #60 (by clausification #[59]): ∀ (a : Iota), % 22.90/23.12 Or (Eq (ilf_type a set_type) False) % 22.90/23.12 (Eq % 22.90/23.12 (∀ (C : Iota), % 22.90/23.12 ilf_type C set_type → % 22.90/23.12 ∀ (D : Iota), % 22.90/23.12 ilf_type D set_type → Iff (member (ordered_pair C D) (identity_relation_of a)) (And (member C a) (Eq C D))) % 22.90/23.12 True) % 22.90/23.12 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), % 22.90/23.12 Or (Eq (ilf_type a set_type) False) % 22.90/23.12 (Eq % 22.90/23.12 (ilf_type a_1 set_type → % 22.90/23.12 ∀ (D : Iota), % 22.90/23.12 ilf_type D set_type → % 22.90/23.12 Iff (member (ordered_pair a_1 D) (identity_relation_of a)) (And (member a_1 a) (Eq a_1 D))) % 22.90/23.12 True) % 22.90/23.12 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), % 22.90/23.12 Or (Eq (ilf_type a set_type) False) % 22.90/23.12 (Or (Eq (ilf_type a_1 set_type) False) % 22.90/23.12 (Eq % 22.90/23.12 (∀ (D : Iota), % 22.90/23.12 ilf_type D set_type → % 22.90/23.12 Iff (member (ordered_pair a_1 D) (identity_relation_of a)) (And (member a_1 a) (Eq a_1 D))) % 22.90/23.12 True)) % 22.90/23.12 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 22.90/23.12 Or (Eq (ilf_type a set_type) False) % 22.90/23.12 (Or (Eq (ilf_type a_1 set_type) False) % 22.90/23.12 (Eq % 22.90/23.12 (ilf_type a_2 set_type → % 22.90/23.12 Iff (member (ordered_pair a_1 a_2) (identity_relation_of a)) (And (member a_1 a) (Eq a_1 a_2))) % 22.98/23.15 True)) % 22.98/23.15 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_1 set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_2 set_type) False) % 22.98/23.15 (Eq (Iff (member (ordered_pair a_1 a_2) (identity_relation_of a)) (And (member a_1 a) (Eq a_1 a_2))) True))) % 22.98/23.15 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_1 set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_2 set_type) False) % 22.98/23.15 (Or (Eq (member (ordered_pair a_1 a_2) (identity_relation_of a)) True) % 22.98/23.15 (Eq (And (member a_1 a) (Eq a_1 a_2)) False)))) % 22.98/23.15 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_1 set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_2 set_type) False) % 22.98/23.15 (Or (Eq (member (ordered_pair a_1 a_2) (identity_relation_of a)) True) % 22.98/23.15 (Or (Eq (member a_1 a) False) (Eq (Eq a_1 a_2) False))))) % 22.98/23.15 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_1 set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_2 set_type) False) % 22.98/23.15 (Or (Eq (member (ordered_pair a_1 a_2) (identity_relation_of a)) True) % 22.98/23.15 (Or (Eq (member a_1 a) False) (Ne a_1 a_2))))) % 22.98/23.15 Clause #69 (by destructive equality resolution #[68]): ∀ (a a_1 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_1 set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_1 set_type) False) % 22.98/23.15 (Or (Eq (member (ordered_pair a_1 a_1) (identity_relation_of a)) True) (Eq (member a_1 a) False)))) % 22.98/23.15 Clause #70 (by eliminate duplicate literals #[69]): ∀ (a a_1 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (ilf_type a_1 set_type) False) % 22.98/23.15 (Or (Eq (member (ordered_pair a_1 a_1) (identity_relation_of a)) True) (Eq (member a_1 a) False))) % 22.98/23.15 Clause #71 (by forward demodulation #[70, 28]): ∀ (a a_1 : Iota), % 22.98/23.15 Or (Eq True False) % 22.98/23.15 (Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (member (ordered_pair a a) (identity_relation_of a_1)) True) (Eq (member a a_1) False))) % 22.98/23.15 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (member (ordered_pair a a) (identity_relation_of a_1)) True) (Eq (member a a_1) False)) % 22.98/23.15 Clause #73 (by forward demodulation #[72, 28]): ∀ (a a_1 : Iota), % 22.98/23.15 Or (Eq True False) (Or (Eq (member (ordered_pair a a) (identity_relation_of a_1)) True) (Eq (member a a_1) False)) % 22.98/23.15 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Or (Eq (member (ordered_pair a a) (identity_relation_of a_1)) True) (Eq (member a a_1) False) % 22.98/23.15 Clause #131 (by clausification #[8]): ∀ (a : Iota), Eq (ilf_type a set_type → Iff (empty a) (∀ (C : Iota), ilf_type C set_type → Not (member C a))) True % 22.98/23.15 Clause #132 (by clausification #[131]): ∀ (a : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) (Eq (Iff (empty a) (∀ (C : Iota), ilf_type C set_type → Not (member C a))) True) % 22.98/23.15 Clause #133 (by clausification #[132]): ∀ (a : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (empty a) True) (Eq (∀ (C : Iota), ilf_type C set_type → Not (member C a)) False)) % 22.98/23.15 Clause #135 (by clausification #[133]): ∀ (a a_1 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (empty a) True) (Eq (Not (ilf_type (skS.0 5 a a_1) set_type → Not (member (skS.0 5 a a_1) a))) True)) % 22.98/23.15 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) % 22.98/23.15 (Or (Eq (empty a) True) (Eq (ilf_type (skS.0 5 a a_1) set_type → Not (member (skS.0 5 a a_1) a)) False)) % 22.98/23.15 Clause #138 (by clausification #[136]): ∀ (a a_1 : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) (Or (Eq (empty a) True) (Eq (Not (member (skS.0 5 a a_1) a)) False)) % 22.98/23.15 Clause #147 (by clausification #[7]): ∀ (a : Iota), Eq (ilf_type a set_type → ∀ (C : Iota), ilf_type C set_type → Iff (not_equal a C) (Ne a C)) True % 22.98/23.15 Clause #148 (by clausification #[147]): ∀ (a : Iota), % 22.98/23.15 Or (Eq (ilf_type a set_type) False) (Eq (∀ (C : Iota), ilf_type C set_type → Iff (not_equal a C) (Ne a C)) True) % 22.98/23.17 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota), % 22.98/23.17 Or (Eq (ilf_type a set_type) False) (Eq (ilf_type a_1 set_type → Iff (not_equal a a_1) (Ne a a_1)) True) % 22.98/23.17 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota), % 22.98/23.17 Or (Eq (ilf_type a set_type) False) % 22.98/23.17 (Or (Eq (ilf_type a_1 set_type) False) (Eq (Iff (not_equal a a_1) (Ne a a_1)) True)) % 22.98/23.17 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), % 22.98/23.17 Or (Eq (ilf_type a set_type) False) % 22.98/23.17 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (not_equal a a_1) True) (Eq (Ne a a_1) False))) % 22.98/23.17 Clause #152 (by clausification #[150]): ∀ (a a_1 : Iota), % 22.98/23.17 Or (Eq (ilf_type a set_type) False) % 22.98/23.17 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (not_equal a a_1) False) (Eq (Ne a a_1) True))) % 22.98/23.17 Clause #153 (by clausification #[151]): ∀ (a a_1 : Iota), % 22.98/23.17 Or (Eq (ilf_type a set_type) False) % 22.98/23.17 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (not_equal a a_1) True) (Eq a a_1))) % 22.98/23.17 Clause #154 (by forward demodulation #[153, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (ilf_type a set_type) False) (Or (Eq (not_equal a_1 a) True) (Eq a_1 a))) % 22.98/23.17 Clause #155 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (ilf_type a set_type) False) (Or (Eq (not_equal a_1 a) True) (Eq a_1 a)) % 22.98/23.17 Clause #156 (by forward demodulation #[155, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (not_equal a a_1) True) (Eq a a_1)) % 22.98/23.17 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) True) (Eq a a_1) % 22.98/23.17 Clause #158 (by superposition #[157, 53]): ∀ (a : Iota), Or (Eq (identity_relation_of (skS.0 1 a)) empty_set) (Eq True False) % 22.98/23.17 Clause #161 (by superposition #[157, 44]): ∀ (a a_1 : Iota), Or (Eq (not_equal empty_set a) True) (Eq (member a_1 a) False) % 22.98/23.17 Clause #358 (by clausification #[158]): ∀ (a : Iota), Eq (identity_relation_of (skS.0 1 a)) empty_set % 22.98/23.17 Clause #447 (by clausification #[138]): ∀ (a a_1 : Iota), Or (Eq (ilf_type a set_type) False) (Or (Eq (empty a) True) (Eq (member (skS.0 5 a a_1) a) True)) % 22.98/23.17 Clause #448 (by forward demodulation #[447, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (empty a) True) (Eq (member (skS.0 5 a a_1) a) True)) % 22.98/23.17 Clause #449 (by clausification #[448]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 5 a a_1) a) True) % 22.98/23.17 Clause #451 (by superposition #[449, 74]): ∀ (a a_1 : Iota), % 22.98/23.17 Or (Eq (empty a) True) % 22.98/23.17 (Or (Eq (member (ordered_pair (skS.0 5 a a_1) (skS.0 5 a a_1)) (identity_relation_of a)) True) (Eq True False)) % 22.98/23.17 Clause #469 (by clausification #[152]): ∀ (a a_1 : Iota), % 22.98/23.17 Or (Eq (ilf_type a set_type) False) % 22.98/23.17 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (not_equal a a_1) False) (Ne a a_1))) % 22.98/23.17 Clause #470 (by destructive equality resolution #[469]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Or (Eq (ilf_type a set_type) False) (Eq (not_equal a a) False)) % 22.98/23.17 Clause #471 (by eliminate duplicate literals #[470]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (not_equal a a) False) % 22.98/23.17 Clause #472 (by forward demodulation #[471, 28]): ∀ (a : Iota), Or (Eq True False) (Eq (not_equal a a) False) % 22.98/23.17 Clause #473 (by clausification #[472]): ∀ (a : Iota), Eq (not_equal a a) False % 22.98/23.17 Clause #6757 (by clausification #[451]): ∀ (a a_1 : Iota), % 22.98/23.17 Or (Eq (empty a) True) (Eq (member (ordered_pair (skS.0 5 a a_1) (skS.0 5 a a_1)) (identity_relation_of a)) True) % 22.98/23.17 Clause #6767 (by superposition #[6757, 161]): ∀ (a : Iota), Or (Eq (empty a) True) (Or (Eq (not_equal empty_set (identity_relation_of a)) True) (Eq True False)) % 22.98/23.17 Clause #6800 (by clausification #[6767]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (not_equal empty_set (identity_relation_of a)) True) % 22.98/23.17 Clause #6803 (by superposition #[6800, 358]): ∀ (a : Iota), Or (Eq (empty (skS.0 1 a)) True) (Eq (not_equal empty_set empty_set) True) % 22.98/23.17 Clause #6951 (by forward demodulation #[6803, 473]): ∀ (a : Iota), Or (Eq (empty (skS.0 1 a)) True) (Eq False True) % 22.98/23.17 Clause #6952 (by clausification #[6951]): ∀ (a : Iota), Eq (empty (skS.0 1 a)) True % 22.98/23.17 Clause #6953 (by superposition #[6952, 56]): Eq True False % 23.03/23.22 Clause #6969 (by clausification #[6953]): False % 23.03/23.22 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------