%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM383+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 07:56:24 PM UTC 2025 % Result : Theorem 4.46s 4.64s % Output : Proof 4.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM383+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n001.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 : Fri Oct 3 07:48:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.46/4.64 SZS status Theorem for theBenchmark.p % 4.46/4.64 SZS output start Proof for theBenchmark.p % 4.46/4.64 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), in A B → Not (in B A)) True % 4.46/4.64 Clause #6 (by assumption #[]): Eq (empty empty_set) True % 4.46/4.64 Clause #20 (by assumption #[]): Eq (∀ (A B : Iota), element A B → Or (empty B) (in A B)) True % 4.46/4.64 Clause #21 (by assumption #[]): Eq (∀ (A B : Iota), Iff (element A (powerset B)) (subset A B)) True % 4.46/4.64 Clause #22 (by assumption #[]): Eq (∀ (A B C : Iota), And (in A B) (element B (powerset C)) → element A C) True % 4.46/4.64 Clause #23 (by assumption #[]): Eq (∀ (A B C : Iota), Not (And (And (in A B) (element B (powerset C))) (empty C))) True % 4.46/4.64 Clause #24 (by assumption #[]): Eq (∀ (A : Iota), empty A → Eq A empty_set) True % 4.46/4.64 Clause #26 (by assumption #[]): Eq (Not (∀ (A B : Iota), Not (And (in A B) (subset B A)))) True % 4.46/4.64 Clause #36 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → Not (in B a)) True % 4.46/4.64 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (in a a_1 → Not (in a_1 a)) True % 4.46/4.64 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (Not (in a_1 a)) True) % 4.46/4.64 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (in a_1 a) False) % 4.46/4.64 Clause #49 (by clausification #[24]): ∀ (a : Iota), Eq (empty a → Eq a empty_set) True % 4.46/4.64 Clause #50 (by clausification #[49]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (Eq a empty_set) True) % 4.46/4.64 Clause #51 (by clausification #[50]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq a empty_set) % 4.46/4.64 Clause #64 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (in a B) (element B (powerset C)) → element a C) True % 4.46/4.64 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (in a a_1) (element a_1 (powerset C)) → element a C) True % 4.46/4.64 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Eq (And (in a a_1) (element a_1 (powerset a_2)) → element a a_2) True % 4.46/4.64 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (in a a_1) (element a_1 (powerset a_2))) False) (Eq (element a a_2) True) % 4.46/4.64 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a a_1) True) (Or (Eq (in a a_2) False) (Eq (element a_2 (powerset a_1)) False)) % 4.46/4.64 Clause #105 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B : Iota), element a B → Or (empty B) (in a B)) True % 4.46/4.64 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (element a a_1 → Or (empty a_1) (in a a_1)) True % 4.46/4.64 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Eq (Or (empty a_1) (in a a_1)) True) % 4.46/4.64 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (empty a_1) True) (Eq (in a a_1) True)) % 4.46/4.64 Clause #114 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (element a (powerset B)) (subset a B)) True % 4.46/4.64 Clause #115 (by clausification #[114]): ∀ (a a_1 : Iota), Eq (Iff (element a (powerset a_1)) (subset a a_1)) True % 4.46/4.64 Clause #116 (by clausification #[115]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) True) (Eq (subset a a_1) False) % 4.46/4.64 Clause #141 (by clausification #[26]): Eq (∀ (A B : Iota), Not (And (in A B) (subset B A))) False % 4.46/4.64 Clause #142 (by clausification #[141]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Not (And (in (skS.0 11 a) B) (subset B (skS.0 11 a))))) True % 4.46/4.64 Clause #143 (by clausification #[142]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (in (skS.0 11 a) B) (subset B (skS.0 11 a)))) False % 4.46/4.64 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota), Eq (Not (Not (And (in (skS.0 11 a) (skS.0 12 a a_1)) (subset (skS.0 12 a a_1) (skS.0 11 a))))) True % 4.46/4.64 Clause #145 (by clausification #[144]): ∀ (a a_1 : Iota), Eq (Not (And (in (skS.0 11 a) (skS.0 12 a a_1)) (subset (skS.0 12 a a_1) (skS.0 11 a)))) False % 4.46/4.64 Clause #146 (by clausification #[145]): ∀ (a a_1 : Iota), Eq (And (in (skS.0 11 a) (skS.0 12 a a_1)) (subset (skS.0 12 a a_1) (skS.0 11 a))) True % 4.46/4.64 Clause #147 (by clausification #[146]): ∀ (a a_1 : Iota), Eq (subset (skS.0 12 a a_1) (skS.0 11 a)) True % 4.46/4.64 Clause #148 (by clausification #[146]): ∀ (a a_1 : Iota), Eq (in (skS.0 11 a) (skS.0 12 a a_1)) True % 4.50/4.66 Clause #149 (by superposition #[147, 116]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 12 a a_1) (powerset (skS.0 11 a))) True) (Eq True False) % 4.50/4.66 Clause #150 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B C : Iota), Not (And (And (in a B) (element B (powerset C))) (empty C))) True % 4.50/4.66 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Not (And (And (in a a_1) (element a_1 (powerset C))) (empty C))) True % 4.50/4.66 Clause #152 (by clausification #[151]): ∀ (a a_1 a_2 : Iota), Eq (Not (And (And (in a a_1) (element a_1 (powerset a_2))) (empty a_2))) True % 4.50/4.66 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 : Iota), Eq (And (And (in a a_1) (element a_1 (powerset a_2))) (empty a_2)) False % 4.50/4.66 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (in a a_1) (element a_1 (powerset a_2))) False) (Eq (empty a_2) False) % 4.50/4.66 Clause #155 (by clausification #[154]): ∀ (a a_1 a_2 : Iota), Or (Eq (empty a) False) (Or (Eq (in a_1 a_2) False) (Eq (element a_2 (powerset a)) False)) % 4.50/4.66 Clause #156 (by superposition #[155, 6]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Or (Eq (element a_1 (powerset empty_set)) False) (Eq False True)) % 4.50/4.66 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (element a_1 (powerset empty_set)) False) % 4.50/4.66 Clause #232 (by superposition #[148, 68]): ∀ (a a_1 a_2 : Iota), % 4.50/4.66 Or (Eq (element (skS.0 11 a) a_1) True) (Or (Eq True False) (Eq (element (skS.0 12 a a_2) (powerset a_1)) False)) % 4.50/4.66 Clause #234 (by superposition #[148, 157]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 12 a a_1) (powerset empty_set)) False) (Eq False True) % 4.50/4.66 Clause #236 (by clausification #[234]): ∀ (a a_1 : Iota), Eq (element (skS.0 12 a a_1) (powerset empty_set)) False % 4.50/4.66 Clause #240 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (element (skS.0 12 a a_1) (powerset (skS.0 11 a))) True % 4.50/4.66 Clause #248 (by clausification #[232]): ∀ (a a_1 a_2 : Iota), Or (Eq (element (skS.0 11 a) a_1) True) (Eq (element (skS.0 12 a a_2) (powerset a_1)) False) % 4.50/4.66 Clause #249 (by superposition #[248, 240]): ∀ (a : Iota), Or (Eq (element (skS.0 11 a) (skS.0 11 a)) True) (Eq False True) % 4.50/4.66 Clause #254 (by clausification #[249]): ∀ (a : Iota), Eq (element (skS.0 11 a) (skS.0 11 a)) True % 4.50/4.66 Clause #255 (by superposition #[254, 108]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (empty (skS.0 11 a)) True) (Eq (in (skS.0 11 a) (skS.0 11 a)) True)) % 4.50/4.66 Clause #256 (by clausification #[255]): ∀ (a : Iota), Or (Eq (empty (skS.0 11 a)) True) (Eq (in (skS.0 11 a) (skS.0 11 a)) True) % 4.50/4.66 Clause #257 (by superposition #[256, 39]): ∀ (a : Iota), Or (Eq (empty (skS.0 11 a)) True) (Or (Eq True False) (Eq True False)) % 4.50/4.66 Clause #262 (by clausification #[257]): ∀ (a : Iota), Or (Eq (empty (skS.0 11 a)) True) (Eq True False) % 4.50/4.66 Clause #263 (by clausification #[262]): ∀ (a : Iota), Eq (empty (skS.0 11 a)) True % 4.50/4.66 Clause #267 (by superposition #[263, 51]): ∀ (a : Iota), Or (Eq True False) (Eq (skS.0 11 a) empty_set) % 4.50/4.66 Clause #270 (by clausification #[267]): ∀ (a : Iota), Eq (skS.0 11 a) empty_set % 4.50/4.66 Clause #275 (by backward demodulation #[270, 240]): ∀ (a a_1 : Iota), Eq (element (skS.0 12 a a_1) (powerset empty_set)) True % 4.50/4.66 Clause #301 (by superposition #[275, 236]): Eq True False % 4.50/4.66 Clause #311 (by clausification #[301]): False % 4.50/4.66 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------