%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU173+1 : TPTP v9.2.0. Released v3.3.0. % 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 08:01:03 PM UTC 2025 % Result : Theorem 7.72s 7.90s % Output : Proof 7.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU173+1 : TPTP v9.2.0. Released v3.3.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n001.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 05:05:23 EDT 2025 % 0.13/0.34 % CPUTime : % 7.72/7.90 SZS status Theorem for theBenchmark.p % 7.72/7.90 SZS output start Proof for theBenchmark.p % 7.72/7.90 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (powerset A)) (∀ (C : Iota), Iff (in C B) (subset C A))) True % 7.72/7.90 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), And (Not (empty A) → Iff (element B A) (in B A)) (empty A → Iff (element B A) (empty B))) True % 7.72/7.90 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 7.72/7.90 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Not (empty (powerset A))) True % 7.72/7.90 Clause #8 (by assumption #[]): Eq (Not (∀ (A B : Iota), (∀ (C : Iota), in C A → in C B) → element A (powerset B))) True % 7.72/7.90 Clause #17 (by clausification #[6]): ∀ (a : Iota), Eq (Not (empty (powerset a))) True % 7.72/7.90 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (empty (powerset a)) False % 7.72/7.90 Clause #37 (by clausification #[8]): Eq (∀ (A B : Iota), (∀ (C : Iota), in C A → in C B) → element A (powerset B)) False % 7.72/7.90 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), (∀ (C : Iota), in C (skS.0 3 a) → in C B) → element (skS.0 3 a) (powerset B))) True % 7.72/7.90 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (C : Iota), in C (skS.0 3 a) → in C B) → element (skS.0 3 a) (powerset B)) False % 7.72/7.90 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 7.72/7.90 Eq (Not ((∀ (C : Iota), in C (skS.0 3 a) → in C (skS.0 4 a a_1)) → element (skS.0 3 a) (powerset (skS.0 4 a a_1)))) % 7.72/7.90 True % 7.72/7.90 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 7.72/7.90 Eq ((∀ (C : Iota), in C (skS.0 3 a) → in C (skS.0 4 a a_1)) → element (skS.0 3 a) (powerset (skS.0 4 a a_1))) False % 7.72/7.90 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), in C (skS.0 3 a) → in C (skS.0 4 a a_1)) True % 7.72/7.90 Clause #43 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (element (skS.0 3 a) (powerset (skS.0 4 a a_1))) False % 7.72/7.90 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Eq (in a (skS.0 3 a_1) → in a (skS.0 4 a_1 a_2)) True % 7.72/7.90 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 3 a_1)) False) (Eq (in a (skS.0 4 a_1 a_2)) True) % 7.72/7.90 Clause #46 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (powerset a)) (∀ (C : Iota), Iff (in C B) (subset C a))) True % 7.72/7.90 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (powerset a_1)) (∀ (C : Iota), Iff (in C a) (subset C a_1))) True % 7.72/7.90 Clause #49 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (Eq a (powerset a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) % 7.72/7.90 Clause #60 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 7.72/7.90 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 7.72/7.90 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 7.72/7.90 Clause #64 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 7.72/7.90 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 6 a a_1 a_2) a → in (skS.0 6 a a_1 a_2) a_1)) True) % 7.72/7.90 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 6 a a_1 a_2) a → in (skS.0 6 a a_1 a_2) a_1) False) % 7.72/7.90 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 6 a a_1 a_2) a) True) % 7.72/7.90 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 6 a a_1 a_2) a_1) False) % 7.72/7.90 Clause #68 (by superposition #[66, 45]): ∀ (a a_1 a_2 a_3 : Iota), % 7.72/7.90 Or (Eq (subset (skS.0 3 a) a_1) True) % 7.72/7.90 (Or (Eq True False) (Eq (in (skS.0 6 (skS.0 3 a) a_1 a_2) (skS.0 4 a a_3)) True)) % 7.72/7.90 Clause #74 (by clausification #[2]): ∀ (a : Iota), % 7.72/7.90 Eq (∀ (B : Iota), And (Not (empty a) → Iff (element B a) (in B a)) (empty a → Iff (element B a) (empty B))) True % 7.72/7.90 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), % 7.72/7.90 Eq (And (Not (empty a) → Iff (element a_1 a) (in a_1 a)) (empty a → Iff (element a_1 a) (empty a_1))) True % 7.72/7.93 Clause #77 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (Not (empty a) → Iff (element a_1 a) (in a_1 a)) True % 7.72/7.93 Clause #82 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (Not (empty a)) False) (Eq (Iff (element a_1 a) (in a_1 a)) True) % 7.72/7.93 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Or (Eq (Iff (element a a_1) (in a a_1)) True) (Eq (empty a_1) True) % 7.72/7.93 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Or (Eq (element a_1 a) True) (Eq (in a_1 a) False)) % 7.72/7.93 Clause #152 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) (Ne a (powerset a_1)) % 7.72/7.93 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Eq (Iff (in a_2 a) (subset a_2 a_1)) True) % 7.72/7.93 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Or (Eq (in a_2 a) True) (Eq (subset a_2 a_1) False)) % 7.72/7.93 Clause #156 (by destructive equality resolution #[154]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (subset a a_1) False) % 7.72/7.93 Clause #209 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota), % 7.72/7.93 Or (Eq (subset (skS.0 3 a) a_1) True) (Eq (in (skS.0 6 (skS.0 3 a) a_1 a_2) (skS.0 4 a a_3)) True) % 7.72/7.93 Clause #210 (by superposition #[209, 67]): ∀ (a a_1 : Iota), % 7.72/7.93 Or (Eq (subset (skS.0 3 a) (skS.0 4 a a_1)) True) (Or (Eq (subset (skS.0 3 a) (skS.0 4 a a_1)) True) (Eq True False)) % 7.72/7.93 Clause #1191 (by clausification #[210]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 3 a) (skS.0 4 a a_1)) True) (Eq (subset (skS.0 3 a) (skS.0 4 a a_1)) True) % 7.72/7.93 Clause #1192 (by eliminate duplicate literals #[1191]): ∀ (a a_1 : Iota), Eq (subset (skS.0 3 a) (skS.0 4 a a_1)) True % 7.72/7.93 Clause #1194 (by superposition #[1192, 156]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 3 a) (powerset (skS.0 4 a a_1))) True) (Eq True False) % 7.72/7.93 Clause #1199 (by clausification #[1194]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a) (powerset (skS.0 4 a a_1))) True % 7.72/7.93 Clause #1203 (by superposition #[1199, 84]): ∀ (a a_1 : Iota), % 7.72/7.93 Or (Eq (empty (powerset (skS.0 4 a a_1))) True) % 7.72/7.93 (Or (Eq (element (skS.0 3 a) (powerset (skS.0 4 a a_1))) True) (Eq True False)) % 7.72/7.93 Clause #1235 (by clausification #[1203]): ∀ (a a_1 : Iota), % 7.72/7.93 Or (Eq (empty (powerset (skS.0 4 a a_1))) True) (Eq (element (skS.0 3 a) (powerset (skS.0 4 a a_1))) True) % 7.72/7.93 Clause #1236 (by forward demodulation #[1235, 18]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (element (skS.0 3 a) (powerset (skS.0 4 a a_1))) True) % 7.72/7.93 Clause #1237 (by clausification #[1236]): ∀ (a a_1 : Iota), Eq (element (skS.0 3 a) (powerset (skS.0 4 a a_1))) True % 7.72/7.93 Clause #1238 (by superposition #[1237, 43]): Eq True False % 7.72/7.93 Clause #1250 (by clausification #[1238]): False % 7.72/7.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------