%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU144+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:00:57 PM UTC 2025 % Result : Theorem 8.25s 8.44s % Output : Proof 8.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU144+1 : TPTP v9.2.0. Released v3.3.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n022.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 05:04:08 EDT 2025 % 0.13/0.35 % CPUTime : % 8.25/8.44 SZS status Theorem for theBenchmark.p % 8.25/8.44 SZS output start Proof for theBenchmark.p % 8.25/8.44 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 8.25/8.44 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 8.25/8.44 Clause #4 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B))) True % 8.25/8.44 Clause #12 (by clausification #[4]): Eq (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B)) False % 8.25/8.44 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Iff (subset (singleton (skS.0 0 a)) B) (in (skS.0 0 a) B))) True % 8.25/8.44 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset (singleton (skS.0 0 a)) B) (in (skS.0 0 a) B)) False % 8.25/8.44 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Not (Iff (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (in (skS.0 0 a) (skS.0 1 a a_1)))) True % 8.25/8.44 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (in (skS.0 0 a) (skS.0 1 a a_1))) False % 8.25/8.44 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 8.25/8.44 Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) False) (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) False) % 8.25/8.44 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), % 8.25/8.44 Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) True) (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) % 8.25/8.44 Clause #19 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 8.25/8.44 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 8.25/8.44 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 8.25/8.44 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (C : Iota), in C a → in C a_1) True) % 8.25/8.44 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 8.25/8.44 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1)) True) % 8.25/8.44 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False) % 8.25/8.44 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a) True) % 8.25/8.44 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a_1) False) % 8.25/8.44 Clause #28 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 8.25/8.44 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 8.25/8.44 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 8.25/8.44 Clause #38 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 8.25/8.44 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 8.25/8.44 Clause #42 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 8.25/8.44 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 8.25/8.44 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False)) % 8.25/8.44 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True)) % 8.25/8.44 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 8.25/8.44 Clause #47 (by destructive equality resolution #[46]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 8.25/8.44 Clause #48 (by destructive equality resolution #[47]): ∀ (a : Iota), Eq (in a (singleton a)) True % 8.25/8.46 Clause #51 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 8.25/8.46 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 8.25/8.46 Clause #54 (by superposition #[52, 25]): ∀ (a a_1 a_2 : Iota), % 8.25/8.46 Or (Eq (skS.0 2 (singleton a) a_1 a_2) a) (Or (Eq (subset (singleton a) a_1) True) (Eq False True)) % 8.25/8.46 Clause #56 (by superposition #[18, 39]): ∀ (a a_1 a_2 : Iota), % 8.25/8.46 Or (Eq (in a (singleton (skS.0 0 a_1))) False) % 8.25/8.46 (Or (Eq (in a (skS.0 1 a_1 a_2)) True) (Or (Eq False True) (Eq (in (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True))) % 8.25/8.46 Clause #62 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 (singleton a) a_1 a_2) a) (Eq (subset (singleton a) a_1) True) % 8.25/8.46 Clause #64 (by superposition #[62, 26]): ∀ (a a_1 : Iota), % 8.25/8.46 Or (Eq (subset (singleton a) a_1) True) (Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False)) % 8.25/8.46 Clause #79 (by eliminate duplicate literals #[64]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False) % 8.25/8.46 Clause #108 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 8.25/8.46 Or (Eq (in a (singleton (skS.0 0 a_1))) False) % 8.25/8.46 (Or (Eq (in a (skS.0 1 a_1 a_2)) True) (Eq (in (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True)) % 8.25/8.46 Clause #109 (by superposition #[108, 48]): ∀ (a a_1 : Iota), % 8.25/8.46 Or (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) (Or (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)) % 8.25/8.46 Clause #2104 (by clausification #[109]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) % 8.25/8.46 Clause #2105 (by eliminate duplicate literals #[2104]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True % 8.25/8.46 Clause #2106 (by backward demodulation #[2105, 17]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) False) (Eq True False) % 8.25/8.46 Clause #2109 (by superposition #[2105, 79]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) True) (Eq True False) % 8.25/8.46 Clause #2168 (by clausification #[2109]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) True % 8.25/8.46 Clause #2205 (by clausification #[2106]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) False % 8.25/8.46 Clause #2206 (by superposition #[2205, 2168]): Eq False True % 8.25/8.46 Clause #2242 (by clausification #[2206]): False % 8.25/8.46 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------