%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU609^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:02:02 PM UTC 2025 % Result : Theorem 3.88s 4.05s % Output : Proof 3.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU609^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 04:02:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.88/4.05 SZS status Theorem for theBenchmark.p % 3.88/4.05 SZS output start Proof for theBenchmark.p % 3.88/4.05 Clause #0 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 3.88/4.05 Clause #1 (by assumption #[]): Eq (Eq setminusEL (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A)) True % 3.88/4.05 Clause #2 (by assumption #[]): Eq (Not (subsetI2 → setminusEL → ∀ (A B : Iota), subset (setminus A B) A)) True % 3.88/4.05 Clause #3 (by clausification #[0]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.88/4.05 Clause #5 (by clausify Prop equality #[3]): Or (Eq subsetI2 False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) True) % 3.88/4.05 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq subsetI2 False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True) % 3.88/4.05 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True) % 3.88/4.05 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True)) % 3.88/4.05 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.88/4.05 Or (Eq subsetI2 False) % 3.88/4.05 (Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1)) True)) % 3.88/4.05 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 3.88/4.05 Or (Eq subsetI2 False) % 3.88/4.05 (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1) False)) % 3.88/4.05 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 3.88/4.05 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 3.88/4.05 Clause #22 (by clausification #[2]): Eq (subsetI2 → setminusEL → ∀ (A B : Iota), subset (setminus A B) A) False % 3.88/4.05 Clause #23 (by clausification #[22]): Eq subsetI2 True % 3.88/4.05 Clause #24 (by clausification #[22]): Eq (setminusEL → ∀ (A B : Iota), subset (setminus A B) A) False % 3.88/4.05 Clause #26 (by backward demodulation #[23, 12]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 3.88/4.05 Clause #28 (by clausification #[1]): Eq setminusEL (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A) % 3.88/4.05 Clause #39 (by clausification #[24]): Eq setminusEL True % 3.88/4.05 Clause #40 (by clausification #[24]): Eq (∀ (A B : Iota), subset (setminus A B) A) False % 3.88/4.05 Clause #41 (by backward demodulation #[39, 28]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A) % 3.88/4.05 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → in Xx a) True % 3.88/4.05 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → in Xx a) True % 3.88/4.05 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → in a a_1) True % 3.88/4.05 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_1) True) % 3.88/4.05 Clause #47 (by clausification #[40]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (setminus (skS.0 4 a) B) (skS.0 4 a))) True % 3.88/4.05 Clause #48 (by clausification #[47]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (setminus (skS.0 4 a) B) (skS.0 4 a)) False % 3.88/4.05 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (Not (subset (setminus (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 4 a))) True % 3.88/4.05 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Eq (subset (setminus (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 4 a)) False % 3.88/4.05 Clause #56 (by forward demodulation #[13, 23]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 3.88/4.05 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False) % 3.88/4.05 Clause #71 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True) % 3.88/4.05 Clause #72 (by superposition #[71, 45]): ∀ (a a_1 a_2 a_3 : Iota), % 3.88/4.05 Or (Eq (subset (setminus a a_1) a_2) True) (Or (Eq True False) (Eq (in (skS.0 0 (setminus a a_1) a_2 a_3) a) True)) % 3.88/4.05 Clause #75 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (subset (setminus a a_1) a_2) True) (Eq (in (skS.0 0 (setminus a a_1) a_2 a_3) a) True) % 3.88/4.05 Clause #77 (by superposition #[75, 57]): ∀ (a a_1 : Iota), Or (Eq (subset (setminus a a_1) a) True) (Or (Eq (subset (setminus a a_1) a) True) (Eq True False)) % 3.88/4.05 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (subset (setminus a a_1) a) True) (Eq (subset (setminus a a_1) a) True) % 3.88/4.05 Clause #79 (by eliminate duplicate literals #[78]): ∀ (a a_1 : Iota), Eq (subset (setminus a a_1) a) True % 3.88/4.05 Clause #80 (by superposition #[79, 50]): Eq True False % 3.88/4.05 Clause #83 (by clausification #[80]): False % 3.88/4.05 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------