%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU599^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:02:00 PM UTC 2025 % Result : Theorem 4.01s 4.18s % Output : Proof 4.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.01/0.12 % Problem : SEU599^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n014.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 05:38:53 EDT 2025 % 0.14/0.34 % CPUTime : % 4.01/4.18 SZS status Theorem for theBenchmark.p % 4.01/4.18 SZS output start Proof for theBenchmark.p % 4.01/4.18 Clause #1 (by assumption #[]): Eq (Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 4.01/4.18 Clause #2 (by assumption #[]): Eq (Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B)) True % 4.01/4.18 Clause #3 (by assumption #[]): Eq (Not (in__Cong → subsetI1 → binintersectER → ∀ (A B : Iota), Eq (binintersect A B) A → subset A B)) True % 4.01/4.18 Clause #4 (by clausification #[1]): Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.01/4.18 Clause #6 (by clausify Prop equality #[4]): Or (Eq subsetI1 False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) True) % 4.01/4.18 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq subsetI1 False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True) % 4.01/4.18 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq subsetI1 False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True) % 4.01/4.18 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq subsetI1 False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True)) % 4.01/4.18 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.01/4.18 Or (Eq subsetI1 False) % 4.01/4.18 (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)) % 4.01/4.18 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.01/4.18 Or (Eq subsetI1 False) % 4.01/4.18 (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)) % 4.01/4.18 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI1 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 4.01/4.18 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI1 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 4.01/4.18 Clause #23 (by clausification #[3]): Eq (in__Cong → subsetI1 → binintersectER → ∀ (A B : Iota), Eq (binintersect A B) A → subset A B) False % 4.01/4.18 Clause #25 (by clausification #[23]): Eq (subsetI1 → binintersectER → ∀ (A B : Iota), Eq (binintersect A B) A → subset A B) False % 4.01/4.18 Clause #40 (by clausification #[25]): Eq subsetI1 True % 4.01/4.18 Clause #41 (by clausification #[25]): Eq (binintersectER → ∀ (A B : Iota), Eq (binintersect A B) A → subset A B) False % 4.01/4.18 Clause #43 (by backward demodulation #[40, 13]): ∀ (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)) % 4.01/4.18 Clause #52 (by clausification #[41]): Eq binintersectER True % 4.01/4.18 Clause #53 (by clausification #[41]): Eq (∀ (A B : Iota), Eq (binintersect A B) A → subset A B) False % 4.01/4.18 Clause #54 (by clausification #[53]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Eq (binintersect (skS.0 4 a) B) (skS.0 4 a) → subset (skS.0 4 a) B)) True % 4.01/4.18 Clause #55 (by clausification #[54]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (binintersect (skS.0 4 a) B) (skS.0 4 a) → subset (skS.0 4 a) B) False % 4.01/4.18 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 4.01/4.18 Eq (Not (Eq (binintersect (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 4 a) → subset (skS.0 4 a) (skS.0 5 a a_1))) True % 4.01/4.18 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), % 4.01/4.18 Eq (Eq (binintersect (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 4 a) → subset (skS.0 4 a) (skS.0 5 a a_1)) False % 4.01/4.18 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (Eq (binintersect (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 4 a)) True % 4.01/4.18 Clause #59 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (subset (skS.0 4 a) (skS.0 5 a a_1)) False % 4.01/4.18 Clause #60 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (binintersect (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 4 a) % 4.01/4.18 Clause #61 (by clausification #[2]): Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 4.01/4.18 Clause #62 (by forward demodulation #[61, 52]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 4.01/4.18 Clause #63 (by clausification #[62]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx B) True % 4.01/4.18 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a_1) True % 4.01/4.19 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_2) True % 4.01/4.19 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_2) True) % 4.01/4.19 Clause #69 (by forward demodulation #[14, 40]): ∀ (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)) % 4.01/4.19 Clause #70 (by clausification #[69]): ∀ (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) % 4.01/4.19 Clause #77 (by clausification #[43]): ∀ (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) % 4.01/4.19 Clause #78 (by superposition #[77, 66]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq (subset (binintersect a a_1) a_2) True) % 4.01/4.19 (Or (Eq True False) (Eq (in (skS.0 0 (binintersect a a_1) a_2 a_3) a_1) True)) % 4.01/4.19 Clause #82 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq (subset (binintersect a a_1) a_2) True) (Eq (in (skS.0 0 (binintersect a a_1) a_2 a_3) a_1) True) % 4.01/4.19 Clause #85 (by superposition #[82, 70]): ∀ (a a_1 : Iota), % 4.01/4.19 Or (Eq (subset (binintersect a a_1) a_1) True) (Or (Eq (subset (binintersect a a_1) a_1) True) (Eq True False)) % 4.01/4.19 Clause #87 (by clausification #[85]): ∀ (a a_1 : Iota), Or (Eq (subset (binintersect a a_1) a_1) True) (Eq (subset (binintersect a a_1) a_1) True) % 4.01/4.19 Clause #88 (by eliminate duplicate literals #[87]): ∀ (a a_1 : Iota), Eq (subset (binintersect a a_1) a_1) True % 4.01/4.19 Clause #89 (by superposition #[88, 60]): ∀ (a a_1 : Iota), Eq (subset (skS.0 4 a) (skS.0 5 a a_1)) True % 4.01/4.19 Clause #94 (by superposition #[89, 59]): Eq True False % 4.01/4.19 Clause #95 (by clausification #[94]): False % 4.01/4.19 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------