%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU760^2 : TPTP v9.2.0. Released v3.7.0. % 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 08:02:23 PM UTC 2025 % Result : Theorem 5.91s 6.15s % Output : Proof 6.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU760^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % 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 05:22:23 EDT 2025 % 0.13/0.34 % CPUTime : % 5.91/6.15 SZS status Theorem for theBenchmark.p % 5.91/6.15 SZS output start Proof for theBenchmark.p % 5.91/6.15 Clause #0 (by assumption #[]): Eq (Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 5.91/6.15 Clause #1 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 5.91/6.15 Clause #2 (by assumption #[]): Eq (Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B)) True % 5.91/6.15 Clause #3 (by assumption #[]): Eq % 5.91/6.15 (Not % 5.91/6.15 (subsetI1 → % 5.91/6.15 subsetE → % 5.91/6.15 binintersectER → % 5.91/6.15 ∀ (A X : Iota), % 5.91/6.15 in X (powerset A) → % 5.91/6.15 ∀ (Y : Iota), % 5.91/6.15 in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset Y Z → subset (binintersect X Y) Z)) % 5.91/6.15 True % 5.91/6.15 Clause #4 (by clausification #[0]): Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 5.91/6.15 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) % 5.91/6.15 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) % 5.91/6.15 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) % 5.91/6.15 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)) % 5.91/6.15 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 5.91/6.15 Or (Eq subsetI1 False) % 5.91/6.15 (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)) % 5.91/6.15 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 5.91/6.15 Or (Eq subsetI1 False) % 5.91/6.15 (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)) % 5.91/6.15 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)) % 5.91/6.15 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)) % 5.91/6.15 Clause #23 (by clausification #[2]): Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 5.91/6.15 Clause #27 (by clausification #[1]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 5.91/6.15 Clause #56 (by clausification #[3]): Eq % 5.91/6.15 (subsetI1 → % 5.91/6.15 subsetE → % 5.91/6.15 binintersectER → % 5.91/6.15 ∀ (A X : Iota), % 5.91/6.15 in X (powerset A) → % 5.91/6.15 ∀ (Y : Iota), % 5.91/6.15 in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset Y Z → subset (binintersect X Y) Z) % 5.91/6.15 False % 5.91/6.15 Clause #57 (by clausification #[56]): Eq subsetI1 True % 5.91/6.15 Clause #58 (by clausification #[56]): Eq % 5.91/6.15 (subsetE → % 5.91/6.15 binintersectER → % 5.91/6.15 ∀ (A X : Iota), % 5.91/6.15 in X (powerset A) → % 5.91/6.15 ∀ (Y : Iota), in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset Y Z → subset (binintersect X Y) Z) % 5.91/6.15 False % 5.91/6.15 Clause #60 (by backward demodulation #[57, 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)) % 5.91/6.15 Clause #69 (by clausification #[58]): Eq subsetE True % 5.91/6.15 Clause #70 (by clausification #[58]): Eq % 5.91/6.15 (binintersectER → % 5.91/6.15 ∀ (A X : Iota), % 5.91/6.15 in X (powerset A) → % 5.91/6.15 ∀ (Y : Iota), in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset Y Z → subset (binintersect X Y) Z) % 5.91/6.15 False % 5.91/6.15 Clause #71 (by backward demodulation #[69, 27]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 5.91/6.15 Clause #74 (by clausification #[71]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 5.91/6.15 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 5.91/6.15 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 5.91/6.15 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 6.00/6.17 Clause #78 (by clausification #[77]): ∀ (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)) % 6.00/6.17 Clause #79 (by forward demodulation #[14, 57]): ∀ (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)) % 6.00/6.17 Clause #80 (by clausification #[79]): ∀ (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) % 6.00/6.17 Clause #81 (by clausification #[70]): Eq binintersectER True % 6.00/6.17 Clause #82 (by clausification #[70]): Eq % 6.00/6.17 (∀ (A X : Iota), % 6.00/6.17 in X (powerset A) → % 6.00/6.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset Y Z → subset (binintersect X Y) Z) % 6.00/6.17 False % 6.00/6.17 Clause #83 (by backward demodulation #[81, 23]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 6.00/6.17 Clause #86 (by clausification #[83]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx B) True % 6.00/6.17 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a_1) True % 6.00/6.17 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_2) True % 6.00/6.17 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_2) True) % 6.00/6.17 Clause #91 (by clausification #[82]): ∀ (a : Iota), % 6.00/6.17 Eq % 6.00/6.17 (Not % 6.00/6.17 (∀ (X : Iota), % 6.00/6.17 in X (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Y : Iota), % 6.00/6.17 in Y (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Z : Iota), in Z (powerset (skS.0 10 a)) → subset Y Z → subset (binintersect X Y) Z)) % 6.00/6.17 True % 6.00/6.17 Clause #92 (by clausification #[91]): ∀ (a : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (X : Iota), % 6.00/6.17 in X (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Y : Iota), % 6.00/6.17 in Y (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Z : Iota), in Z (powerset (skS.0 10 a)) → subset Y Z → subset (binintersect X Y) Z) % 6.00/6.17 False % 6.00/6.17 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (Not % 6.00/6.17 (in (skS.0 11 a a_1) (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Y : Iota), % 6.00/6.17 in Y (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Z : Iota), in Z (powerset (skS.0 10 a)) → subset Y Z → subset (binintersect (skS.0 11 a a_1) Y) Z)) % 6.00/6.17 True % 6.00/6.17 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (in (skS.0 11 a a_1) (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Y : Iota), % 6.00/6.17 in Y (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Z : Iota), in Z (powerset (skS.0 10 a)) → subset Y Z → subset (binintersect (skS.0 11 a a_1) Y) Z) % 6.00/6.17 False % 6.00/6.17 Clause #96 (by clausification #[94]): ∀ (a a_1 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (Y : Iota), % 6.00/6.17 in Y (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Z : Iota), in Z (powerset (skS.0 10 a)) → subset Y Z → subset (binintersect (skS.0 11 a a_1) Y) Z) % 6.00/6.17 False % 6.00/6.17 Clause #103 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (Not % 6.00/6.17 (in (skS.0 12 a a_1 a_2) (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Z : Iota), % 6.00/6.17 in Z (powerset (skS.0 10 a)) → % 6.00/6.17 subset (skS.0 12 a a_1 a_2) Z → subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) Z)) % 6.00/6.17 True % 6.00/6.17 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (in (skS.0 12 a a_1 a_2) (powerset (skS.0 10 a)) → % 6.00/6.17 ∀ (Z : Iota), % 6.00/6.17 in Z (powerset (skS.0 10 a)) → % 6.00/6.17 subset (skS.0 12 a a_1 a_2) Z → subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) Z) % 6.00/6.17 False % 6.00/6.17 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (Z : Iota), % 6.00/6.17 in Z (powerset (skS.0 10 a)) → % 6.00/6.17 subset (skS.0 12 a a_1 a_2) Z → subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) Z) % 6.00/6.17 False % 6.00/6.17 Clause #107 (by clausification #[60]): ∀ (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) % 6.00/6.17 Clause #108 (by superposition #[107, 89]): ∀ (a a_1 a_2 a_3 : Iota), % 6.00/6.17 Or (Eq (subset (binintersect a a_1) a_2) True) % 6.00/6.17 (Or (Eq True False) (Eq (in (skS.0 0 (binintersect a a_1) a_2 a_3) a_1) True)) % 6.00/6.17 Clause #111 (by clausification #[108]): ∀ (a a_1 a_2 a_3 : Iota), % 6.00/6.19 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) % 6.00/6.19 Clause #122 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota), % 6.00/6.19 Eq % 6.00/6.19 (Not % 6.00/6.19 (in (skS.0 13 a a_1 a_2 a_3) (powerset (skS.0 10 a)) → % 6.00/6.19 subset (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3) → % 6.00/6.19 subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (skS.0 13 a a_1 a_2 a_3))) % 6.00/6.19 True % 6.00/6.19 Clause #123 (by clausification #[122]): ∀ (a a_1 a_2 a_3 : Iota), % 6.00/6.19 Eq % 6.00/6.19 (in (skS.0 13 a a_1 a_2 a_3) (powerset (skS.0 10 a)) → % 6.00/6.19 subset (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3) → % 6.00/6.19 subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (skS.0 13 a a_1 a_2 a_3)) % 6.00/6.19 False % 6.00/6.19 Clause #125 (by clausification #[123]): ∀ (a a_1 a_2 a_3 : Iota), % 6.00/6.19 Eq % 6.00/6.19 (subset (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3) → % 6.00/6.19 subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (skS.0 13 a a_1 a_2 a_3)) % 6.00/6.19 False % 6.00/6.19 Clause #150 (by clausification #[125]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)) True % 6.00/6.19 Clause #151 (by clausification #[125]): ∀ (a a_1 a_2 a_3 : Iota), % 6.00/6.19 Eq (subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (skS.0 13 a a_1 a_2 a_3)) False % 6.00/6.19 Clause #152 (by superposition #[150, 78]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.00/6.19 Or (Eq True False) (Or (Eq (in a (skS.0 12 a_1 a_2 a_3)) False) (Eq (in a (skS.0 13 a_1 a_2 a_3 a_4)) True)) % 6.00/6.19 Clause #160 (by clausification #[152]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (in a (skS.0 12 a_1 a_2 a_3)) False) (Eq (in a (skS.0 13 a_1 a_2 a_3 a_4)) True) % 6.00/6.19 Clause #163 (by superposition #[160, 111]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.00/6.19 Or (Eq (in (skS.0 0 (binintersect a (skS.0 12 a_1 a_2 a_3)) a_4 a_5) (skS.0 13 a_1 a_2 a_3 a_6)) True) % 6.00/6.19 (Or (Eq (subset (binintersect a (skS.0 12 a_1 a_2 a_3)) a_4) True) (Eq False True)) % 6.00/6.19 Clause #262 (by clausification #[163]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.00/6.19 Or (Eq (in (skS.0 0 (binintersect a (skS.0 12 a_1 a_2 a_3)) a_4 a_5) (skS.0 13 a_1 a_2 a_3 a_6)) True) % 6.00/6.19 (Eq (subset (binintersect a (skS.0 12 a_1 a_2 a_3)) a_4) True) % 6.00/6.19 Clause #263 (by superposition #[262, 80]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.00/6.19 Or (Eq (subset (binintersect a (skS.0 12 a_1 a_2 a_3)) (skS.0 13 a_1 a_2 a_3 a_4)) True) % 6.00/6.19 (Or (Eq (subset (binintersect a (skS.0 12 a_1 a_2 a_3)) (skS.0 13 a_1 a_2 a_3 a_4)) True) (Eq True False)) % 6.00/6.19 Clause #296 (by clausification #[263]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.00/6.19 Or (Eq (subset (binintersect a (skS.0 12 a_1 a_2 a_3)) (skS.0 13 a_1 a_2 a_3 a_4)) True) % 6.00/6.19 (Eq (subset (binintersect a (skS.0 12 a_1 a_2 a_3)) (skS.0 13 a_1 a_2 a_3 a_4)) True) % 6.00/6.19 Clause #297 (by eliminate duplicate literals #[296]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (subset (binintersect a (skS.0 12 a_1 a_2 a_3)) (skS.0 13 a_1 a_2 a_3 a_4)) True % 6.00/6.19 Clause #298 (by superposition #[297, 151]): Eq True False % 6.00/6.19 Clause #301 (by clausification #[298]): False % 6.00/6.19 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------