%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU735^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:02:19 PM UTC 2025 % Result : Theorem 3.82s 4.06s % Output : Proof 3.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU735^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n017.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 06:32:23 EDT 2025 % 0.14/0.34 % CPUTime : % 3.82/4.06 SZS status Theorem for theBenchmark.p % 3.82/4.06 SZS output start Proof for theBenchmark.p % 3.82/4.06 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True % 3.82/4.06 Clause #1 (by assumption #[]): Eq % 3.82/4.06 (Eq complementSubsetComplementIntersect % 3.82/4.06 (∀ (A X : Iota), % 3.82/4.06 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset (setminus A X) (setminus A (binintersect X Y)))) % 3.82/4.06 True % 3.82/4.06 Clause #2 (by assumption #[]): Eq % 3.82/4.06 (Not % 3.82/4.06 (powersetI1 → % 3.82/4.06 complementSubsetComplementIntersect → % 3.82/4.06 ∀ (A X : Iota), % 3.82/4.06 in X (powerset A) → % 3.82/4.06 ∀ (Y : Iota), in Y (powerset A) → in (setminus A X) (powerset (setminus A (binintersect X Y))))) % 3.82/4.06 True % 3.82/4.06 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A)) % 3.82/4.06 Clause #16 (by clausification #[1]): Eq complementSubsetComplementIntersect % 3.82/4.06 (∀ (A X : Iota), % 3.82/4.06 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset (setminus A X) (setminus A (binintersect X Y))) % 3.82/4.06 Clause #20 (by clausification #[2]): Eq % 3.82/4.06 (powersetI1 → % 3.82/4.06 complementSubsetComplementIntersect → % 3.82/4.06 ∀ (A X : Iota), % 3.82/4.06 in X (powerset A) → % 3.82/4.06 ∀ (Y : Iota), in Y (powerset A) → in (setminus A X) (powerset (setminus A (binintersect X Y)))) % 3.82/4.06 False % 3.82/4.06 Clause #21 (by clausification #[20]): Eq powersetI1 True % 3.82/4.06 Clause #22 (by clausification #[20]): Eq % 3.82/4.06 (complementSubsetComplementIntersect → % 3.82/4.06 ∀ (A X : Iota), % 3.82/4.06 in X (powerset A) → % 3.82/4.06 ∀ (Y : Iota), in Y (powerset A) → in (setminus A X) (powerset (setminus A (binintersect X Y)))) % 3.82/4.06 False % 3.82/4.06 Clause #23 (by backward demodulation #[21, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A)) % 3.82/4.06 Clause #26 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True % 3.82/4.06 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True % 3.82/4.06 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True) % 3.82/4.06 Clause #40 (by clausification #[22]): Eq complementSubsetComplementIntersect True % 3.82/4.06 Clause #41 (by clausification #[22]): Eq % 3.82/4.06 (∀ (A X : Iota), % 3.82/4.06 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus A X) (powerset (setminus A (binintersect X Y)))) % 3.82/4.06 False % 3.82/4.06 Clause #42 (by backward demodulation #[40, 16]): Eq True % 3.82/4.06 (∀ (A X : Iota), % 3.82/4.06 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset (setminus A X) (setminus A (binintersect X Y))) % 3.82/4.06 Clause #46 (by clausification #[42]): ∀ (a : Iota), % 3.82/4.06 Eq % 3.82/4.06 (∀ (X : Iota), % 3.82/4.06 in X (powerset a) → ∀ (Y : Iota), in Y (powerset a) → subset (setminus a X) (setminus a (binintersect X Y))) % 3.82/4.06 True % 3.82/4.06 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), % 3.82/4.06 Eq % 3.82/4.06 (in a (powerset a_1) → % 3.82/4.06 ∀ (Y : Iota), in Y (powerset a_1) → subset (setminus a_1 a) (setminus a_1 (binintersect a Y))) % 3.82/4.06 True % 3.82/4.06 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 3.82/4.06 Or (Eq (in a (powerset a_1)) False) % 3.82/4.06 (Eq (∀ (Y : Iota), in Y (powerset a_1) → subset (setminus a_1 a) (setminus a_1 (binintersect a Y))) True) % 3.82/4.06 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), % 3.82/4.06 Or (Eq (in a (powerset a_1)) False) % 3.82/4.06 (Eq (in a_2 (powerset a_1) → subset (setminus a_1 a) (setminus a_1 (binintersect a a_2))) True) % 3.82/4.06 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 3.82/4.06 Or (Eq (in a (powerset a_1)) False) % 3.82/4.06 (Or (Eq (in a_2 (powerset a_1)) False) (Eq (subset (setminus a_1 a) (setminus a_1 (binintersect a a_2))) True)) % 3.82/4.06 Clause #51 (by clausification #[41]): ∀ (a : Iota), % 3.82/4.06 Eq % 3.82/4.06 (Not % 3.82/4.06 (∀ (X : Iota), % 3.82/4.06 in X (powerset (skS.0 4 a)) → % 3.82/4.06 ∀ (Y : Iota), % 3.82/4.06 in Y (powerset (skS.0 4 a)) → % 3.82/4.06 in (setminus (skS.0 4 a) X) (powerset (setminus (skS.0 4 a) (binintersect X Y))))) % 3.82/4.06 True % 3.82/4.06 Clause #52 (by clausification #[51]): ∀ (a : Iota), % 3.82/4.06 Eq % 3.82/4.06 (∀ (X : Iota), % 3.82/4.06 in X (powerset (skS.0 4 a)) → % 3.82/4.06 ∀ (Y : Iota), % 3.82/4.06 in Y (powerset (skS.0 4 a)) → % 3.82/4.06 in (setminus (skS.0 4 a) X) (powerset (setminus (skS.0 4 a) (binintersect X Y)))) % 3.82/4.08 False % 3.82/4.08 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 3.82/4.08 Eq % 3.82/4.08 (Not % 3.82/4.08 (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) → % 3.82/4.08 ∀ (Y : Iota), % 3.82/4.08 in Y (powerset (skS.0 4 a)) → % 3.82/4.08 in (setminus (skS.0 4 a) (skS.0 5 a a_1)) % 3.82/4.08 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) Y))))) % 3.82/4.08 True % 3.82/4.08 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), % 3.82/4.08 Eq % 3.82/4.08 (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) → % 3.82/4.08 ∀ (Y : Iota), % 3.82/4.08 in Y (powerset (skS.0 4 a)) → % 3.82/4.08 in (setminus (skS.0 4 a) (skS.0 5 a a_1)) (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) Y)))) % 3.82/4.08 False % 3.82/4.08 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True % 3.82/4.08 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), % 3.82/4.08 Eq % 3.82/4.08 (∀ (Y : Iota), % 3.82/4.08 in Y (powerset (skS.0 4 a)) → % 3.82/4.08 in (setminus (skS.0 4 a) (skS.0 5 a a_1)) (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) Y)))) % 3.82/4.08 False % 3.82/4.08 Clause #57 (by superposition #[55, 50]): ∀ (a a_1 a_2 : Iota), % 3.82/4.08 Or (Eq True False) % 3.82/4.08 (Or (Eq (in a (powerset (skS.0 4 a_1))) False) % 3.82/4.08 (Eq % 3.82/4.08 (subset (setminus (skS.0 4 a_1) (skS.0 5 a_1 a_2)) (setminus (skS.0 4 a_1) (binintersect (skS.0 5 a_1 a_2) a))) % 3.82/4.08 True)) % 3.82/4.08 Clause #63 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 3.82/4.08 Eq % 3.82/4.08 (Not % 3.82/4.08 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 4 a)) → % 3.82/4.08 in (setminus (skS.0 4 a) (skS.0 5 a a_1)) % 3.82/4.08 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_1 a_2)))))) % 3.82/4.08 True % 3.82/4.08 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 3.82/4.08 Eq % 3.82/4.08 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 4 a)) → % 3.82/4.08 in (setminus (skS.0 4 a) (skS.0 5 a a_1)) % 3.82/4.08 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_1 a_2))))) % 3.82/4.08 False % 3.82/4.08 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1 a_2) (powerset (skS.0 4 a))) True % 3.82/4.08 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 3.82/4.08 Eq % 3.82/4.08 (in (setminus (skS.0 4 a) (skS.0 5 a a_1)) % 3.82/4.08 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_1 a_2))))) % 3.82/4.08 False % 3.82/4.08 Clause #69 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 3.82/4.08 Or (Eq (in a (powerset (skS.0 4 a_1))) False) % 3.82/4.08 (Eq (subset (setminus (skS.0 4 a_1) (skS.0 5 a_1 a_2)) (setminus (skS.0 4 a_1) (binintersect (skS.0 5 a_1 a_2) a))) % 3.82/4.08 True) % 3.82/4.08 Clause #71 (by superposition #[69, 65]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/4.08 Or % 3.82/4.08 (Eq % 3.82/4.08 (subset (setminus (skS.0 4 a) (skS.0 5 a a_1)) % 3.82/4.08 (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_2 a_3)))) % 3.82/4.08 True) % 3.82/4.08 (Eq False True) % 3.82/4.08 Clause #79 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/4.08 Eq % 3.82/4.08 (subset (setminus (skS.0 4 a) (skS.0 5 a a_1)) % 3.82/4.08 (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_2 a_3)))) % 3.82/4.08 True % 3.82/4.08 Clause #80 (by superposition #[79, 28]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/4.08 Or (Eq True False) % 3.82/4.08 (Eq % 3.82/4.08 (in (setminus (skS.0 4 a) (skS.0 5 a a_1)) % 3.82/4.08 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_2 a_3))))) % 3.82/4.08 True) % 3.82/4.08 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/4.08 Eq % 3.82/4.08 (in (setminus (skS.0 4 a) (skS.0 5 a a_1)) % 3.82/4.08 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_2 a_3))))) % 3.82/4.08 True % 3.82/4.08 Clause #82 (by superposition #[81, 66]): Eq True False % 3.82/4.08 Clause #84 (by clausification #[82]): False % 3.82/4.08 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------