%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU714^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:02:16 PM UTC 2025 % Result : Theorem 3.81s 4.00s % Output : Proof 3.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU714^2 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.14 % Command : duper %s % 0.13/0.35 % Computer : n013.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 05:47:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.81/4.00 SZS status Theorem for theBenchmark.p % 3.81/4.00 SZS output start Proof for theBenchmark.p % 3.81/4.00 Clause #0 (by assumption #[]): Eq (Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True % 3.81/4.00 Clause #1 (by assumption #[]): Eq (Eq setminusEL (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A)) True % 3.81/4.00 Clause #2 (by assumption #[]): Eq (Not (powersetI → setminusEL → ∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A))) True % 3.81/4.00 Clause #3 (by clausification #[1]): Eq setminusEL (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A) % 3.81/4.00 Clause #19 (by clausification #[0]): Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 3.81/4.00 Clause #21 (by clausify Prop equality #[19]): Or (Eq powersetI False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) True) % 3.81/4.00 Clause #23 (by clausification #[2]): Eq (powersetI → setminusEL → ∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A)) False % 3.81/4.00 Clause #24 (by clausification #[23]): Eq powersetI True % 3.81/4.00 Clause #25 (by clausification #[23]): Eq (setminusEL → ∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A)) False % 3.81/4.00 Clause #43 (by clausification #[21]): ∀ (a : Iota), Or (Eq powersetI False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx a) → in B (powerset a)) True) % 3.81/4.00 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq powersetI False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → in a (powerset a_1)) True) % 3.81/4.00 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), % 3.81/4.00 Or (Eq powersetI False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (in a (powerset a_1)) True)) % 3.81/4.00 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 3.81/4.00 Or (Eq powersetI False) % 3.81/4.00 (Or (Eq (in a (powerset a_1)) True) (Eq (Not (in (skS.0 6 a a_1 a_2) a → in (skS.0 6 a a_1 a_2) a_1)) True)) % 3.81/4.00 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 3.81/4.00 Or (Eq powersetI False) % 3.81/4.00 (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 6 a a_1 a_2) a → in (skS.0 6 a a_1 a_2) a_1) False)) % 3.81/4.00 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq powersetI False) (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 6 a a_1 a_2) a) True)) % 3.81/4.00 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 3.81/4.00 Or (Eq powersetI False) (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 6 a a_1 a_2) a_1) False)) % 3.81/4.00 Clause #50 (by forward demodulation #[48, 24]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 6 a a_1 a_2) a) True)) % 3.81/4.00 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 6 a a_1 a_2) a) True) % 3.81/4.00 Clause #52 (by clausification #[25]): Eq setminusEL True % 3.81/4.00 Clause #53 (by clausification #[25]): Eq (∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A)) False % 3.81/4.00 Clause #54 (by backward demodulation #[52, 3]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A) % 3.81/4.00 Clause #57 (by clausification #[54]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → in Xx a) True % 3.81/4.00 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → in Xx a) True % 3.81/4.00 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → in a a_1) True % 3.81/4.00 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_1) True) % 3.81/4.00 Clause #62 (by superposition #[60, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 3.81/4.00 Or (Eq (in (skS.0 6 (setminus a a_1) a_2 a_3) a) True) % 3.81/4.00 (Or (Eq (in (setminus a a_1) (powerset a_2)) True) (Eq False True)) % 3.81/4.00 Clause #64 (by clausification #[53]): ∀ (a : Iota), % 3.81/4.00 Eq (Not (∀ (X : Iota), in X (powerset (skS.0 7 a)) → in (setminus (skS.0 7 a) X) (powerset (skS.0 7 a)))) True % 3.81/4.00 Clause #65 (by clausification #[64]): ∀ (a : Iota), Eq (∀ (X : Iota), in X (powerset (skS.0 7 a)) → in (setminus (skS.0 7 a) X) (powerset (skS.0 7 a))) False % 3.81/4.00 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 3.81/4.00 Eq % 3.81/4.00 (Not (in (skS.0 8 a a_1) (powerset (skS.0 7 a)) → in (setminus (skS.0 7 a) (skS.0 8 a a_1)) (powerset (skS.0 7 a)))) % 3.81/4.01 True % 3.81/4.01 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 3.81/4.01 Eq (in (skS.0 8 a a_1) (powerset (skS.0 7 a)) → in (setminus (skS.0 7 a) (skS.0 8 a a_1)) (powerset (skS.0 7 a))) % 3.81/4.01 False % 3.81/4.01 Clause #69 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (in (setminus (skS.0 7 a) (skS.0 8 a a_1)) (powerset (skS.0 7 a))) False % 3.81/4.01 Clause #74 (by forward demodulation #[49, 24]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 6 a a_1 a_2) a_1) False)) % 3.81/4.01 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 6 a a_1 a_2) a_1) False) % 3.81/4.01 Clause #76 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 3.81/4.01 Or (Eq (in (skS.0 6 (setminus a a_1) a_2 a_3) a) True) (Eq (in (setminus a a_1) (powerset a_2)) True) % 3.81/4.01 Clause #78 (by superposition #[76, 75]): ∀ (a a_1 : Iota), % 3.81/4.01 Or (Eq (in (setminus a a_1) (powerset a)) True) (Or (Eq (in (setminus a a_1) (powerset a)) True) (Eq True False)) % 3.81/4.01 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Or (Eq (in (setminus a a_1) (powerset a)) True) (Eq (in (setminus a a_1) (powerset a)) True) % 3.81/4.01 Clause #80 (by eliminate duplicate literals #[79]): ∀ (a a_1 : Iota), Eq (in (setminus a a_1) (powerset a)) True % 3.81/4.01 Clause #81 (by superposition #[80, 69]): Eq True False % 3.81/4.01 Clause #82 (by clausification #[81]): False % 3.81/4.01 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------