%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU713^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 5.64s 5.78s % Output : Proof 5.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU713^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 04:55:23 EDT 2025 % 0.13/0.35 % CPUTime : % 5.64/5.78 SZS status Theorem for theBenchmark.p % 5.64/5.78 SZS output start Proof for theBenchmark.p % 5.64/5.78 Clause #0 (by assumption #[]): Eq (Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True % 5.64/5.78 Clause #1 (by assumption #[]): Eq (Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)) True % 5.64/5.78 Clause #2 (by assumption #[]): Eq (Eq setminusEL (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A)) True % 5.64/5.78 Clause #3 (by assumption #[]): Eq % 5.64/5.78 (Not % 5.64/5.78 (powersetI → % 5.64/5.78 powersetE → % 5.64/5.78 setminusEL → % 5.64/5.78 ∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A))) % 5.64/5.78 True % 5.64/5.78 Clause #4 (by clausification #[2]): Eq setminusEL (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A) % 5.64/5.78 Clause #20 (by clausification #[0]): Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 5.64/5.78 Clause #24 (by clausification #[1]): Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 5.64/5.79 Clause #56 (by clausification #[3]): Eq % 5.64/5.79 (powersetI → % 5.64/5.79 powersetE → % 5.64/5.79 setminusEL → ∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A)) % 5.64/5.79 False % 5.64/5.79 Clause #57 (by clausification #[56]): Eq powersetI True % 5.64/5.79 Clause #58 (by clausification #[56]): Eq % 5.64/5.79 (powersetE → % 5.64/5.79 setminusEL → ∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A)) % 5.64/5.79 False % 5.64/5.79 Clause #59 (by backward demodulation #[57, 20]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 5.64/5.79 Clause #62 (by clausification #[59]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx a) → in B (powerset a)) True % 5.64/5.79 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → in a (powerset a_1)) True % 5.64/5.79 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (in a (powerset a_1)) True) % 5.64/5.79 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 5.64/5.79 Or (Eq (in a (powerset a_1)) True) (Eq (Not (in (skS.0 9 a a_1 a_2) a → in (skS.0 9 a a_1 a_2) a_1)) True) % 5.64/5.79 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 5.64/5.79 Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 9 a a_1 a_2) a → in (skS.0 9 a a_1 a_2) a_1) False) % 5.64/5.79 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 9 a a_1 a_2) a) True) % 5.64/5.79 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 9 a a_1 a_2) a_1) False) % 5.64/5.79 Clause #69 (by clausification #[58]): Eq powersetE True % 5.64/5.79 Clause #70 (by clausification #[58]): Eq (setminusEL → ∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A)) % 5.64/5.79 False % 5.64/5.79 Clause #71 (by backward demodulation #[69, 24]): Eq True (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 5.64/5.79 Clause #74 (by clausification #[71]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in B (powerset a) → in Xx B → in Xx a) True % 5.64/5.79 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in a (powerset a_1) → in Xx a → in Xx a_1) True % 5.64/5.79 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (in a (powerset a_1) → in a_2 a → in a_2 a_1) True % 5.64/5.79 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (in a_2 a → in a_2 a_1) True) % 5.64/5.79 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 5.64/5.79 Clause #80 (by clausification #[70]): Eq setminusEL True % 5.64/5.79 Clause #81 (by clausification #[70]): Eq (∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A)) False % 5.64/5.79 Clause #82 (by backward demodulation #[80, 4]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A) % 5.64/5.79 Clause #86 (by clausification #[82]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → in Xx a) True % 5.64/5.81 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → in Xx a) True % 5.64/5.81 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → in a a_1) True % 5.64/5.81 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_1) True) % 5.64/5.81 Clause #90 (by superposition #[89, 67]): ∀ (a a_1 a_2 a_3 : Iota), % 5.64/5.81 Or (Eq (in (skS.0 9 (setminus a a_1) a_2 a_3) a) True) % 5.64/5.81 (Or (Eq (in (setminus a a_1) (powerset a_2)) True) (Eq False True)) % 5.64/5.81 Clause #91 (by clausification #[81]): ∀ (a : Iota), % 5.64/5.81 Eq % 5.64/5.81 (Not % 5.64/5.81 (∀ (X : Iota), % 5.64/5.81 in X (powerset (skS.0 10 a)) → % 5.64/5.81 ∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus X Y) (powerset (skS.0 10 a)))) % 5.64/5.81 True % 5.64/5.81 Clause #92 (by clausification #[91]): ∀ (a : Iota), % 5.64/5.81 Eq % 5.64/5.81 (∀ (X : Iota), % 5.64/5.81 in X (powerset (skS.0 10 a)) → % 5.64/5.81 ∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus X Y) (powerset (skS.0 10 a))) % 5.64/5.81 False % 5.64/5.81 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), % 5.64/5.81 Eq % 5.64/5.81 (Not % 5.64/5.81 (in (skS.0 11 a a_1) (powerset (skS.0 10 a)) → % 5.64/5.81 ∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus (skS.0 11 a a_1) Y) (powerset (skS.0 10 a)))) % 5.64/5.81 True % 5.64/5.81 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), % 5.64/5.81 Eq % 5.64/5.81 (in (skS.0 11 a a_1) (powerset (skS.0 10 a)) → % 5.64/5.81 ∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus (skS.0 11 a a_1) Y) (powerset (skS.0 10 a))) % 5.64/5.81 False % 5.64/5.81 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Eq (in (skS.0 11 a a_1) (powerset (skS.0 10 a))) True % 5.64/5.81 Clause #96 (by clausification #[94]): ∀ (a a_1 : Iota), % 5.64/5.81 Eq (∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus (skS.0 11 a a_1) Y) (powerset (skS.0 10 a))) False % 5.64/5.81 Clause #97 (by superposition #[95, 78]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 11 a_1 a_2)) False) (Eq (in a (skS.0 10 a_1)) True)) % 5.64/5.81 Clause #114 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 5.64/5.81 Eq % 5.64/5.81 (Not % 5.64/5.81 (in (skS.0 12 a a_1 a_2) (powerset (skS.0 10 a)) → % 5.64/5.81 in (setminus (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (powerset (skS.0 10 a)))) % 5.64/5.81 True % 5.64/5.81 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), % 5.64/5.81 Eq % 5.64/5.81 (in (skS.0 12 a a_1 a_2) (powerset (skS.0 10 a)) → % 5.64/5.81 in (setminus (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (powerset (skS.0 10 a))) % 5.64/5.81 False % 5.64/5.81 Clause #117 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), Eq (in (setminus (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (powerset (skS.0 10 a))) False % 5.64/5.81 Clause #119 (by clausification #[97]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 11 a_1 a_2)) False) (Eq (in a (skS.0 10 a_1)) True) % 5.64/5.81 Clause #137 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota), % 5.64/5.81 Or (Eq (in (skS.0 9 (setminus a a_1) a_2 a_3) a) True) (Eq (in (setminus a a_1) (powerset a_2)) True) % 5.64/5.81 Clause #140 (by superposition #[137, 119]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.64/5.81 Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset a_3)) True) % 5.64/5.81 (Or (Eq True False) (Eq (in (skS.0 9 (setminus (skS.0 11 a a_1) a_2) a_3 a_4) (skS.0 10 a)) True)) % 5.64/5.81 Clause #417 (by clausification #[140]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.64/5.81 Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset a_3)) True) % 5.64/5.81 (Eq (in (skS.0 9 (setminus (skS.0 11 a a_1) a_2) a_3 a_4) (skS.0 10 a)) True) % 5.64/5.81 Clause #418 (by superposition #[417, 68]): ∀ (a a_1 a_2 : Iota), % 5.64/5.81 Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True) % 5.64/5.81 (Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True) (Eq True False)) % 5.64/5.81 Clause #420 (by clausification #[418]): ∀ (a a_1 a_2 : Iota), % 5.64/5.81 Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True) % 5.64/5.81 (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True) % 5.64/5.81 Clause #421 (by eliminate duplicate literals #[420]): ∀ (a a_1 a_2 : Iota), Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True % 5.64/5.81 Clause #422 (by superposition #[421, 117]): Eq True False % 5.64/5.81 Clause #424 (by clausification #[422]): False % 5.64/5.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------