%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET101+1 : TPTP v9.2.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 07:59:38 PM UTC 2025 % Result : Theorem 6.19s 6.37s % Output : Proof 6.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET101+1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 14:18:53 EDT 2025 % 0.12/0.34 % CPUTime : % 6.19/6.37 SZS status Theorem for theBenchmark.p % 6.19/6.37 SZS output start Proof for theBenchmark.p % 6.19/6.37 Clause #3 (by assumption #[]): Eq (∀ (U X Y : Iota), Iff (member U (unordered_pair X Y)) (And (member U universal_class) (Or (Eq U X) (Eq U Y)))) True % 6.19/6.37 Clause #4 (by assumption #[]): Eq (∀ (X Y : Iota), member (unordered_pair X Y) universal_class) True % 6.19/6.37 Clause #5 (by assumption #[]): Eq (∀ (X : Iota), Eq (singleton X) (unordered_pair X X)) True % 6.19/6.37 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), Eq (ordered_pair X Y) (unordered_pair (singleton X) (unordered_pair X (singleton Y)))) True % 6.19/6.37 Clause #43 (by assumption #[]): Eq (Not (∀ (X Y : Iota), member (singleton X) (ordered_pair X Y))) True % 6.19/6.37 Clause #63 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y : Iota), member (unordered_pair a Y) universal_class) True % 6.19/6.37 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Eq (member (unordered_pair a a_1) universal_class) True % 6.19/6.37 Clause #67 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (singleton a) (unordered_pair a a)) True % 6.19/6.37 Clause #68 (by clausification #[67]): ∀ (a : Iota), Eq (singleton a) (unordered_pair a a) % 6.19/6.37 Clause #69 (by superposition #[68, 64]): ∀ (a : Iota), Eq (member (singleton a) universal_class) True % 6.19/6.37 Clause #93 (by clausification #[3]): ∀ (a : Iota), % 6.19/6.37 Eq (∀ (X Y : Iota), Iff (member a (unordered_pair X Y)) (And (member a universal_class) (Or (Eq a X) (Eq a Y)))) True % 6.19/6.37 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), % 6.19/6.37 Eq (∀ (Y : Iota), Iff (member a (unordered_pair a_1 Y)) (And (member a universal_class) (Or (Eq a a_1) (Eq a Y)))) % 6.19/6.37 True % 6.19/6.37 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), % 6.19/6.37 Eq (Iff (member a (unordered_pair a_1 a_2)) (And (member a universal_class) (Or (Eq a a_1) (Eq a a_2)))) True % 6.19/6.37 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), % 6.19/6.37 Or (Eq (member a (unordered_pair a_1 a_2)) True) % 6.19/6.37 (Eq (And (member a universal_class) (Or (Eq a a_1) (Eq a a_2))) False) % 6.19/6.37 Clause #98 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 6.19/6.37 Or (Eq (member a (unordered_pair a_1 a_2)) True) % 6.19/6.37 (Or (Eq (member a universal_class) False) (Eq (Or (Eq a a_1) (Eq a a_2)) False)) % 6.19/6.37 Clause #100 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), % 6.19/6.37 Or (Eq (member a (unordered_pair a_1 a_2)) True) (Or (Eq (member a universal_class) False) (Eq (Eq a a_1) False)) % 6.19/6.37 Clause #125 (by clausification #[6]): ∀ (a : Iota), % 6.19/6.37 Eq (∀ (Y : Iota), Eq (ordered_pair a Y) (unordered_pair (singleton a) (unordered_pair a (singleton Y)))) True % 6.19/6.37 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), Eq (Eq (ordered_pair a a_1) (unordered_pair (singleton a) (unordered_pair a (singleton a_1)))) True % 6.19/6.37 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), Eq (ordered_pair a a_1) (unordered_pair (singleton a) (unordered_pair a (singleton a_1))) % 6.19/6.37 Clause #214 (by clausification #[43]): Eq (∀ (X Y : Iota), member (singleton X) (ordered_pair X Y)) False % 6.19/6.37 Clause #215 (by clausification #[214]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), member (singleton (skS.0 1 a)) (ordered_pair (skS.0 1 a) Y))) True % 6.19/6.37 Clause #216 (by clausification #[215]): ∀ (a : Iota), Eq (∀ (Y : Iota), member (singleton (skS.0 1 a)) (ordered_pair (skS.0 1 a) Y)) False % 6.19/6.37 Clause #217 (by clausification #[216]): ∀ (a a_1 : Iota), Eq (Not (member (singleton (skS.0 1 a)) (ordered_pair (skS.0 1 a) (skS.0 2 a a_1)))) True % 6.19/6.37 Clause #218 (by clausification #[217]): ∀ (a a_1 : Iota), Eq (member (singleton (skS.0 1 a)) (ordered_pair (skS.0 1 a) (skS.0 2 a a_1))) False % 6.19/6.37 Clause #1468 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), % 6.19/6.37 Or (Eq (member a (unordered_pair a_1 a_2)) True) (Or (Eq (member a universal_class) False) (Ne a a_1)) % 6.19/6.37 Clause #1469 (by destructive equality resolution #[1468]): ∀ (a a_1 : Iota), Or (Eq (member a (unordered_pair a a_1)) True) (Eq (member a universal_class) False) % 6.19/6.37 Clause #1471 (by superposition #[1469, 69]): ∀ (a a_1 : Iota), Or (Eq (member (singleton a) (unordered_pair (singleton a) a_1)) True) (Eq False True) % 6.19/6.37 Clause #1513 (by clausification #[1471]): ∀ (a a_1 : Iota), Eq (member (singleton a) (unordered_pair (singleton a) a_1)) True % 6.19/6.37 Clause #1519 (by superposition #[1513, 127]): ∀ (a a_1 : Iota), Eq (member (singleton a) (ordered_pair a a_1)) True % 6.19/6.37 Clause #1521 (by superposition #[1519, 218]): Eq True False % 6.19/6.37 Clause #1528 (by clausification #[1521]): False % 6.19/6.37 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------