%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET102+1 : TPTP v9.2.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 6.86s 7.04s % Output : Proof 6.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET102+1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n026.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 : Thu Oct 2 14:08:38 EDT 2025 % 0.13/0.35 % CPUTime : % 6.86/7.04 SZS status Theorem for theBenchmark.p % 6.86/7.04 SZS output start Proof for theBenchmark.p % 6.86/7.04 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 % 6.86/7.04 Clause #4 (by assumption #[]): Eq (∀ (X Y : Iota), member (unordered_pair X Y) universal_class) True % 6.86/7.04 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), Eq (ordered_pair X Y) (unordered_pair (singleton X) (unordered_pair X (singleton Y)))) True % 6.86/7.04 Clause #43 (by assumption #[]): Eq (Not (∀ (X Y : Iota), member (unordered_pair X (singleton Y)) (ordered_pair X Y))) True % 6.86/7.04 Clause #63 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y : Iota), member (unordered_pair a Y) universal_class) True % 6.86/7.04 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Eq (member (unordered_pair a a_1) universal_class) True % 6.86/7.04 Clause #93 (by clausification #[3]): ∀ (a : Iota), % 6.86/7.04 Eq (∀ (X Y : Iota), Iff (member a (unordered_pair X Y)) (And (member a universal_class) (Or (Eq a X) (Eq a Y)))) True % 6.86/7.04 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), % 6.86/7.04 Eq (∀ (Y : Iota), Iff (member a (unordered_pair a_1 Y)) (And (member a universal_class) (Or (Eq a a_1) (Eq a Y)))) % 6.86/7.04 True % 6.86/7.04 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), % 6.86/7.04 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 % 6.86/7.04 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), % 6.86/7.04 Or (Eq (member a (unordered_pair a_1 a_2)) True) % 6.86/7.04 (Eq (And (member a universal_class) (Or (Eq a a_1) (Eq a a_2))) False) % 6.86/7.04 Clause #98 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 6.86/7.04 Or (Eq (member a (unordered_pair a_1 a_2)) True) % 6.86/7.04 (Or (Eq (member a universal_class) False) (Eq (Or (Eq a a_1) (Eq a a_2)) False)) % 6.86/7.04 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), % 6.86/7.04 Or (Eq (member a (unordered_pair a_1 a_2)) True) (Or (Eq (member a universal_class) False) (Eq (Eq a a_2) False)) % 6.86/7.04 Clause #101 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), % 6.86/7.04 Or (Eq (member a (unordered_pair a_1 a_2)) True) (Or (Eq (member a universal_class) False) (Ne a a_2)) % 6.86/7.04 Clause #102 (by destructive equality resolution #[101]): ∀ (a a_1 : Iota), Or (Eq (member a (unordered_pair a_1 a)) True) (Eq (member a universal_class) False) % 6.86/7.04 Clause #103 (by superposition #[102, 64]): ∀ (a a_1 a_2 : Iota), % 6.86/7.04 Or (Eq (member (unordered_pair a a_1) (unordered_pair a_2 (unordered_pair a a_1))) True) (Eq False True) % 6.86/7.04 Clause #125 (by clausification #[6]): ∀ (a : Iota), % 6.86/7.04 Eq (∀ (Y : Iota), Eq (ordered_pair a Y) (unordered_pair (singleton a) (unordered_pair a (singleton Y)))) True % 6.86/7.04 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 % 6.86/7.04 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))) % 6.86/7.04 Clause #1374 (by clausification #[43]): Eq (∀ (X Y : Iota), member (unordered_pair X (singleton Y)) (ordered_pair X Y)) False % 6.86/7.04 Clause #1375 (by clausification #[1374]): ∀ (a : Iota), % 6.86/7.04 Eq (Not (∀ (Y : Iota), member (unordered_pair (skS.0 5 a) (singleton Y)) (ordered_pair (skS.0 5 a) Y))) True % 6.86/7.04 Clause #1376 (by clausification #[1375]): ∀ (a : Iota), Eq (∀ (Y : Iota), member (unordered_pair (skS.0 5 a) (singleton Y)) (ordered_pair (skS.0 5 a) Y)) False % 6.86/7.04 Clause #1377 (by clausification #[1376]): ∀ (a a_1 : Iota), % 6.86/7.04 Eq (Not (member (unordered_pair (skS.0 5 a) (singleton (skS.0 6 a a_1))) (ordered_pair (skS.0 5 a) (skS.0 6 a a_1)))) % 6.86/7.04 True % 6.86/7.04 Clause #1378 (by clausification #[1377]): ∀ (a a_1 : Iota), % 6.86/7.04 Eq (member (unordered_pair (skS.0 5 a) (singleton (skS.0 6 a a_1))) (ordered_pair (skS.0 5 a) (skS.0 6 a a_1))) False % 6.86/7.04 Clause #1754 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), Eq (member (unordered_pair a a_1) (unordered_pair a_2 (unordered_pair a a_1))) True % 6.86/7.04 Clause #1760 (by superposition #[1754, 127]): ∀ (a a_1 : Iota), Eq (member (unordered_pair a (singleton a_1)) (ordered_pair a a_1)) True % 6.86/7.04 Clause #1775 (by superposition #[1760, 1378]): Eq True False % 6.86/7.04 Clause #1784 (by clausification #[1775]): False % 6.86/7.04 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------