TSTP Solution File: SET102+1 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SET102+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n001.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 : Thu Aug 31 14:45:39 EDT 2023
% Result : Theorem 7.10s 7.30s
% Output : Proof 7.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET102+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n001.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 : Sat Aug 26 09:31:00 EDT 2023
% 0.13/0.34 % CPUTime :
% 7.10/7.30 SZS status Theorem for theBenchmark.p
% 7.10/7.30 SZS output start Proof for theBenchmark.p
% 7.10/7.30 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
% 7.10/7.30 Clause #4 (by assumption #[]): Eq (∀ (X Y : Iota), member (unordered_pair X Y) universal_class) True
% 7.10/7.30 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), Eq (ordered_pair X Y) (unordered_pair (singleton X) (unordered_pair X (singleton Y)))) True
% 7.10/7.30 Clause #43 (by assumption #[]): Eq (Not (∀ (X Y : Iota), member (unordered_pair X (singleton Y)) (ordered_pair X Y))) True
% 7.10/7.30 Clause #63 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y : Iota), member (unordered_pair a Y) universal_class) True
% 7.10/7.30 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Eq (member (unordered_pair a a_1) universal_class) True
% 7.10/7.30 Clause #93 (by clausification #[3]): ∀ (a : Iota),
% 7.10/7.30 Eq (∀ (X Y : Iota), Iff (member a (unordered_pair X Y)) (And (member a universal_class) (Or (Eq a X) (Eq a Y)))) True
% 7.10/7.30 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota),
% 7.10/7.30 Eq (∀ (Y : Iota), Iff (member a (unordered_pair a_1 Y)) (And (member a universal_class) (Or (Eq a a_1) (Eq a Y))))
% 7.10/7.30 True
% 7.10/7.30 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota),
% 7.10/7.30 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
% 7.10/7.30 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota),
% 7.10/7.30 Or (Eq (member a (unordered_pair a_1 a_2)) True)
% 7.10/7.30 (Eq (And (member a universal_class) (Or (Eq a a_1) (Eq a a_2))) False)
% 7.10/7.30 Clause #98 (by clausification #[96]): ∀ (a a_1 a_2 : Iota),
% 7.10/7.30 Or (Eq (member a (unordered_pair a_1 a_2)) True)
% 7.10/7.30 (Or (Eq (member a universal_class) False) (Eq (Or (Eq a a_1) (Eq a a_2)) False))
% 7.10/7.30 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota),
% 7.10/7.30 Or (Eq (member a (unordered_pair a_1 a_2)) True) (Or (Eq (member a universal_class) False) (Eq (Eq a a_2) False))
% 7.10/7.30 Clause #101 (by clausification #[99]): ∀ (a a_1 a_2 : Iota),
% 7.10/7.30 Or (Eq (member a (unordered_pair a_1 a_2)) True) (Or (Eq (member a universal_class) False) (Ne a a_2))
% 7.10/7.30 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)
% 7.10/7.30 Clause #103 (by superposition #[102, 64]): ∀ (a a_1 a_2 : Iota),
% 7.10/7.30 Or (Eq (member (unordered_pair a a_1) (unordered_pair a_2 (unordered_pair a a_1))) True) (Eq False True)
% 7.10/7.30 Clause #125 (by clausification #[6]): ∀ (a : Iota),
% 7.10/7.30 Eq (∀ (Y : Iota), Eq (ordered_pair a Y) (unordered_pair (singleton a) (unordered_pair a (singleton Y)))) True
% 7.10/7.30 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
% 7.10/7.30 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)))
% 7.10/7.30 Clause #1374 (by clausification #[43]): Eq (∀ (X Y : Iota), member (unordered_pair X (singleton Y)) (ordered_pair X Y)) False
% 7.10/7.30 Clause #1375 (by clausification #[1374]): ∀ (a : Iota),
% 7.10/7.30 Eq (Not (∀ (Y : Iota), member (unordered_pair (skS.0 5 a) (singleton Y)) (ordered_pair (skS.0 5 a) Y))) True
% 7.10/7.30 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
% 7.10/7.30 Clause #1377 (by clausification #[1376]): ∀ (a a_1 : Iota),
% 7.10/7.30 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))))
% 7.10/7.30 True
% 7.10/7.30 Clause #1378 (by clausification #[1377]): ∀ (a a_1 : Iota),
% 7.10/7.30 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
% 7.10/7.30 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
% 7.10/7.30 Clause #1760 (by superposition #[1754, 127]): ∀ (a a_1 : Iota), Eq (member (unordered_pair a (singleton a_1)) (ordered_pair a a_1)) True
% 7.10/7.30 Clause #1775 (by superposition #[1760, 1378]): Eq True False
% 7.10/7.31 Clause #1784 (by clausification #[1775]): False
% 7.10/7.31 SZS output end Proof for theBenchmark.p
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