TSTP Solution File: SET900+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET900+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 14:47:58 EDT 2023
% Result : Theorem 4.49s 4.68s
% Output : Proof 4.49s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET900+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 09:56:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.49/4.68 SZS status Theorem for theBenchmark.p
% 4.49/4.68 SZS output start Proof for theBenchmark.p
% 4.49/4.68 Clause #4 (by assumption #[]): Eq
% 4.49/4.68 (Not
% 4.49/4.68 (∀ (A B : Iota), Not (And (And (Ne A (singleton B)) (Ne A empty_set)) (∀ (C : Iota), Not (And (in C A) (Ne C B))))))
% 4.49/4.68 True
% 4.49/4.68 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (And (Ne A (singleton B)) (Ne A empty_set)) (∀ (C : Iota), Not (And (in C A) (Ne C B)))))
% 4.49/4.68 True
% 4.49/4.68 Clause #14 (by clausification #[5]): ∀ (a : Iota),
% 4.49/4.68 Eq (∀ (B : Iota), Not (And (And (Ne a (singleton B)) (Ne a empty_set)) (∀ (C : Iota), Not (And (in C a) (Ne C B)))))
% 4.49/4.68 True
% 4.49/4.68 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota),
% 4.49/4.68 Eq (Not (And (And (Ne a (singleton a_1)) (Ne a empty_set)) (∀ (C : Iota), Not (And (in C a) (Ne C a_1))))) True
% 4.49/4.68 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota),
% 4.49/4.68 Eq (And (And (Ne a (singleton a_1)) (Ne a empty_set)) (∀ (C : Iota), Not (And (in C a) (Ne C a_1)))) False
% 4.49/4.68 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota),
% 4.49/4.68 Or (Eq (And (Ne a (singleton a_1)) (Ne a empty_set)) False) (Eq (∀ (C : Iota), Not (And (in C a) (Ne C a_1))) False)
% 4.49/4.68 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 4.49/4.68 Or (Eq (∀ (C : Iota), Not (And (in C a) (Ne C a_1))) False)
% 4.49/4.68 (Or (Eq (Ne a (singleton a_1)) False) (Eq (Ne a empty_set) False))
% 4.49/4.68 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 4.49/4.68 Or (Eq (Ne a (singleton a_1)) False)
% 4.49/4.68 (Or (Eq (Ne a empty_set) False) (Eq (Not (Not (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1)))) True))
% 4.49/4.68 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 4.49/4.68 Or (Eq (Ne a empty_set) False)
% 4.49/4.68 (Or (Eq (Not (Not (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1)))) True) (Eq a (singleton a_1)))
% 4.49/4.68 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 4.49/4.68 Or (Eq (Not (Not (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1)))) True)
% 4.49/4.68 (Or (Eq a (singleton a_1)) (Eq a empty_set))
% 4.49/4.68 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 4.49/4.68 Or (Eq a (singleton a_1))
% 4.49/4.68 (Or (Eq a empty_set) (Eq (Not (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1))) False))
% 4.49/4.68 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 4.49/4.68 Or (Eq a (singleton a_1))
% 4.49/4.68 (Or (Eq a empty_set) (Eq (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1)) True))
% 4.49/4.68 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq a empty_set) (Eq (Ne (skS.0 2 a a_1 a_2) a_1) True))
% 4.49/4.68 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq a empty_set) (Eq (in (skS.0 2 a a_1 a_2) a) True))
% 4.49/4.68 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq a empty_set) (Ne (skS.0 2 a a_1 a_2) a_1))
% 4.49/4.68 Clause #27 (by clausification #[4]): Eq (∀ (A B : Iota), Not (And (And (Ne A (singleton B)) (Ne A empty_set)) (∀ (C : Iota), Not (And (in C A) (Ne C B)))))
% 4.49/4.68 False
% 4.49/4.68 Clause #28 (by clausification #[27]): ∀ (a : Iota),
% 4.49/4.68 Eq
% 4.49/4.68 (Not
% 4.49/4.68 (∀ (B : Iota),
% 4.49/4.68 Not
% 4.49/4.68 (And (And (Ne (skS.0 3 a) (singleton B)) (Ne (skS.0 3 a) empty_set))
% 4.49/4.68 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C B))))))
% 4.49/4.68 True
% 4.49/4.68 Clause #29 (by clausification #[28]): ∀ (a : Iota),
% 4.49/4.68 Eq
% 4.49/4.68 (∀ (B : Iota),
% 4.49/4.68 Not
% 4.49/4.68 (And (And (Ne (skS.0 3 a) (singleton B)) (Ne (skS.0 3 a) empty_set))
% 4.49/4.68 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C B)))))
% 4.49/4.68 False
% 4.49/4.68 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota),
% 4.49/4.68 Eq
% 4.49/4.68 (Not
% 4.49/4.68 (Not
% 4.49/4.68 (And (And (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Ne (skS.0 3 a) empty_set))
% 4.49/4.68 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C (skS.0 4 a a_1)))))))
% 4.49/4.68 True
% 4.49/4.68 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 4.49/4.68 Eq
% 4.49/4.68 (Not
% 4.49/4.68 (And (And (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Ne (skS.0 3 a) empty_set))
% 4.49/4.68 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C (skS.0 4 a a_1))))))
% 4.49/4.68 False
% 4.49/4.68 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota),
% 4.49/4.68 Eq
% 4.49/4.68 (And (And (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Ne (skS.0 3 a) empty_set))
% 4.49/4.69 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C (skS.0 4 a a_1)))))
% 4.49/4.69 True
% 4.49/4.69 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C (skS.0 4 a a_1)))) True
% 4.49/4.69 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (And (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Ne (skS.0 3 a) empty_set)) True
% 4.49/4.69 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (Not (And (in a (skS.0 3 a_1)) (Ne a (skS.0 4 a_1 a_2)))) True
% 4.49/4.69 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Eq (And (in a (skS.0 3 a_1)) (Ne a (skS.0 4 a_1 a_2))) False
% 4.49/4.69 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 3 a_1)) False) (Eq (Ne a (skS.0 4 a_1 a_2)) False)
% 4.49/4.69 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 3 a_1)) False) (Eq a (skS.0 4 a_1 a_2))
% 4.49/4.69 Clause #43 (by superposition #[25, 38]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.49/4.69 Or (Eq (skS.0 2 (skS.0 3 a) a_1 a_2) (skS.0 4 a a_3))
% 4.49/4.69 (Or (Eq (skS.0 3 a) (singleton a_1)) (Or (Eq (skS.0 3 a) empty_set) (Eq False True)))
% 4.49/4.69 Clause #55 (by clausification #[34]): ∀ (a : Iota), Eq (Ne (skS.0 3 a) empty_set) True
% 4.49/4.69 Clause #56 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) True
% 4.49/4.69 Clause #57 (by clausification #[55]): ∀ (a : Iota), Ne (skS.0 3 a) empty_set
% 4.49/4.69 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))
% 4.49/4.69 Clause #241 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.49/4.69 Or (Eq (skS.0 2 (skS.0 3 a) a_1 a_2) (skS.0 4 a a_3)) (Or (Eq (skS.0 3 a) (singleton a_1)) (Eq (skS.0 3 a) empty_set))
% 4.49/4.69 Clause #242 (by forward contextual literal cutting #[241, 57]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 2 (skS.0 3 a) a_1 a_2) (skS.0 4 a a_3)) (Eq (skS.0 3 a) (singleton a_1))
% 4.49/4.69 Clause #244 (by superposition #[242, 26]): ∀ (a a_1 a_2 : Iota),
% 4.49/4.69 Or (Eq (skS.0 3 a) (singleton a_1))
% 4.49/4.69 (Or (Eq (skS.0 3 a) (singleton a_1)) (Or (Eq (skS.0 3 a) empty_set) (Ne (skS.0 4 a a_2) a_1)))
% 4.49/4.69 Clause #349 (by eliminate duplicate literals #[244]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 3 a) (singleton a_1)) (Or (Eq (skS.0 3 a) empty_set) (Ne (skS.0 4 a a_2) a_1))
% 4.49/4.69 Clause #350 (by destructive equality resolution #[349]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Eq (skS.0 3 a) empty_set)
% 4.49/4.69 Clause #351 (by forward contextual literal cutting #[350, 58]): ∀ (a : Iota), Eq (skS.0 3 a) empty_set
% 4.49/4.69 Clause #352 (by forward contextual literal cutting #[351, 57]): False
% 4.49/4.69 SZS output end Proof for theBenchmark.p
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