TSTP Solution File: SEU160+3 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU160+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 16:40:31 EDT 2023
% Result : Theorem 5.91s 6.15s
% Output : Proof 5.91s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU160+3 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12 % Command : duper %s
% 0.11/0.33 % Computer : n031.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 23 15:46:05 EDT 2023
% 0.11/0.33 % CPUTime :
% 5.91/6.15 SZS status Theorem for theBenchmark.p
% 5.91/6.15 SZS output start Proof for theBenchmark.p
% 5.91/6.15 Clause #0 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True
% 5.91/6.15 Clause #4 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B))))) True
% 5.91/6.15 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) True
% 5.91/6.15 Clause #6 (by clausification #[0]): ∀ (a : Iota), Eq (Iota → subset a a) True
% 5.91/6.15 Clause #7 (by clausification #[6]): ∀ (a : Iota), Iota → Eq (subset a a) True
% 5.91/6.15 Clause #12 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a (singleton B)) (Or (Eq a empty_set) (Eq a (singleton B)))) True
% 5.91/6.15 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Iff (subset a (singleton a_1)) (Or (Eq a empty_set) (Eq a (singleton a_1)))) True
% 5.91/6.15 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) False)
% 5.91/6.15 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) True)
% 5.91/6.15 Clause #17 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Eq (Eq a empty_set) False)
% 5.91/6.15 Clause #20 (by clausification #[4]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) False
% 5.91/6.15 Clause #21 (by clausification #[20]): ∀ (a : Iota),
% 5.91/6.15 Eq
% 5.91/6.15 (Not
% 5.91/6.15 (∀ (B : Iota),
% 5.91/6.15 Iff (subset (skS.0 2 a) (singleton B)) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton B)))))
% 5.91/6.15 True
% 5.91/6.15 Clause #22 (by clausification #[21]): ∀ (a : Iota),
% 5.91/6.15 Eq
% 5.91/6.15 (∀ (B : Iota),
% 5.91/6.15 Iff (subset (skS.0 2 a) (singleton B)) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton B))))
% 5.91/6.15 False
% 5.91/6.15 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 5.91/6.15 Eq
% 5.91/6.15 (Not
% 5.91/6.15 (Iff (subset (skS.0 2 a) (singleton (skS.0 3 a a_1)))
% 5.91/6.15 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))))
% 5.91/6.15 True
% 5.91/6.15 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota),
% 5.91/6.15 Eq
% 5.91/6.15 (Iff (subset (skS.0 2 a) (singleton (skS.0 3 a a_1)))
% 5.91/6.15 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))))
% 5.91/6.15 False
% 5.91/6.15 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota),
% 5.91/6.15 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False)
% 5.91/6.15 (Eq (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) False)
% 5.91/6.15 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota),
% 5.91/6.15 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True)
% 5.91/6.15 (Eq (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) True)
% 5.91/6.15 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota),
% 5.91/6.15 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) False)
% 5.91/6.15 Clause #28 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) (Eq (Eq (skS.0 2 a) empty_set) False)
% 5.91/6.15 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota),
% 5.91/6.15 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1)))
% 5.91/6.15 Clause #30 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Ne a empty_set)
% 5.91/6.15 Clause #31 (by destructive equality resolution #[30]): ∀ (a : Iota), Eq (subset empty_set (singleton a)) True
% 5.91/6.15 Clause #32 (by clausification #[15]): ∀ (a a_1 : Iota),
% 5.91/6.15 Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq a (singleton a_1)) True))
% 5.91/6.15 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a (singleton a_1)) True) (Eq a empty_set))
% 5.91/6.15 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq a empty_set) (Eq a (singleton a_1)))
% 5.91/6.15 Clause #39 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) (Ne (skS.0 2 a) empty_set)
% 5.91/6.15 Clause #40 (by clausification #[26]): ∀ (a a_1 : Iota),
% 5.91/6.18 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True)
% 5.91/6.18 (Or (Eq (Eq (skS.0 2 a) empty_set) True) (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) True))
% 5.91/6.18 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota),
% 5.91/6.18 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True)
% 5.91/6.18 (Or (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Eq (skS.0 2 a) empty_set))
% 5.91/6.18 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 5.91/6.18 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True)
% 5.91/6.18 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))
% 5.91/6.18 Clause #45 (by superposition #[42, 34]): ∀ (a a_1 : Iota),
% 5.91/6.18 Or (Eq (skS.0 2 a) empty_set)
% 5.91/6.18 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))
% 5.91/6.18 (Or (Eq True False) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))))
% 5.91/6.18 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota),
% 5.91/6.18 Or (Eq (skS.0 2 a) empty_set)
% 5.91/6.18 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))
% 5.91/6.18 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))))
% 5.91/6.18 Clause #49 (by eliminate duplicate literals #[48]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))
% 5.91/6.18 Clause #50 (by superposition #[49, 29]): ∀ (a : Iota),
% 5.91/6.18 Or (Eq (skS.0 2 a) empty_set) (Or (Eq (subset (skS.0 2 a) (skS.0 2 a)) False) (Ne (skS.0 2 a) (skS.0 2 a)))
% 5.91/6.18 Clause #56 (by eliminate resolved literals #[50]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (subset (skS.0 2 a) (skS.0 2 a)) False)
% 5.91/6.18 Clause #57 (by superposition #[56, 7]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq False True)
% 5.91/6.18 Clause #58 (by clausification #[57]): ∀ (a : Iota), Eq (skS.0 2 a) empty_set
% 5.91/6.18 Clause #65 (by backward contextual literal cutting #[58, 39]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False
% 5.91/6.18 Clause #66 (by forward demodulation #[65, 58]): ∀ (a a_1 : Iota), Eq (subset empty_set (singleton (skS.0 3 a a_1))) False
% 5.91/6.18 Clause #67 (by superposition #[66, 31]): Eq False True
% 5.91/6.18 Clause #68 (by clausification #[67]): False
% 5.91/6.18 SZS output end Proof for theBenchmark.p
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