TSTP Solution File: SET882+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 14:47:55 EDT 2023
% Result : Theorem 3.71s 3.88s
% Output : Proof 3.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n005.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 16:12:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.71/3.88 SZS status Theorem for theBenchmark.p
% 3.71/3.88 SZS output start Proof for theBenchmark.p
% 3.71/3.88 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 3.71/3.88 Clause #3 (by assumption #[]): Eq
% 3.71/3.88 (∀ (A B C : Iota),
% 3.71/3.88 Iff (Eq (set_difference (unordered_pair A B) C) (singleton A)) (And (Not (in A C)) (Or (in B C) (Eq A B))))
% 3.71/3.88 True
% 3.71/3.88 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), Ne A B → Eq (set_difference (unordered_pair A B) (singleton B)) (singleton A))) True
% 3.71/3.88 Clause #18 (by clausification #[6]): Eq (∀ (A B : Iota), Ne A B → Eq (set_difference (unordered_pair A B) (singleton B)) (singleton A)) False
% 3.71/3.88 Clause #19 (by clausification #[18]): ∀ (a : Iota),
% 3.71/3.88 Eq
% 3.71/3.88 (Not
% 3.71/3.88 (∀ (B : Iota),
% 3.71/3.88 Ne (skS.0 2 a) B → Eq (set_difference (unordered_pair (skS.0 2 a) B) (singleton B)) (singleton (skS.0 2 a))))
% 3.71/3.88 True
% 3.71/3.88 Clause #20 (by clausification #[19]): ∀ (a : Iota),
% 3.71/3.88 Eq
% 3.71/3.88 (∀ (B : Iota),
% 3.71/3.88 Ne (skS.0 2 a) B → Eq (set_difference (unordered_pair (skS.0 2 a) B) (singleton B)) (singleton (skS.0 2 a)))
% 3.71/3.88 False
% 3.71/3.88 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota),
% 3.71/3.88 Eq
% 3.71/3.88 (Not
% 3.71/3.88 (Ne (skS.0 2 a) (skS.0 3 a a_1) →
% 3.71/3.88 Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 3 a a_1)))
% 3.71/3.88 (singleton (skS.0 2 a))))
% 3.71/3.88 True
% 3.71/3.88 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota),
% 3.71/3.88 Eq
% 3.71/3.88 (Ne (skS.0 2 a) (skS.0 3 a a_1) →
% 3.71/3.88 Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 3 a a_1)))
% 3.71/3.88 (singleton (skS.0 2 a)))
% 3.71/3.88 False
% 3.71/3.88 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 2 a) (skS.0 3 a a_1)) True
% 3.71/3.88 Clause #24 (by clausification #[22]): ∀ (a a_1 : Iota),
% 3.71/3.88 Eq
% 3.71/3.88 (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 3 a a_1)))
% 3.71/3.88 (singleton (skS.0 2 a)))
% 3.71/3.88 False
% 3.71/3.88 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (skS.0 3 a a_1)
% 3.71/3.88 Clause #26 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True
% 3.71/3.88 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True
% 3.71/3.88 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True)
% 3.71/3.88 Clause #36 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1))
% 3.71/3.88 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True)
% 3.71/3.88 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False))
% 3.71/3.88 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True))
% 3.71/3.88 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1))
% 3.71/3.88 Clause #41 (by destructive equality resolution #[40]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1)
% 3.71/3.88 Clause #42 (by destructive equality resolution #[41]): ∀ (a : Iota), Eq (in a (singleton a)) True
% 3.71/3.88 Clause #45 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1))
% 3.71/3.88 Clause #46 (by destructive equality resolution #[45]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1)
% 3.71/3.88 Clause #49 (by clausification #[3]): ∀ (a : Iota),
% 3.71/3.88 Eq
% 3.71/3.88 (∀ (B C : Iota),
% 3.71/3.88 Iff (Eq (set_difference (unordered_pair a B) C) (singleton a)) (And (Not (in a C)) (Or (in B C) (Eq a B))))
% 3.71/3.88 True
% 3.71/3.88 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 3.71/3.88 Eq
% 3.71/3.88 (∀ (C : Iota),
% 3.71/3.88 Iff (Eq (set_difference (unordered_pair a a_1) C) (singleton a)) (And (Not (in a C)) (Or (in a_1 C) (Eq a a_1))))
% 3.71/3.88 True
% 3.71/3.88 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 3.71/3.88 Eq
% 3.71/3.88 (Iff (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a))
% 3.73/3.89 (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1))))
% 3.73/3.89 True
% 3.73/3.89 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 3.73/3.89 Or (Eq (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) True)
% 3.73/3.89 (Eq (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1))) False)
% 3.73/3.89 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota),
% 3.73/3.89 Or (Eq (And (Not (in a a_1)) (Or (in a_2 a_1) (Eq a a_2))) False)
% 3.73/3.89 (Eq (set_difference (unordered_pair a a_2) a_1) (singleton a))
% 3.73/3.89 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota),
% 3.73/3.89 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a))
% 3.73/3.89 (Or (Eq (Not (in a a_2)) False) (Eq (Or (in a_1 a_2) (Eq a a_1)) False))
% 3.73/3.89 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 3.73/3.89 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a))
% 3.73/3.89 (Or (Eq (Or (in a_1 a_2) (Eq a a_1)) False) (Eq (in a a_2) True))
% 3.73/3.89 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 3.73/3.89 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a a_2) True) (Eq (in a_1 a_2) False))
% 3.73/3.89 Clause #61 (by clausification #[24]): ∀ (a a_1 : Iota),
% 3.73/3.89 Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a))
% 3.73/3.89 Clause #62 (by superposition #[58, 42]): ∀ (a a_1 : Iota),
% 3.73/3.89 Or (Eq (set_difference (unordered_pair a a_1) (singleton a_1)) (singleton a))
% 3.73/3.89 (Or (Eq (in a (singleton a_1)) True) (Eq False True))
% 3.73/3.89 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota),
% 3.73/3.89 Or (Eq (set_difference (unordered_pair a a_1) (singleton a_1)) (singleton a)) (Eq (in a (singleton a_1)) True)
% 3.73/3.89 Clause #64 (by superposition #[63, 61]): ∀ (a a_1 : Iota),
% 3.73/3.89 Or (Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a)))
% 3.73/3.89 Clause #95 (by eliminate resolved literals #[64]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True
% 3.73/3.89 Clause #96 (by superposition #[95, 46]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.73/3.89 Clause #100 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1)
% 3.73/3.89 Clause #101 (by forward contextual literal cutting #[100, 25]): False
% 3.73/3.89 SZS output end Proof for theBenchmark.p
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