TSTP Solution File: SEU147+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU147+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 16:40:26 EDT 2023
% Result : Theorem 3.94s 4.31s
% Output : Proof 3.94s
% 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 : SEU147+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 20:38:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.94/4.31 SZS status Theorem for theBenchmark.p
% 3.94/4.31 SZS output start Proof for theBenchmark.p
% 3.94/4.31 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 3.94/4.31 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (powerset A)) (∀ (C : Iota), Iff (in C B) (subset C A))) True
% 3.94/4.31 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True
% 3.94/4.31 Clause #8 (by assumption #[]): Eq (Not (Eq (powerset empty_set) (singleton empty_set))) True
% 3.94/4.31 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), subset A empty_set → Eq A empty_set) True
% 3.94/4.31 Clause #13 (by clausification #[7]): ∀ (a : Iota), Eq (Iota → subset a a) True
% 3.94/4.31 Clause #14 (by clausification #[13]): ∀ (a : Iota), Iota → Eq (subset a a) True
% 3.94/4.31 Clause #21 (by clausification #[10]): ∀ (a : Iota), Eq (subset a empty_set → Eq a empty_set) True
% 3.94/4.31 Clause #22 (by clausification #[21]): ∀ (a : Iota), Or (Eq (subset a empty_set) False) (Eq (Eq a empty_set) True)
% 3.94/4.31 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (subset a empty_set) False) (Eq a empty_set)
% 3.94/4.31 Clause #34 (by clausification #[8]): Eq (Eq (powerset empty_set) (singleton empty_set)) False
% 3.94/4.31 Clause #35 (by clausification #[34]): Ne (powerset empty_set) (singleton empty_set)
% 3.94/4.31 Clause #36 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (powerset a)) (∀ (C : Iota), Iff (in C B) (subset C a))) True
% 3.94/4.31 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (powerset a_1)) (∀ (C : Iota), Iff (in C a) (subset C a_1))) True
% 3.94/4.31 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (Eq a (powerset a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True)
% 3.94/4.31 Clause #45 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True
% 3.94/4.31 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True
% 3.94/4.31 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) True) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) False)
% 3.94/4.31 Clause #49 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) False) (Eq a (singleton a_1))
% 3.94/4.31 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.31 Or (Eq a (singleton a_1)) (Eq (Not (Iff (in (skS.0 4 a a_1 a_2) a) (Eq (skS.0 4 a a_1 a_2) a_1))) True)
% 3.94/4.31 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Eq (Iff (in (skS.0 4 a a_1 a_2) a) (Eq (skS.0 4 a a_1 a_2) a_1)) False)
% 3.94/4.31 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.31 Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) False) (Eq (Eq (skS.0 4 a a_1 a_2) a_1) False))
% 3.94/4.31 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.31 Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Eq (Eq (skS.0 4 a a_1 a_2) a_1) True))
% 3.94/4.31 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) False) (Ne (skS.0 4 a a_1 a_2) a_1))
% 3.94/4.31 Clause #55 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) (Ne a (powerset a_1))
% 3.94/4.31 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Eq (Iff (in a_2 a) (subset a_2 a_1)) True)
% 3.94/4.31 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Or (Eq (in a_2 a) True) (Eq (subset a_2 a_1) False))
% 3.94/4.31 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Or (Eq (in a_2 a) False) (Eq (subset a_2 a_1) True))
% 3.94/4.31 Clause #59 (by destructive equality resolution #[57]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (subset a a_1) False)
% 3.94/4.31 Clause #60 (by superposition #[59, 14]): ∀ (a : Iota), Or (Eq (in a (powerset a)) True) (Eq False True)
% 3.94/4.31 Clause #61 (by clausification #[60]): ∀ (a : Iota), Eq (in a (powerset a)) True
% 3.94/4.31 Clause #64 (by destructive equality resolution #[58]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (subset a a_1) True)
% 3.94/4.33 Clause #160 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Eq (skS.0 4 a a_1 a_2) a_1))
% 3.94/4.33 Clause #170 (by superposition #[160, 54]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.33 Or (Eq a (singleton a_1))
% 3.94/4.33 (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Or (Eq a (singleton a_1)) (Or (Eq (in a_1 a) False) (Ne a_1 a_1))))
% 3.94/4.33 Clause #173 (by eliminate duplicate literals #[170]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.33 Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Or (Eq (in a_1 a) False) (Ne a_1 a_1)))
% 3.94/4.33 Clause #174 (by eliminate resolved literals #[173]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Eq (in a_1 a) False))
% 3.94/4.33 Clause #177 (by superposition #[174, 61]): ∀ (a a_1 : Iota),
% 3.94/4.33 Or (Eq (powerset a) (singleton a)) (Or (Eq (in (skS.0 4 (powerset a) a a_1) (powerset a)) True) (Eq False True))
% 3.94/4.33 Clause #186 (by clausification #[177]): ∀ (a a_1 : Iota), Or (Eq (powerset a) (singleton a)) (Eq (in (skS.0 4 (powerset a) a a_1) (powerset a)) True)
% 3.94/4.33 Clause #187 (by superposition #[186, 64]): ∀ (a a_1 : Iota),
% 3.94/4.33 Or (Eq (powerset a) (singleton a)) (Or (Eq True False) (Eq (subset (skS.0 4 (powerset a) a a_1) a) True))
% 3.94/4.33 Clause #197 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (powerset a) (singleton a)) (Eq (subset (skS.0 4 (powerset a) a a_1) a) True)
% 3.94/4.33 Clause #198 (by superposition #[197, 23]): ∀ (a : Iota),
% 3.94/4.33 Or (Eq (powerset empty_set) (singleton empty_set))
% 3.94/4.33 (Or (Eq True False) (Eq (skS.0 4 (powerset empty_set) empty_set a) empty_set))
% 3.94/4.33 Clause #206 (by clausification #[198]): ∀ (a : Iota),
% 3.94/4.33 Or (Eq (powerset empty_set) (singleton empty_set)) (Eq (skS.0 4 (powerset empty_set) empty_set a) empty_set)
% 3.94/4.33 Clause #207 (by forward contextual literal cutting #[206, 35]): ∀ (a : Iota), Eq (skS.0 4 (powerset empty_set) empty_set a) empty_set
% 3.94/4.33 Clause #208 (by superposition #[207, 54]): Or (Eq (powerset empty_set) (singleton empty_set))
% 3.94/4.33 (Or (Eq (in empty_set (powerset empty_set)) False) (Ne empty_set empty_set))
% 3.94/4.33 Clause #219 (by eliminate resolved literals #[208]): Or (Eq (powerset empty_set) (singleton empty_set)) (Eq (in empty_set (powerset empty_set)) False)
% 3.94/4.33 Clause #220 (by forward contextual literal cutting #[219, 35]): Eq (in empty_set (powerset empty_set)) False
% 3.94/4.33 Clause #221 (by superposition #[220, 61]): Eq False True
% 3.94/4.33 Clause #227 (by clausification #[221]): False
% 3.94/4.33 SZS output end Proof for theBenchmark.p
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