TSTP Solution File: SEU155+1 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SEU155+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n006.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 16:40:29 EDT 2023
% Result : Theorem 3.90s 4.13s
% Output : Proof 3.90s
% 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 : SEU155+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n006.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 : Thu Aug 24 01:08:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.90/4.13 SZS status Theorem for theBenchmark.p
% 3.90/4.13 SZS output start Proof for theBenchmark.p
% 3.90/4.13 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True
% 3.90/4.13 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (union A)) (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in C D) (in D A)))) True
% 3.90/4.13 Clause #4 (by assumption #[]): Eq (Not (∀ (A B : Iota), in A B → subset A (union B))) True
% 3.90/4.13 Clause #12 (by clausification #[4]): Eq (∀ (A B : Iota), in A B → subset A (union B)) False
% 3.90/4.13 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), in (skS.0 0 a) B → subset (skS.0 0 a) (union B))) True
% 3.90/4.13 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (B : Iota), in (skS.0 0 a) B → subset (skS.0 0 a) (union B)) False
% 3.90/4.13 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 0 a) (skS.0 1 a a_1) → subset (skS.0 0 a) (union (skS.0 1 a a_1)))) True
% 3.90/4.13 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1) → subset (skS.0 0 a) (union (skS.0 1 a a_1))) False
% 3.90/4.13 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True
% 3.90/4.13 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) False
% 3.90/4.13 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True
% 3.90/4.13 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True
% 3.90/4.13 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False)
% 3.90/4.13 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 3.90/4.13 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1)) True)
% 3.90/4.13 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False)
% 3.90/4.13 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a) True)
% 3.90/4.13 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a_1) False)
% 3.90/4.13 Clause #29 (by clausification #[2]): ∀ (a : Iota),
% 3.90/4.13 Eq (∀ (B : Iota), Iff (Eq B (union a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in C D) (in D a)))) True
% 3.90/4.13 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota),
% 3.90/4.13 Eq (Iff (Eq a (union a_1)) (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1)))) True
% 3.90/4.13 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota),
% 3.90/4.13 Or (Eq (Eq a (union a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1))) True)
% 3.90/4.13 Clause #49 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1))) True) (Ne a (union a_1))
% 3.90/4.13 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Ne a (union a_1)) (Eq (Iff (in a_2 a) (Exists fun D => And (in a_2 D) (in D a_1))) True)
% 3.90/4.13 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 3.90/4.13 Or (Ne a (union a_1)) (Or (Eq (in a_2 a) True) (Eq (Exists fun D => And (in a_2 D) (in D a_1)) False))
% 3.90/4.13 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (union a_1)) (Or (Eq (in a_2 a) True) (Eq (And (in a_2 a_3) (in a_3 a_1)) False))
% 3.90/4.13 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.90/4.13 Or (Ne a (union a_1)) (Or (Eq (in a_2 a) True) (Or (Eq (in a_2 a_3) False) (Eq (in a_3 a_1) False)))
% 3.90/4.13 Clause #55 (by destructive equality resolution #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (union a_1)) True) (Or (Eq (in a a_2) False) (Eq (in a_2 a_1) False))
% 3.90/4.13 Clause #57 (by superposition #[55, 26]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.90/4.13 Or (Eq (in (skS.0 2 a a_1 a_2) (union a_3)) True)
% 3.90/4.13 (Or (Eq (in a a_3) False) (Or (Eq (subset a a_1) True) (Eq False True)))
% 3.90/4.13 Clause #82 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.90/4.13 Or (Eq (in (skS.0 2 a a_1 a_2) (union a_3)) True) (Or (Eq (in a a_3) False) (Eq (subset a a_1) True))
% 3.90/4.14 Clause #83 (by superposition #[82, 17]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.90/4.14 Or (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (union (skS.0 1 a a_3))) True)
% 3.90/4.14 (Or (Eq (subset (skS.0 0 a) a_1) True) (Eq False True))
% 3.90/4.14 Clause #110 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.90/4.14 Or (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (union (skS.0 1 a a_3))) True) (Eq (subset (skS.0 0 a) a_1) True)
% 3.90/4.14 Clause #113 (by superposition #[110, 27]): ∀ (a a_1 : Iota),
% 3.90/4.14 Or (Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True)
% 3.90/4.14 (Or (Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True) (Eq True False))
% 3.90/4.14 Clause #119 (by clausification #[113]): ∀ (a a_1 : Iota),
% 3.90/4.14 Or (Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True) (Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True)
% 3.90/4.14 Clause #120 (by eliminate duplicate literals #[119]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True
% 3.90/4.14 Clause #121 (by superposition #[120, 18]): Eq True False
% 3.90/4.14 Clause #124 (by clausification #[121]): False
% 3.90/4.14 SZS output end Proof for theBenchmark.p
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