TSTP Solution File: SEU747^2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU747^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 16:43:42 EDT 2023
% Result : Theorem 3.77s 3.93s
% Output : Proof 3.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU747^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 23:05:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.77/3.93 SZS status Theorem for theBenchmark.p
% 3.77/3.93 SZS output start Proof for theBenchmark.p
% 3.77/3.93 Clause #0 (by assumption #[]): Eq (Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))) True
% 3.77/3.93 Clause #1 (by assumption #[]): Eq
% 3.77/3.93 (Not
% 3.77/3.93 (binunionE →
% 3.77/3.93 ∀ (A X : Iota),
% 3.77/3.93 in X (powerset A) →
% 3.77/3.93 ∀ (Y : Iota),
% 3.77/3.93 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y))))
% 3.77/3.93 True
% 3.77/3.93 Clause #2 (by clausification #[0]): Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))
% 3.77/3.93 Clause #19 (by clausification #[1]): Eq
% 3.77/3.93 (binunionE →
% 3.77/3.93 ∀ (A X : Iota),
% 3.77/3.93 in X (powerset A) →
% 3.77/3.93 ∀ (Y : Iota),
% 3.77/3.93 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y)))
% 3.77/3.93 False
% 3.77/3.93 Clause #20 (by clausification #[19]): Eq binunionE True
% 3.77/3.93 Clause #21 (by clausification #[19]): Eq
% 3.77/3.93 (∀ (A X : Iota),
% 3.77/3.93 in X (powerset A) →
% 3.77/3.93 ∀ (Y : Iota),
% 3.77/3.93 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y)))
% 3.77/3.93 False
% 3.77/3.93 Clause #22 (by backward demodulation #[20, 2]): Eq True (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))
% 3.77/3.93 Clause #28 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binunion a B) → Or (in Xx a) (in Xx B)) True
% 3.77/3.93 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binunion a a_1) → Or (in Xx a) (in Xx a_1)) True
% 3.77/3.93 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (in a (binunion a_1 a_2) → Or (in a a_1) (in a a_2)) True
% 3.77/3.93 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Eq (Or (in a a_1) (in a a_2)) True)
% 3.77/3.93 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq (in a a_1) True) (Eq (in a a_2) True))
% 3.77/3.93 Clause #33 (by clausification #[21]): ∀ (a : Iota),
% 3.77/3.93 Eq
% 3.77/3.93 (Not
% 3.77/3.93 (∀ (X : Iota),
% 3.77/3.93 in X (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Y : Iota),
% 3.77/3.93 in Y (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y))))
% 3.77/3.93 True
% 3.77/3.93 Clause #34 (by clausification #[33]): ∀ (a : Iota),
% 3.77/3.93 Eq
% 3.77/3.93 (∀ (X : Iota),
% 3.77/3.93 in X (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Y : Iota),
% 3.77/3.93 in Y (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y)))
% 3.77/3.93 False
% 3.77/3.93 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 3.77/3.93 Eq
% 3.77/3.93 (Not
% 3.77/3.93 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Y : Iota),
% 3.77/3.93 in Y (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Xx : Iota),
% 3.77/3.93 in Xx (skS.0 3 a) →
% 3.77/3.93 Not (in Xx (skS.0 4 a a_1)) → Not (in Xx Y) → Not (in Xx (binunion (skS.0 4 a a_1) Y))))
% 3.77/3.93 True
% 3.77/3.93 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 3.77/3.93 Eq
% 3.77/3.93 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Y : Iota),
% 3.77/3.93 in Y (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Xx : Iota),
% 3.77/3.93 in Xx (skS.0 3 a) → Not (in Xx (skS.0 4 a a_1)) → Not (in Xx Y) → Not (in Xx (binunion (skS.0 4 a a_1) Y)))
% 3.77/3.93 False
% 3.77/3.93 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota),
% 3.77/3.93 Eq
% 3.77/3.93 (∀ (Y : Iota),
% 3.77/3.93 in Y (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Xx : Iota),
% 3.77/3.93 in Xx (skS.0 3 a) → Not (in Xx (skS.0 4 a a_1)) → Not (in Xx Y) → Not (in Xx (binunion (skS.0 4 a a_1) Y)))
% 3.77/3.93 False
% 3.77/3.93 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 3.77/3.93 Eq
% 3.77/3.93 (Not
% 3.77/3.93 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Xx : Iota),
% 3.77/3.93 in Xx (skS.0 3 a) →
% 3.77/3.93 Not (in Xx (skS.0 4 a a_1)) →
% 3.77/3.93 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))))
% 3.77/3.93 True
% 3.77/3.93 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 3.77/3.93 Eq
% 3.77/3.93 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) →
% 3.77/3.93 ∀ (Xx : Iota),
% 3.77/3.95 in Xx (skS.0 3 a) →
% 3.77/3.95 Not (in Xx (skS.0 4 a a_1)) →
% 3.77/3.95 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))
% 3.77/3.95 False
% 3.77/3.95 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 3.77/3.95 Eq
% 3.77/3.95 (∀ (Xx : Iota),
% 3.77/3.95 in Xx (skS.0 3 a) →
% 3.77/3.95 Not (in Xx (skS.0 4 a a_1)) →
% 3.77/3.95 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))
% 3.77/3.95 False
% 3.77/3.95 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.77/3.95 Eq
% 3.77/3.95 (Not
% 3.77/3.95 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))))
% 3.77/3.95 True
% 3.77/3.95 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.77/3.95 Eq
% 3.77/3.95 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))
% 3.77/3.95 False
% 3.77/3.95 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.77/3.95 Eq
% 3.77/3.95 (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))
% 3.77/3.95 False
% 3.77/3.95 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1))) True
% 3.77/3.95 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.77/3.95 Eq
% 3.77/3.95 (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) →
% 3.77/3.95 Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))
% 3.77/3.95 False
% 3.77/3.95 Clause #50 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) False
% 3.77/3.95 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2))) True
% 3.77/3.95 Clause #52 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) False
% 3.77/3.95 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) False
% 3.77/3.95 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) True
% 3.77/3.95 Clause #55 (by superposition #[54, 32]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.77/3.95 Or (Eq True False)
% 3.77/3.95 (Or (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) True)
% 3.77/3.95 (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) True))
% 3.77/3.95 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.77/3.95 Or (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) True) (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) True)
% 3.77/3.95 Clause #57 (by forward demodulation #[56, 50]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq False True) (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) True)
% 3.77/3.95 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) True
% 3.77/3.95 Clause #59 (by superposition #[58, 53]): Eq True False
% 3.77/3.95 Clause #60 (by clausification #[59]): False
% 3.77/3.95 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------