TSTP Solution File: SET625+3 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET625+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 14:47:08 EDT 2023
% Result : Theorem 4.03s 4.22s
% Output : Proof 4.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET625+3 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n023.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 : Sat Aug 26 12:18:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.03/4.22 SZS status Theorem for theBenchmark.p
% 4.03/4.22 SZS output start Proof for theBenchmark.p
% 4.03/4.22 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True
% 4.03/4.22 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True
% 4.03/4.22 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), intersect B C → intersect C B) True
% 4.03/4.22 Clause #4 (by assumption #[]): Eq (Not (∀ (B C D : Iota), And (intersect B C) (subset C D) → intersect B D)) True
% 4.03/4.22 Clause #6 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), intersect a C → intersect C a) True
% 4.03/4.22 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (intersect a a_1 → intersect a_1 a) True
% 4.03/4.22 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (intersect a_1 a) True)
% 4.03/4.22 Clause #9 (by clausification #[4]): Eq (∀ (B C D : Iota), And (intersect B C) (subset C D) → intersect B D) False
% 4.03/4.22 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (Not (∀ (C D : Iota), And (intersect (skS.0 0 a) C) (subset C D) → intersect (skS.0 0 a) D)) True
% 4.03/4.22 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (C D : Iota), And (intersect (skS.0 0 a) C) (subset C D) → intersect (skS.0 0 a) D) False
% 4.03/4.22 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota),
% 4.03/4.22 Eq
% 4.03/4.22 (Not
% 4.03/4.22 (∀ (D : Iota), And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) D) → intersect (skS.0 0 a) D))
% 4.03/4.22 True
% 4.03/4.22 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota),
% 4.03/4.22 Eq (∀ (D : Iota), And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) D) → intersect (skS.0 0 a) D)
% 4.03/4.22 False
% 4.03/4.22 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.22 Eq
% 4.03/4.22 (Not
% 4.03/4.22 (And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) →
% 4.03/4.22 intersect (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.03/4.22 True
% 4.03/4.22 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.22 Eq
% 4.03/4.22 (And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) →
% 4.03/4.22 intersect (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 4.03/4.22 False
% 4.03/4.22 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Eq (And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True
% 4.03/4.22 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Eq (intersect (skS.0 0 a) (skS.0 2 a a_1 a_2)) False
% 4.03/4.22 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True
% 4.03/4.22 Clause #19 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (intersect (skS.0 0 a) (skS.0 1 a a_1)) True
% 4.03/4.22 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True
% 4.03/4.22 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True
% 4.03/4.22 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (D : Iota), member D a → member D a_1) True)
% 4.03/4.22 Clause #28 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (member a_2 a → member a_2 a_1) True)
% 4.03/4.22 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) True))
% 4.03/4.22 Clause #30 (by superposition #[29, 18]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.03/4.22 Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Or (Eq (member a (skS.0 2 a_1 a_2 a_3)) True) (Eq False True))
% 4.03/4.22 Clause #32 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True
% 4.03/4.22 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True
% 4.03/4.22 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) True) (Eq (Exists fun D => And (member D a) (member D a_1)) False)
% 4.03/4.22 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (Exists fun D => And (member D a) (member D a_1)) True)
% 4.08/4.24 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Eq (And (member a_2 a) (member a_2 a_1)) False)
% 4.08/4.24 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) False))
% 4.08/4.24 Clause #40 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 4.08/4.24 Or (Eq (intersect a a_1) False) (Eq (And (member (skS.0 4 a a_1 a_2) a) (member (skS.0 4 a a_1 a_2) a_1)) True)
% 4.08/4.24 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 4 a a_1 a_2) a_1) True)
% 4.08/4.24 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 4 a a_1 a_2) a) True)
% 4.08/4.24 Clause #43 (by superposition #[19, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (intersect (skS.0 1 a a_1) (skS.0 0 a)) True)
% 4.08/4.24 Clause #48 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (intersect (skS.0 1 a a_1) (skS.0 0 a)) True
% 4.08/4.24 Clause #50 (by superposition #[48, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True)
% 4.08/4.24 Clause #51 (by superposition #[48, 42]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True)
% 4.08/4.24 Clause #58 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Eq (member a (skS.0 2 a_1 a_2 a_3)) True)
% 4.08/4.24 Clause #80 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True
% 4.08/4.24 Clause #81 (by superposition #[80, 37]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.08/4.24 Or (Eq (intersect (skS.0 0 a) a_1) True)
% 4.08/4.24 (Or (Eq True False) (Eq (member (skS.0 4 (skS.0 1 a a_2) (skS.0 0 a) a_3) a_1) False))
% 4.08/4.24 Clause #89 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True
% 4.08/4.24 Clause #90 (by superposition #[89, 58]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.08/4.24 Or (Eq True False) (Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 2 a a_1 a_3)) True)
% 4.08/4.24 Clause #95 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.08/4.24 Or (Eq (intersect (skS.0 0 a) a_1) True) (Eq (member (skS.0 4 (skS.0 1 a a_2) (skS.0 0 a) a_3) a_1) False)
% 4.08/4.24 Clause #115 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota), Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 2 a a_1 a_3)) True
% 4.08/4.24 Clause #116 (by superposition #[115, 95]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq True False)
% 4.08/4.24 Clause #120 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), Eq (intersect (skS.0 0 a) (skS.0 2 a a_1 a_2)) True
% 4.08/4.24 Clause #121 (by superposition #[120, 17]): Eq True False
% 4.08/4.24 Clause #131 (by clausification #[121]): False
% 4.08/4.24 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------