TSTP Solution File: SEU167+3 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n015.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 16:40:35 EDT 2023
% Result : Theorem 5.68s 5.96s
% Output : Proof 5.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.22/0.36 % CPULimit : 300
% 0.22/0.36 % WCLimit : 300
% 0.22/0.36 % DateTime : Wed Aug 23 15:29:05 EDT 2023
% 0.22/0.36 % CPUTime :
% 5.68/5.96 SZS status Theorem for theBenchmark.p
% 5.68/5.96 SZS output start Proof for theBenchmark.p
% 5.68/5.96 Clause #3 (by assumption #[]): Eq
% 5.68/5.96 (∀ (A B C : Iota),
% 5.68/5.96 subset A B →
% 5.68/5.96 And (subset (cartesian_product2 A C) (cartesian_product2 B C))
% 5.68/5.96 (subset (cartesian_product2 C A) (cartesian_product2 C B)))
% 5.68/5.96 True
% 5.68/5.96 Clause #4 (by assumption #[]): Eq (Not (∀ (A B C D : Iota), And (subset A B) (subset C D) → subset (cartesian_product2 A C) (cartesian_product2 B D)))
% 5.68/5.96 True
% 5.68/5.96 Clause #5 (by assumption #[]): Eq (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C) True
% 5.68/5.96 Clause #12 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset a B) (subset B C) → subset a C) True
% 5.68/5.96 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (subset a a_1) (subset a_1 C) → subset a C) True
% 5.68/5.96 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True
% 5.68/5.96 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a_2)) False) (Eq (subset a a_2) True)
% 5.68/5.96 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Or (Eq (subset a a_2) False) (Eq (subset a_2 a_1) False))
% 5.68/5.96 Clause #19 (by clausification #[3]): ∀ (a : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (∀ (B C : Iota),
% 5.68/5.96 subset a B →
% 5.68/5.96 And (subset (cartesian_product2 a C) (cartesian_product2 B C))
% 5.68/5.96 (subset (cartesian_product2 C a) (cartesian_product2 C B)))
% 5.68/5.96 True
% 5.68/5.96 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (∀ (C : Iota),
% 5.68/5.96 subset a a_1 →
% 5.68/5.96 And (subset (cartesian_product2 a C) (cartesian_product2 a_1 C))
% 5.68/5.96 (subset (cartesian_product2 C a) (cartesian_product2 C a_1)))
% 5.68/5.96 True
% 5.68/5.96 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (subset a a_1 →
% 5.68/5.96 And (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2))
% 5.68/5.96 (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1)))
% 5.68/5.96 True
% 5.68/5.96 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 5.68/5.96 Or (Eq (subset a a_1) False)
% 5.68/5.96 (Eq
% 5.68/5.96 (And (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2))
% 5.68/5.96 (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1)))
% 5.68/5.96 True)
% 5.68/5.96 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 5.68/5.96 Or (Eq (subset a a_1) False) (Eq (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1)) True)
% 5.68/5.96 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 5.68/5.96 Or (Eq (subset a a_1) False) (Eq (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)) True)
% 5.68/5.96 Clause #27 (by clausification #[4]): Eq (∀ (A B C D : Iota), And (subset A B) (subset C D) → subset (cartesian_product2 A C) (cartesian_product2 B D)) False
% 5.68/5.96 Clause #28 (by clausification #[27]): ∀ (a : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (Not
% 5.68/5.96 (∀ (B C D : Iota),
% 5.68/5.96 And (subset (skS.0 2 a) B) (subset C D) → subset (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 B D)))
% 5.68/5.96 True
% 5.68/5.96 Clause #29 (by clausification #[28]): ∀ (a : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (∀ (B C D : Iota),
% 5.68/5.96 And (subset (skS.0 2 a) B) (subset C D) → subset (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 B D))
% 5.68/5.96 False
% 5.68/5.96 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (Not
% 5.68/5.96 (∀ (C D : Iota),
% 5.68/5.96 And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset C D) →
% 5.68/5.96 subset (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 3 a a_1) D)))
% 5.68/5.96 True
% 5.68/5.96 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (∀ (C D : Iota),
% 5.68/5.96 And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset C D) →
% 5.68/5.96 subset (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 3 a a_1) D))
% 5.68/5.96 False
% 5.68/5.96 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (Not
% 5.68/5.96 (∀ (D : Iota),
% 5.68/5.96 And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) D) →
% 5.68/5.96 subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 3 a a_1) D)))
% 5.68/5.96 True
% 5.68/5.96 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota),
% 5.68/5.96 Eq
% 5.68/5.96 (∀ (D : Iota),
% 5.82/5.98 And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) D) →
% 5.82/5.98 subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 3 a a_1) D))
% 5.82/5.98 False
% 5.82/5.98 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.82/5.98 Eq
% 5.82/5.98 (Not
% 5.82/5.98 (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) →
% 5.82/5.98 subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 5.82/5.98 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))))
% 5.82/5.98 True
% 5.82/5.98 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.82/5.98 Eq
% 5.82/5.98 (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) →
% 5.82/5.98 subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 5.82/5.98 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))
% 5.82/5.98 False
% 5.82/5.98 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.82/5.98 Eq (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) True
% 5.82/5.98 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.82/5.98 Eq
% 5.82/5.98 (subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 5.82/5.98 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))
% 5.82/5.98 False
% 5.82/5.98 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) True
% 5.82/5.98 Clause #39 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True
% 5.82/5.98 Clause #41 (by superposition #[38, 23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.82/5.98 Or (Eq True False)
% 5.82/5.98 (Eq (subset (cartesian_product2 a (skS.0 4 a_1 a_2 a_3)) (cartesian_product2 a (skS.0 5 a_1 a_2 a_3 a_4))) True)
% 5.82/5.98 Clause #45 (by superposition #[39, 24]): ∀ (a a_1 a_2 : Iota),
% 5.82/5.98 Or (Eq True False) (Eq (subset (cartesian_product2 (skS.0 2 a) a_1) (cartesian_product2 (skS.0 3 a a_2) a_1)) True)
% 5.82/5.98 Clause #52 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Eq (subset (cartesian_product2 (skS.0 2 a) a_1) (cartesian_product2 (skS.0 3 a a_2) a_1)) True
% 5.82/5.98 Clause #53 (by superposition #[52, 16]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.82/5.98 Or (Eq (subset (cartesian_product2 (skS.0 2 a) a_1) a_2) True)
% 5.82/5.98 (Or (Eq True False) (Eq (subset (cartesian_product2 (skS.0 3 a a_3) a_1) a_2) False))
% 5.82/5.98 Clause #75 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.82/5.98 Or (Eq (subset (cartesian_product2 (skS.0 2 a) a_1) a_2) True)
% 5.82/5.98 (Eq (subset (cartesian_product2 (skS.0 3 a a_3) a_1) a_2) False)
% 5.82/5.98 Clause #78 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.82/5.98 Eq (subset (cartesian_product2 a (skS.0 4 a_1 a_2 a_3)) (cartesian_product2 a (skS.0 5 a_1 a_2 a_3 a_4))) True
% 5.82/5.98 Clause #79 (by superposition #[78, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.82/5.98 Or
% 5.82/5.98 (Eq
% 5.82/5.98 (subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a_1 a_2 a_3))
% 5.82/5.98 (cartesian_product2 (skS.0 3 a a_4) (skS.0 5 a_1 a_2 a_3 a_5)))
% 5.82/5.98 True)
% 5.82/5.98 (Eq True False)
% 5.82/5.98 Clause #339 (by clausification #[79]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.82/5.98 Eq
% 5.82/5.98 (subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a_1 a_2 a_3))
% 5.82/5.98 (cartesian_product2 (skS.0 3 a a_4) (skS.0 5 a_1 a_2 a_3 a_5)))
% 5.82/5.98 True
% 5.82/5.98 Clause #340 (by superposition #[339, 37]): Eq True False
% 5.82/5.98 Clause #344 (by clausification #[340]): False
% 5.82/5.98 SZS output end Proof for theBenchmark.p
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