TSTP Solution File: SET985+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n007.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 14:48:13 EDT 2023
% Result : Theorem 4.61s 4.86s
% Output : Proof 4.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 15:33:41 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.61/4.86 SZS status Theorem for theBenchmark.p
% 4.61/4.86 SZS output start Proof for theBenchmark.p
% 4.61/4.86 Clause #0 (by assumption #[]): Eq (empty empty_set) True
% 4.61/4.86 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (cartesian_product2 A B) empty_set) (Or (Eq A empty_set) (Eq B empty_set))) True
% 4.61/4.86 Clause #5 (by assumption #[]): Eq
% 4.61/4.86 (∀ (A B C D : Iota),
% 4.61/4.86 subset (cartesian_product2 A B) (cartesian_product2 C D) →
% 4.61/4.86 Or (Eq (cartesian_product2 A B) empty_set) (And (subset A C) (subset B D)))
% 4.61/4.86 True
% 4.61/4.86 Clause #6 (by assumption #[]): Eq
% 4.61/4.86 (Not
% 4.61/4.86 (∀ (A : Iota),
% 4.61/4.86 Not (empty A) →
% 4.61/4.86 ∀ (B C D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 A B) (cartesian_product2 C D))
% 4.61/4.86 (subset (cartesian_product2 B A) (cartesian_product2 D C)) →
% 4.61/4.86 subset B D))
% 4.61/4.86 True
% 4.61/4.86 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), subset empty_set A) True
% 4.61/4.86 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (subset empty_set a) True
% 4.61/4.86 Clause #15 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (cartesian_product2 a B) empty_set) (Or (Eq a empty_set) (Eq B empty_set))) True
% 4.61/4.86 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (Eq (cartesian_product2 a a_1) empty_set) (Or (Eq a empty_set) (Eq a_1 empty_set))) True
% 4.61/4.86 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota),
% 4.61/4.86 Or (Eq (Eq (cartesian_product2 a a_1) empty_set) False) (Eq (Or (Eq a empty_set) (Eq a_1 empty_set)) True)
% 4.61/4.86 Clause #26 (by clausification #[6]): Eq
% 4.61/4.86 (∀ (A : Iota),
% 4.61/4.86 Not (empty A) →
% 4.61/4.86 ∀ (B C D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 A B) (cartesian_product2 C D))
% 4.61/4.86 (subset (cartesian_product2 B A) (cartesian_product2 D C)) →
% 4.61/4.86 subset B D)
% 4.61/4.86 False
% 4.61/4.86 Clause #27 (by clausification #[26]): ∀ (a : Iota),
% 4.61/4.86 Eq
% 4.61/4.86 (Not
% 4.61/4.86 (Not (empty (skS.0 2 a)) →
% 4.61/4.86 ∀ (B C D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 (skS.0 2 a) B) (cartesian_product2 C D))
% 4.61/4.86 (subset (cartesian_product2 B (skS.0 2 a)) (cartesian_product2 D C)) →
% 4.61/4.86 subset B D))
% 4.61/4.86 True
% 4.61/4.86 Clause #28 (by clausification #[27]): ∀ (a : Iota),
% 4.61/4.86 Eq
% 4.61/4.86 (Not (empty (skS.0 2 a)) →
% 4.61/4.86 ∀ (B C D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 (skS.0 2 a) B) (cartesian_product2 C D))
% 4.61/4.86 (subset (cartesian_product2 B (skS.0 2 a)) (cartesian_product2 D C)) →
% 4.61/4.86 subset B D)
% 4.61/4.86 False
% 4.61/4.86 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (Not (empty (skS.0 2 a))) True
% 4.61/4.86 Clause #30 (by clausification #[28]): ∀ (a : Iota),
% 4.61/4.86 Eq
% 4.61/4.86 (∀ (B C D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 (skS.0 2 a) B) (cartesian_product2 C D))
% 4.61/4.86 (subset (cartesian_product2 B (skS.0 2 a)) (cartesian_product2 D C)) →
% 4.61/4.86 subset B D)
% 4.61/4.86 False
% 4.61/4.86 Clause #31 (by clausification #[29]): ∀ (a : Iota), Eq (empty (skS.0 2 a)) False
% 4.61/4.86 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota),
% 4.61/4.86 Eq
% 4.61/4.86 (Not
% 4.61/4.86 (∀ (C D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 C D))
% 4.61/4.86 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D C)) →
% 4.61/4.86 subset (skS.0 3 a a_1) D))
% 4.61/4.86 True
% 4.61/4.86 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota),
% 4.61/4.86 Eq
% 4.61/4.86 (∀ (C D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 C D))
% 4.61/4.86 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D C)) →
% 4.61/4.86 subset (skS.0 3 a a_1) D)
% 4.61/4.86 False
% 4.61/4.86 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota),
% 4.61/4.86 Eq
% 4.61/4.86 (Not
% 4.61/4.86 (∀ (D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) D))
% 4.61/4.86 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D (skS.0 4 a a_1 a_2))) →
% 4.61/4.86 subset (skS.0 3 a a_1) D))
% 4.61/4.86 True
% 4.61/4.86 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 4.61/4.86 Eq
% 4.61/4.86 (∀ (D : Iota),
% 4.61/4.86 Or (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) D))
% 4.61/4.86 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D (skS.0 4 a a_1 a_2))) →
% 4.69/4.88 subset (skS.0 3 a a_1) D)
% 4.69/4.88 False
% 4.69/4.88 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.88 Eq
% 4.69/4.88 (Not
% 4.69/4.88 (Or
% 4.69/4.88 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1))
% 4.69/4.88 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.88 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a))
% 4.69/4.88 (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))) →
% 4.69/4.88 subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.88 True
% 4.69/4.88 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.88 Eq
% 4.69/4.88 (Or
% 4.69/4.88 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1))
% 4.69/4.88 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.88 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a))
% 4.69/4.88 (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))) →
% 4.69/4.88 subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))
% 4.69/4.88 False
% 4.69/4.88 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.88 Eq
% 4.69/4.88 (Or
% 4.69/4.88 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1))
% 4.69/4.88 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.88 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a))
% 4.69/4.88 (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))))
% 4.69/4.88 True
% 4.69/4.88 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) False
% 4.69/4.88 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.88 Or
% 4.69/4.88 (Eq
% 4.69/4.88 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1))
% 4.69/4.88 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.88 True)
% 4.69/4.88 (Eq
% 4.69/4.88 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a))
% 4.69/4.88 (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2)))
% 4.69/4.88 True)
% 4.69/4.88 Clause #41 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (Or (Eq a empty_set) (Eq a_1 empty_set)) True) (Ne (cartesian_product2 a a_1) empty_set)
% 4.69/4.88 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 4.69/4.88 Or (Ne (cartesian_product2 a a_1) empty_set) (Or (Eq (Eq a empty_set) True) (Eq (Eq a_1 empty_set) True))
% 4.69/4.88 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Ne (cartesian_product2 a a_1) empty_set) (Or (Eq (Eq a_1 empty_set) True) (Eq a empty_set))
% 4.69/4.88 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Ne (cartesian_product2 a a_1) empty_set) (Or (Eq a empty_set) (Eq a_1 empty_set))
% 4.69/4.88 Clause #45 (by clausification #[5]): ∀ (a : Iota),
% 4.69/4.88 Eq
% 4.69/4.88 (∀ (B C D : Iota),
% 4.69/4.88 subset (cartesian_product2 a B) (cartesian_product2 C D) →
% 4.69/4.88 Or (Eq (cartesian_product2 a B) empty_set) (And (subset a C) (subset B D)))
% 4.69/4.88 True
% 4.69/4.88 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota),
% 4.69/4.88 Eq
% 4.69/4.88 (∀ (C D : Iota),
% 4.69/4.88 subset (cartesian_product2 a a_1) (cartesian_product2 C D) →
% 4.69/4.88 Or (Eq (cartesian_product2 a a_1) empty_set) (And (subset a C) (subset a_1 D)))
% 4.69/4.88 True
% 4.69/4.88 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota),
% 4.69/4.88 Eq
% 4.69/4.88 (∀ (D : Iota),
% 4.69/4.88 subset (cartesian_product2 a a_1) (cartesian_product2 a_2 D) →
% 4.69/4.88 Or (Eq (cartesian_product2 a a_1) empty_set) (And (subset a a_2) (subset a_1 D)))
% 4.69/4.88 True
% 4.69/4.88 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.88 Eq
% 4.69/4.88 (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) →
% 4.69/4.88 Or (Eq (cartesian_product2 a a_1) empty_set) (And (subset a a_2) (subset a_1 a_3)))
% 4.69/4.88 True
% 4.69/4.88 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.88 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False)
% 4.69/4.88 (Eq (Or (Eq (cartesian_product2 a a_1) empty_set) (And (subset a a_2) (subset a_1 a_3))) True)
% 4.69/4.88 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.88 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False)
% 4.69/4.88 (Or (Eq (Eq (cartesian_product2 a a_1) empty_set) True) (Eq (And (subset a a_2) (subset a_1 a_3)) True))
% 4.69/4.88 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.88 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False)
% 4.69/4.90 (Or (Eq (And (subset a a_2) (subset a_1 a_3)) True) (Eq (cartesian_product2 a a_1) empty_set))
% 4.69/4.90 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.90 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False)
% 4.69/4.90 (Or (Eq (cartesian_product2 a a_1) empty_set) (Eq (subset a_1 a_3) True))
% 4.69/4.90 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.90 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False)
% 4.69/4.90 (Or (Eq (cartesian_product2 a a_1) empty_set) (Eq (subset a a_2) True))
% 4.69/4.90 Clause #59 (by superposition #[53, 40]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set)
% 4.69/4.90 (Or (Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True)
% 4.69/4.90 (Or
% 4.69/4.90 (Eq
% 4.69/4.90 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1))
% 4.69/4.90 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.90 True)
% 4.69/4.90 (Eq False True)))
% 4.69/4.90 Clause #70 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set)
% 4.69/4.90 (Or (Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True)
% 4.69/4.90 (Eq
% 4.69/4.90 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1))
% 4.69/4.90 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.90 True))
% 4.69/4.90 Clause #71 (by forward demodulation #[70, 39]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set)
% 4.69/4.90 (Or (Eq False True)
% 4.69/4.90 (Eq
% 4.69/4.90 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1))
% 4.69/4.90 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.90 True))
% 4.69/4.90 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set)
% 4.69/4.90 (Eq
% 4.69/4.90 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1))
% 4.69/4.90 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 4.69/4.90 True)
% 4.69/4.90 Clause #73 (by superposition #[72, 52]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set)
% 4.69/4.90 (Or (Eq True False)
% 4.69/4.90 (Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set)
% 4.69/4.90 (Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True)))
% 4.69/4.90 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set)
% 4.69/4.90 (Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set)
% 4.69/4.90 (Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True))
% 4.69/4.90 Clause #76 (by superposition #[75, 39]): ∀ (a a_1 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set)
% 4.69/4.90 (Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set) (Eq True False))
% 4.69/4.90 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set)
% 4.69/4.90 (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set)
% 4.69/4.90 Clause #79 (by superposition #[77, 44]): ∀ (a a_1 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set)
% 4.69/4.90 (Or (Ne empty_set empty_set) (Or (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 2 a) empty_set)))
% 4.69/4.90 Clause #82 (by eliminate resolved literals #[79]): ∀ (a a_1 : Iota),
% 4.69/4.90 Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set)
% 4.69/4.90 (Or (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 2 a) empty_set))
% 4.69/4.90 Clause #83 (by forward contextual literal cutting #[82, 44]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 2 a) empty_set)
% 4.69/4.90 Clause #85 (by superposition #[83, 39]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (subset empty_set (skS.0 5 a a_1 a_2 a_3)) False)
% 4.69/4.90 Clause #88 (by superposition #[85, 8]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq False True)
% 4.69/4.90 Clause #89 (by clausification #[88]): ∀ (a : Iota), Eq (skS.0 2 a) empty_set
% 4.69/4.90 Clause #90 (by backward demodulation #[89, 31]): Eq (empty empty_set) False
% 4.69/4.90 Clause #96 (by superposition #[90, 0]): Eq False True
% 4.69/4.90 Clause #100 (by clausification #[96]): False
% 4.69/4.90 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------