TSTP Solution File: SET974+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n018.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 14:48:12 EDT 2023
% Result : Theorem 62.87s 63.50s
% Output : Proof 63.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n018.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 12:53:30 EDT 2023
% 0.14/0.34 % CPUTime :
% 62.87/63.50 SZS status Theorem for theBenchmark.p
% 62.87/63.50 SZS output start Proof for theBenchmark.p
% 62.87/63.50 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A B) (set_intersection2 B A)) True
% 62.87/63.50 Clause #8 (by assumption #[]): Eq (∀ (A B : Iota), disjoint A B → disjoint B A) True
% 62.87/63.50 Clause #9 (by assumption #[]): Eq
% 62.87/63.50 (∀ (A B C D E : Iota),
% 62.87/63.50 Not
% 62.87/63.50 (And (in A (set_intersection2 (cartesian_product2 B C) (cartesian_product2 D E)))
% 62.87/63.50 (∀ (F G : Iota),
% 62.87/63.50 Not (And (And (Eq A (ordered_pair F G)) (in F (set_intersection2 B D))) (in G (set_intersection2 C E))))))
% 62.87/63.50 True
% 62.87/63.50 Clause #10 (by assumption #[]): Eq
% 62.87/63.50 (Not
% 62.87/63.50 (∀ (A B C D : Iota), Or (disjoint A B) (disjoint C D) → disjoint (cartesian_product2 A C) (cartesian_product2 B D)))
% 62.87/63.50 True
% 62.87/63.50 Clause #11 (by assumption #[]): Eq
% 62.87/63.50 (∀ (A B : Iota),
% 62.87/63.50 And (Not (And (Not (disjoint A B)) (∀ (C : Iota), Not (in C (set_intersection2 A B)))))
% 62.87/63.50 (Not (And (Exists fun C => in C (set_intersection2 A B)) (disjoint A B))))
% 62.87/63.50 True
% 62.87/63.50 Clause #16 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), disjoint a B → disjoint B a) True
% 62.87/63.50 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (disjoint a a_1 → disjoint a_1 a) True
% 62.87/63.50 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (disjoint a_1 a) True)
% 62.87/63.50 Clause #32 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a B) (set_intersection2 B a)) True
% 62.87/63.50 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)) True
% 62.87/63.50 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)
% 62.87/63.50 Clause #35 (by clausification #[10]): Eq (∀ (A B C D : Iota), Or (disjoint A B) (disjoint C D) → disjoint (cartesian_product2 A C) (cartesian_product2 B D))
% 62.87/63.50 False
% 62.87/63.50 Clause #36 (by clausification #[35]): ∀ (a : Iota),
% 62.87/63.50 Eq
% 62.87/63.50 (Not
% 62.87/63.50 (∀ (B C D : Iota),
% 62.87/63.50 Or (disjoint (skS.0 2 a) B) (disjoint C D) →
% 62.87/63.50 disjoint (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 B D)))
% 62.87/63.50 True
% 62.87/63.50 Clause #37 (by clausification #[36]): ∀ (a : Iota),
% 62.87/63.50 Eq
% 62.87/63.50 (∀ (B C D : Iota),
% 62.87/63.50 Or (disjoint (skS.0 2 a) B) (disjoint C D) → disjoint (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 B D))
% 62.87/63.50 False
% 62.87/63.50 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 62.87/63.50 Eq
% 62.87/63.50 (Not
% 62.87/63.50 (∀ (C D : Iota),
% 62.87/63.50 Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint C D) →
% 62.87/63.50 disjoint (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 3 a a_1) D)))
% 62.87/63.50 True
% 62.87/63.50 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota),
% 62.87/63.50 Eq
% 62.87/63.50 (∀ (C D : Iota),
% 62.87/63.50 Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint C D) →
% 62.87/63.50 disjoint (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 3 a a_1) D))
% 62.87/63.50 False
% 62.87/63.50 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 62.87/63.50 Eq
% 62.87/63.50 (Not
% 62.87/63.50 (∀ (D : Iota),
% 62.87/63.50 Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) D) →
% 62.87/63.50 disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 3 a a_1) D)))
% 62.87/63.50 True
% 62.87/63.50 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 62.87/63.50 Eq
% 62.87/63.50 (∀ (D : Iota),
% 62.87/63.50 Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) D) →
% 62.87/63.50 disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 3 a a_1) D))
% 62.87/63.50 False
% 62.87/63.50 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.87/63.50 Eq
% 62.87/63.50 (Not
% 62.87/63.50 (Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) →
% 62.87/63.50 disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 62.87/63.50 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))))
% 62.87/63.50 True
% 62.87/63.50 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.87/63.50 Eq
% 62.87/63.50 (Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) →
% 62.87/63.50 disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 62.87/63.50 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))
% 62.95/63.52 False
% 62.95/63.52 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.95/63.52 Eq (Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) True
% 62.95/63.52 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.95/63.52 Eq
% 62.95/63.52 (disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 62.95/63.52 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))
% 62.95/63.52 False
% 62.95/63.52 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.95/63.52 Or (Eq (disjoint (skS.0 2 a) (skS.0 3 a a_1)) True) (Eq (disjoint (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) True)
% 62.95/63.52 Clause #60 (by clausification #[9]): ∀ (a : Iota),
% 62.95/63.52 Eq
% 62.95/63.52 (∀ (B C D E : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And (in a (set_intersection2 (cartesian_product2 B C) (cartesian_product2 D E)))
% 62.95/63.52 (∀ (F G : Iota),
% 62.95/63.52 Not (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 B D))) (in G (set_intersection2 C E))))))
% 62.95/63.52 True
% 62.95/63.52 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota),
% 62.95/63.52 Eq
% 62.95/63.52 (∀ (C D E : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And (in a (set_intersection2 (cartesian_product2 a_1 C) (cartesian_product2 D E)))
% 62.95/63.52 (∀ (F G : Iota),
% 62.95/63.52 Not (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 D))) (in G (set_intersection2 C E))))))
% 62.95/63.52 True
% 62.95/63.52 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 62.95/63.52 Eq
% 62.95/63.52 (∀ (D E : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 D E)))
% 62.95/63.52 (∀ (F G : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 D))) (in G (set_intersection2 a_2 E))))))
% 62.95/63.52 True
% 62.95/63.52 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.95/63.52 Eq
% 62.95/63.52 (∀ (E : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 E)))
% 62.95/63.52 (∀ (F G : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 a_3)))
% 62.95/63.52 (in G (set_intersection2 a_2 E))))))
% 62.95/63.52 True
% 62.95/63.52 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 62.95/63.52 Eq
% 62.95/63.52 (Not
% 62.95/63.52 (And (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4)))
% 62.95/63.52 (∀ (F G : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 a_3)))
% 62.95/63.52 (in G (set_intersection2 a_2 a_4))))))
% 62.95/63.52 True
% 62.95/63.52 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 62.95/63.52 Eq
% 62.95/63.52 (And (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4)))
% 62.95/63.52 (∀ (F G : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 a_3))) (in G (set_intersection2 a_2 a_4)))))
% 62.95/63.52 False
% 62.95/63.52 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 62.95/63.52 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.52 (Eq
% 62.95/63.52 (∀ (F G : Iota),
% 62.95/63.52 Not (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 a_3))) (in G (set_intersection2 a_2 a_4))))
% 62.95/63.52 False)
% 62.95/63.52 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 62.95/63.52 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.52 (Eq
% 62.95/63.52 (Not
% 62.95/63.52 (∀ (G : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And
% 62.95/63.52 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) G))
% 62.95/63.52 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3)))
% 62.95/63.52 (in G (set_intersection2 a_2 a_4)))))
% 62.95/63.52 True)
% 62.95/63.52 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 62.95/63.52 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.52 (Eq
% 62.95/63.52 (∀ (G : Iota),
% 62.95/63.52 Not
% 62.95/63.52 (And
% 62.95/63.52 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) G))
% 62.95/63.52 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3)))
% 62.95/63.52 (in G (set_intersection2 a_2 a_4))))
% 62.95/63.52 False)
% 62.95/63.52 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 62.95/63.52 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.54 (Eq
% 62.95/63.54 (Not
% 62.95/63.54 (Not
% 62.95/63.54 (And
% 62.95/63.54 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6)))
% 62.95/63.54 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3)))
% 62.95/63.54 (in (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6) (set_intersection2 a_2 a_4)))))
% 62.95/63.54 True)
% 62.95/63.54 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 62.95/63.54 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.54 (Eq
% 62.95/63.54 (Not
% 62.95/63.54 (And
% 62.95/63.54 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6)))
% 62.95/63.54 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3)))
% 62.95/63.54 (in (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6) (set_intersection2 a_2 a_4))))
% 62.95/63.54 False)
% 62.95/63.54 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 62.95/63.54 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.54 (Eq
% 62.95/63.54 (And
% 62.95/63.54 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6)))
% 62.95/63.54 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3)))
% 62.95/63.54 (in (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6) (set_intersection2 a_2 a_4)))
% 62.95/63.54 True)
% 62.95/63.54 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 62.95/63.54 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.54 (Eq (in (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6) (set_intersection2 a_2 a_4)) True)
% 62.95/63.54 Clause #73 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 62.95/63.54 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.54 (Eq
% 62.95/63.54 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6)))
% 62.95/63.54 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3)))
% 62.95/63.54 True)
% 62.95/63.54 Clause #87 (by clausification #[11]): ∀ (a : Iota),
% 62.95/63.54 Eq
% 62.95/63.54 (∀ (B : Iota),
% 62.95/63.54 And (Not (And (Not (disjoint a B)) (∀ (C : Iota), Not (in C (set_intersection2 a B)))))
% 62.95/63.54 (Not (And (Exists fun C => in C (set_intersection2 a B)) (disjoint a B))))
% 62.95/63.54 True
% 62.95/63.54 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota),
% 62.95/63.54 Eq
% 62.95/63.54 (And (Not (And (Not (disjoint a a_1)) (∀ (C : Iota), Not (in C (set_intersection2 a a_1)))))
% 62.95/63.54 (Not (And (Exists fun C => in C (set_intersection2 a a_1)) (disjoint a a_1))))
% 62.95/63.54 True
% 62.95/63.54 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (Not (And (Exists fun C => in C (set_intersection2 a a_1)) (disjoint a a_1))) True
% 62.95/63.54 Clause #90 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (Not (And (Not (disjoint a a_1)) (∀ (C : Iota), Not (in C (set_intersection2 a a_1))))) True
% 62.95/63.54 Clause #91 (by clausification #[89]): ∀ (a a_1 : Iota), Eq (And (Exists fun C => in C (set_intersection2 a a_1)) (disjoint a a_1)) False
% 62.95/63.54 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Or (Eq (Exists fun C => in C (set_intersection2 a a_1)) False) (Eq (disjoint a a_1) False)
% 62.95/63.54 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), Or (Eq (disjoint a a_1) False) (Eq (in a_2 (set_intersection2 a a_1)) False)
% 62.95/63.54 Clause #94 (by superposition #[93, 46]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 62.95/63.54 Or (Eq (in a (set_intersection2 (skS.0 4 a_1 a_2 a_3) (skS.0 5 a_1 a_2 a_3 a_4))) False)
% 62.95/63.54 (Or (Eq (disjoint (skS.0 2 a_1) (skS.0 3 a_1 a_2)) True) (Eq False True))
% 62.95/63.54 Clause #130 (by clausification #[90]): ∀ (a a_1 : Iota), Eq (And (Not (disjoint a a_1)) (∀ (C : Iota), Not (in C (set_intersection2 a a_1)))) False
% 62.95/63.54 Clause #131 (by clausification #[130]): ∀ (a a_1 : Iota), Or (Eq (Not (disjoint a a_1)) False) (Eq (∀ (C : Iota), Not (in C (set_intersection2 a a_1))) False)
% 62.95/63.54 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Not (in C (set_intersection2 a a_1))) False) (Eq (disjoint a a_1) True)
% 62.95/63.54 Clause #133 (by clausification #[132]): ∀ (a a_1 a_2 : Iota),
% 62.95/63.54 Or (Eq (disjoint a a_1) True) (Eq (Not (Not (in (skS.0 8 a a_1 a_2) (set_intersection2 a a_1)))) True)
% 62.95/63.56 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Not (in (skS.0 8 a a_1 a_2) (set_intersection2 a a_1))) False)
% 62.95/63.56 Clause #135 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), Or (Eq (disjoint a a_1) True) (Eq (in (skS.0 8 a a_1 a_2) (set_intersection2 a a_1)) True)
% 62.95/63.56 Clause #136 (by superposition #[135, 72]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 62.95/63.56 Or (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True)
% 62.95/63.56 (Or (Eq True False)
% 62.95/63.56 (Eq
% 62.95/63.56 (in (skS.0 7 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5 a_6)
% 62.95/63.56 (set_intersection2 a_1 a_3))
% 62.95/63.56 True))
% 62.95/63.56 Clause #149 (by clausification #[73]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 62.95/63.56 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False)
% 62.95/63.56 (Eq (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3)) True)
% 62.95/63.56 Clause #151 (by superposition #[149, 135]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 62.95/63.56 Or
% 62.95/63.56 (Eq
% 62.95/63.56 (in (skS.0 6 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5)
% 62.95/63.56 (set_intersection2 a a_2))
% 62.95/63.56 True)
% 62.95/63.56 (Or (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True) (Eq False True))
% 62.95/63.56 Clause #285 (by clausification #[94]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 62.95/63.56 Or (Eq (in a (set_intersection2 (skS.0 4 a_1 a_2 a_3) (skS.0 5 a_1 a_2 a_3 a_4))) False)
% 62.95/63.56 (Eq (disjoint (skS.0 2 a_1) (skS.0 3 a_1 a_2)) True)
% 62.95/63.56 Clause #740 (by clausification #[136]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 62.95/63.56 Or (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True)
% 62.95/63.56 (Eq
% 62.95/63.56 (in (skS.0 7 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5 a_6)
% 62.95/63.56 (set_intersection2 a_1 a_3))
% 62.95/63.56 True)
% 62.95/63.56 Clause #744 (by superposition #[740, 285]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 62.95/63.56 Or
% 62.95/63.56 (Eq (disjoint (cartesian_product2 a (skS.0 4 a_1 a_2 a_3)) (cartesian_product2 a_4 (skS.0 5 a_1 a_2 a_3 a_5))) True)
% 62.95/63.56 (Or (Eq True False) (Eq (disjoint (skS.0 2 a_1) (skS.0 3 a_1 a_2)) True))
% 62.95/63.56 Clause #926 (by clausification #[151]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 62.95/63.56 Or
% 62.95/63.56 (Eq
% 62.95/63.56 (in (skS.0 6 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5)
% 62.95/63.56 (set_intersection2 a a_2))
% 62.95/63.56 True)
% 62.95/63.56 (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True)
% 62.95/63.56 Clause #935 (by superposition #[926, 34]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 62.95/63.56 Or
% 62.95/63.56 (Eq
% 62.95/63.56 (in (skS.0 6 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5)
% 62.95/63.56 (set_intersection2 a_2 a))
% 62.95/63.56 True)
% 62.95/63.56 (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True)
% 62.95/63.56 Clause #5203 (by clausification #[744]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 62.95/63.56 Or
% 62.95/63.56 (Eq (disjoint (cartesian_product2 a (skS.0 4 a_1 a_2 a_3)) (cartesian_product2 a_4 (skS.0 5 a_1 a_2 a_3 a_5))) True)
% 62.95/63.56 (Eq (disjoint (skS.0 2 a_1) (skS.0 3 a_1 a_2)) True)
% 62.95/63.56 Clause #5204 (by superposition #[5203, 45]): ∀ (a a_1 : Iota), Or (Eq (disjoint (skS.0 2 a) (skS.0 3 a a_1)) True) (Eq True False)
% 62.95/63.56 Clause #5207 (by clausification #[5204]): ∀ (a a_1 : Iota), Eq (disjoint (skS.0 2 a) (skS.0 3 a a_1)) True
% 62.95/63.56 Clause #5213 (by superposition #[5207, 93]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in a (set_intersection2 (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False)
% 62.95/63.56 Clause #5217 (by clausification #[5213]): ∀ (a a_1 a_2 : Iota), Eq (in a (set_intersection2 (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False
% 62.95/63.56 Clause #5224 (by superposition #[5217, 935]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.95/63.56 Or (Eq False True) (Eq (disjoint (cartesian_product2 (skS.0 3 a a_1) a_2) (cartesian_product2 (skS.0 2 a) a_3)) True)
% 62.95/63.56 Clause #5382 (by clausification #[5224]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.95/63.56 Eq (disjoint (cartesian_product2 (skS.0 3 a a_1) a_2) (cartesian_product2 (skS.0 2 a) a_3)) True
% 62.95/63.56 Clause #5383 (by superposition #[5382, 18]): ∀ (a a_1 a_2 a_3 : Iota),
% 62.95/63.56 Or (Eq True False) (Eq (disjoint (cartesian_product2 (skS.0 2 a) a_1) (cartesian_product2 (skS.0 3 a a_2) a_3)) True)
% 63.02/63.62 Clause #5385 (by clausification #[5383]): ∀ (a a_1 a_2 a_3 : Iota),
% 63.02/63.62 Eq (disjoint (cartesian_product2 (skS.0 2 a) a_1) (cartesian_product2 (skS.0 3 a a_2) a_3)) True
% 63.02/63.62 Clause #5386 (by superposition #[5385, 45]): Eq True False
% 63.02/63.62 Clause #5489 (by clausification #[5386]): False
% 63.02/63.62 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------