TSTP Solution File: SET979+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n008.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 3.99s 4.14s
% Output : Proof 3.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n008.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 09:17:17 EDT 2023
% 0.14/0.34 % CPUTime :
% 3.99/4.14 SZS status Theorem for theBenchmark.p
% 3.99/4.14 SZS output start Proof for theBenchmark.p
% 3.99/4.14 Clause #7 (by assumption #[]): Eq
% 3.99/4.14 (∀ (A B C : Iota),
% 3.99/4.14 And (Eq (cartesian_product2 (set_union2 A B) C) (set_union2 (cartesian_product2 A C) (cartesian_product2 B C)))
% 3.99/4.14 (Eq (cartesian_product2 C (set_union2 A B)) (set_union2 (cartesian_product2 C A) (cartesian_product2 C B))))
% 3.99/4.14 True
% 3.99/4.14 Clause #8 (by assumption #[]): Eq
% 3.99/4.14 (Not
% 3.99/4.14 (∀ (A B C : Iota),
% 3.99/4.14 And
% 3.99/4.14 (Eq (cartesian_product2 (unordered_pair A B) C)
% 3.99/4.14 (set_union2 (cartesian_product2 (singleton A) C) (cartesian_product2 (singleton B) C)))
% 3.99/4.14 (Eq (cartesian_product2 C (unordered_pair A B))
% 3.99/4.14 (set_union2 (cartesian_product2 C (singleton A)) (cartesian_product2 C (singleton B))))))
% 3.99/4.14 True
% 3.99/4.14 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (set_union2 (singleton A) (singleton B))) True
% 3.99/4.14 Clause #34 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (set_union2 (singleton a) (singleton B))) True
% 3.99/4.14 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (set_union2 (singleton a) (singleton a_1))) True
% 3.99/4.14 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (set_union2 (singleton a) (singleton a_1))
% 3.99/4.14 Clause #39 (by clausification #[7]): ∀ (a : Iota),
% 3.99/4.14 Eq
% 3.99/4.14 (∀ (B C : Iota),
% 3.99/4.14 And (Eq (cartesian_product2 (set_union2 a B) C) (set_union2 (cartesian_product2 a C) (cartesian_product2 B C)))
% 3.99/4.14 (Eq (cartesian_product2 C (set_union2 a B)) (set_union2 (cartesian_product2 C a) (cartesian_product2 C B))))
% 3.99/4.14 True
% 3.99/4.14 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 3.99/4.14 Eq
% 3.99/4.14 (∀ (C : Iota),
% 3.99/4.14 And
% 3.99/4.14 (Eq (cartesian_product2 (set_union2 a a_1) C) (set_union2 (cartesian_product2 a C) (cartesian_product2 a_1 C)))
% 3.99/4.14 (Eq (cartesian_product2 C (set_union2 a a_1)) (set_union2 (cartesian_product2 C a) (cartesian_product2 C a_1))))
% 3.99/4.14 True
% 3.99/4.14 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.14 Eq
% 3.99/4.14 (And
% 3.99/4.14 (Eq (cartesian_product2 (set_union2 a a_1) a_2)
% 3.99/4.14 (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)))
% 3.99/4.14 (Eq (cartesian_product2 a_2 (set_union2 a a_1))
% 3.99/4.14 (set_union2 (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1))))
% 3.99/4.14 True
% 3.99/4.14 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.14 Eq (Eq (cartesian_product2 a (set_union2 a_1 a_2)) (set_union2 (cartesian_product2 a a_1) (cartesian_product2 a a_2)))
% 3.99/4.14 True
% 3.99/4.14 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.14 Eq
% 3.99/4.14 (Eq (cartesian_product2 (set_union2 a a_1) a_2)
% 3.99/4.14 (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)))
% 3.99/4.14 True
% 3.99/4.14 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.14 Eq (cartesian_product2 a (set_union2 a_1 a_2)) (set_union2 (cartesian_product2 a a_1) (cartesian_product2 a a_2))
% 3.99/4.14 Clause #56 (by clausification #[8]): Eq
% 3.99/4.14 (∀ (A B C : Iota),
% 3.99/4.14 And
% 3.99/4.14 (Eq (cartesian_product2 (unordered_pair A B) C)
% 3.99/4.14 (set_union2 (cartesian_product2 (singleton A) C) (cartesian_product2 (singleton B) C)))
% 3.99/4.14 (Eq (cartesian_product2 C (unordered_pair A B))
% 3.99/4.14 (set_union2 (cartesian_product2 C (singleton A)) (cartesian_product2 C (singleton B)))))
% 3.99/4.14 False
% 3.99/4.14 Clause #57 (by clausification #[56]): ∀ (a : Iota),
% 3.99/4.14 Eq
% 3.99/4.14 (Not
% 3.99/4.14 (∀ (B C : Iota),
% 3.99/4.14 And
% 3.99/4.14 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) B) C)
% 3.99/4.14 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) C) (cartesian_product2 (singleton B) C)))
% 3.99/4.14 (Eq (cartesian_product2 C (unordered_pair (skS.0 2 a) B))
% 3.99/4.14 (set_union2 (cartesian_product2 C (singleton (skS.0 2 a))) (cartesian_product2 C (singleton B))))))
% 3.99/4.14 True
% 3.99/4.14 Clause #58 (by clausification #[57]): ∀ (a : Iota),
% 3.99/4.14 Eq
% 3.99/4.14 (∀ (B C : Iota),
% 3.99/4.14 And
% 3.99/4.14 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) B) C)
% 3.99/4.14 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) C) (cartesian_product2 (singleton B) C)))
% 3.99/4.14 (Eq (cartesian_product2 C (unordered_pair (skS.0 2 a) B))
% 3.99/4.14 (set_union2 (cartesian_product2 C (singleton (skS.0 2 a))) (cartesian_product2 C (singleton B)))))
% 3.99/4.16 False
% 3.99/4.16 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota),
% 3.99/4.16 Eq
% 3.99/4.16 (Not
% 3.99/4.16 (∀ (C : Iota),
% 3.99/4.16 And
% 3.99/4.16 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C)
% 3.99/4.16 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) C)
% 3.99/4.16 (cartesian_product2 (singleton (skS.0 3 a a_1)) C)))
% 3.99/4.16 (Eq (cartesian_product2 C (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.99/4.16 (set_union2 (cartesian_product2 C (singleton (skS.0 2 a)))
% 3.99/4.16 (cartesian_product2 C (singleton (skS.0 3 a a_1)))))))
% 3.99/4.16 True
% 3.99/4.16 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota),
% 3.99/4.16 Eq
% 3.99/4.16 (∀ (C : Iota),
% 3.99/4.16 And
% 3.99/4.16 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C)
% 3.99/4.16 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) C)
% 3.99/4.16 (cartesian_product2 (singleton (skS.0 3 a a_1)) C)))
% 3.99/4.16 (Eq (cartesian_product2 C (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.99/4.16 (set_union2 (cartesian_product2 C (singleton (skS.0 2 a)))
% 3.99/4.16 (cartesian_product2 C (singleton (skS.0 3 a a_1))))))
% 3.99/4.16 False
% 3.99/4.16 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.16 Eq
% 3.99/4.16 (Not
% 3.99/4.16 (And
% 3.99/4.16 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 3.99/4.16 (Eq (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.99/4.16 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 3.99/4.16 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1)))))))
% 3.99/4.16 True
% 3.99/4.16 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.16 Eq
% 3.99/4.16 (And
% 3.99/4.16 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 3.99/4.16 (Eq (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.99/4.16 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 3.99/4.16 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1))))))
% 3.99/4.16 False
% 3.99/4.16 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.16 Or
% 3.99/4.16 (Eq
% 3.99/4.16 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 3.99/4.16 False)
% 3.99/4.16 (Eq
% 3.99/4.16 (Eq (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.99/4.16 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 3.99/4.16 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1)))))
% 3.99/4.16 False)
% 3.99/4.16 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.16 Or
% 3.99/4.16 (Eq
% 3.99/4.16 (Eq (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.99/4.16 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 3.99/4.16 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1)))))
% 3.99/4.16 False)
% 3.99/4.16 (Ne (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 3.99/4.16 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.16 Or
% 3.99/4.16 (Ne (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.16 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 3.99/4.16 (Ne (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.99/4.16 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 3.99/4.17 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1)))))
% 3.99/4.17 Clause #66 (by forward demodulation #[65, 36]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.17 Or
% 3.99/4.17 (Ne (cartesian_product2 (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (skS.0 4 a a_1 a_2))
% 3.99/4.17 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.17 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 3.99/4.17 (Ne (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.99/4.17 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 3.99/4.17 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1)))))
% 3.99/4.17 Clause #67 (by forward demodulation #[66, 36]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.17 Or
% 3.99/4.17 (Ne (cartesian_product2 (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (skS.0 4 a a_1 a_2))
% 3.99/4.17 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.17 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 3.99/4.17 (Ne (cartesian_product2 (skS.0 4 a a_1 a_2) (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))))
% 3.99/4.17 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 3.99/4.17 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1)))))
% 3.99/4.17 Clause #68 (by forward demodulation #[67, 44]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.17 Or
% 3.99/4.17 (Ne (cartesian_product2 (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (skS.0 4 a a_1 a_2))
% 3.99/4.17 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.17 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 3.99/4.17 (Ne (cartesian_product2 (skS.0 4 a a_1 a_2) (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))))
% 3.99/4.17 (cartesian_product2 (skS.0 4 a a_1 a_2) (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)))))
% 3.99/4.17 Clause #69 (by eliminate resolved literals #[68]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.17 Ne (cartesian_product2 (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (skS.0 4 a a_1 a_2))
% 3.99/4.17 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2))
% 3.99/4.17 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))
% 3.99/4.17 Clause #70 (by clausification #[43]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.17 Eq (cartesian_product2 (set_union2 a a_1) a_2) (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2))
% 3.99/4.17 Clause #72 (by backward contextual literal cutting #[70, 69]): False
% 3.99/4.17 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------