TSTP Solution File: SET920+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET920+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n026.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 14:48:03 EDT 2023
% Result : Theorem 17.39s 17.58s
% Output : Proof 17.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET920+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:58:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 17.39/17.58 SZS status Theorem for theBenchmark.p
% 17.39/17.58 SZS output start Proof for theBenchmark.p
% 17.39/17.58 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True
% 17.39/17.58 Clause #3 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (unordered_pair A B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D A) (Eq D B)))) True
% 17.39/17.58 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_intersection2 A B)) (∀ (D : Iota), Iff (in D C) (And (in D A) (in D B)))) True
% 17.39/17.58 Clause #8 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Eq (set_intersection2 (unordered_pair A B) C) (unordered_pair A B) → in A C)) True
% 17.39/17.58 Clause #17 (by clausification #[8]): Eq (∀ (A B C : Iota), Eq (set_intersection2 (unordered_pair A B) C) (unordered_pair A B) → in A C) False
% 17.39/17.58 Clause #18 (by clausification #[17]): ∀ (a : Iota),
% 17.39/17.58 Eq
% 17.39/17.58 (Not
% 17.39/17.58 (∀ (B C : Iota),
% 17.39/17.58 Eq (set_intersection2 (unordered_pair (skS.0 2 a) B) C) (unordered_pair (skS.0 2 a) B) → in (skS.0 2 a) C))
% 17.39/17.58 True
% 17.39/17.58 Clause #19 (by clausification #[18]): ∀ (a : Iota),
% 17.39/17.58 Eq
% 17.39/17.58 (∀ (B C : Iota),
% 17.39/17.58 Eq (set_intersection2 (unordered_pair (skS.0 2 a) B) C) (unordered_pair (skS.0 2 a) B) → in (skS.0 2 a) C)
% 17.39/17.58 False
% 17.39/17.58 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 17.39/17.58 Eq
% 17.39/17.58 (Not
% 17.39/17.58 (∀ (C : Iota),
% 17.39/17.58 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C)
% 17.39/17.58 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) →
% 17.39/17.58 in (skS.0 2 a) C))
% 17.39/17.58 True
% 17.39/17.58 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota),
% 17.39/17.58 Eq
% 17.39/17.58 (∀ (C : Iota),
% 17.39/17.58 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C)
% 17.39/17.58 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) →
% 17.39/17.58 in (skS.0 2 a) C)
% 17.39/17.58 False
% 17.39/17.58 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 17.39/17.58 Eq
% 17.39/17.58 (Not
% 17.39/17.58 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 17.39/17.58 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) →
% 17.39/17.58 in (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 17.39/17.58 True
% 17.39/17.58 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 17.39/17.58 Eq
% 17.39/17.58 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 17.39/17.58 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) →
% 17.39/17.58 in (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 17.39/17.58 False
% 17.39/17.58 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 17.39/17.58 Eq
% 17.39/17.58 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 17.39/17.58 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 17.39/17.58 True
% 17.39/17.58 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False
% 17.39/17.58 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 17.39/17.58 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 17.39/17.58 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))
% 17.39/17.58 Clause #30 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True
% 17.39/17.58 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True
% 17.39/17.58 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a)
% 17.39/17.58 Clause #37 (by clausification #[4]): ∀ (a : Iota),
% 17.39/17.58 Eq (∀ (B C : Iota), Iff (Eq C (set_intersection2 a B)) (∀ (D : Iota), Iff (in D C) (And (in D a) (in D B)))) True
% 17.39/17.58 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 17.39/17.58 Eq (∀ (C : Iota), Iff (Eq C (set_intersection2 a a_1)) (∀ (D : Iota), Iff (in D C) (And (in D a) (in D a_1)))) True
% 17.39/17.58 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 17.39/17.58 Eq (Iff (Eq a (set_intersection2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2)))) True
% 17.39/17.58 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 17.39/17.58 Or (Eq (Eq a (set_intersection2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2))) True)
% 17.39/17.58 Clause #48 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 17.39/17.58 Or (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2))) True) (Ne a (set_intersection2 a_1 a_2))
% 17.39/17.58 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota),
% 17.46/17.64 Or (Ne a (set_intersection2 a_1 a_2)) (Eq (Iff (in a_3 a) (And (in a_3 a_1) (in a_3 a_2))) True)
% 17.46/17.64 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 17.46/17.64 Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) False) (Eq (And (in a_3 a_1) (in a_3 a_2)) True))
% 17.46/17.64 Clause #54 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) False) (Eq (in a_3 a_2) True))
% 17.46/17.64 Clause #56 (by destructive equality resolution #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_intersection2 a_1 a_2)) False) (Eq (in a a_2) True)
% 17.46/17.64 Clause #57 (by superposition #[56, 26]): ∀ (a a_1 a_2 a_3 : Iota),
% 17.46/17.64 Or (Eq (in a (unordered_pair (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False) (Eq (in a (skS.0 4 a_1 a_2 a_3)) True)
% 17.46/17.64 Clause #60 (by clausification #[3]): ∀ (a : Iota),
% 17.46/17.64 Eq (∀ (B C : Iota), Iff (Eq C (unordered_pair a B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D B)))) True
% 17.46/17.64 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota),
% 17.46/17.64 Eq (∀ (C : Iota), Iff (Eq C (unordered_pair a a_1)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D a_1)))) True
% 17.46/17.65 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 17.46/17.65 Eq (Iff (Eq a (unordered_pair a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2)))) True
% 17.46/17.65 Clause #64 (by clausification #[62]): ∀ (a a_1 a_2 : Iota),
% 17.46/17.65 Or (Eq (Eq a (unordered_pair a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True)
% 17.46/17.65 Clause #74 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 17.46/17.65 Or (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) (Ne a (unordered_pair a_1 a_2))
% 17.46/17.65 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Eq (Iff (in a_3 a) (Or (Eq a_3 a_1) (Eq a_3 a_2))) True)
% 17.46/17.65 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota),
% 17.46/17.65 Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (Eq a_3 a_1) (Eq a_3 a_2)) False))
% 17.46/17.65 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Eq a_3 a_2) False))
% 17.46/17.65 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Ne a_3 a_2))
% 17.46/17.65 Clause #81 (by destructive equality resolution #[80]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2)
% 17.46/17.65 Clause #82 (by destructive equality resolution #[81]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True
% 17.46/17.65 Clause #85 (by superposition #[82, 32]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True
% 17.46/17.65 Clause #134 (by superposition #[57, 85]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True)
% 17.46/17.65 Clause #4834 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True
% 17.46/17.65 Clause #4835 (by superposition #[4834, 25]): Eq True False
% 17.46/17.65 Clause #4854 (by clausification #[4835]): False
% 17.46/17.65 SZS output end Proof for theBenchmark.p
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