TSTP Solution File: SET912+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET912+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 14:48:01 EDT 2023
% Result : Theorem 4.14s 4.33s
% Output : Proof 4.19s
% 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 : SET912+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n023.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 11:04:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.14/4.33 SZS status Theorem for theBenchmark.p
% 4.14/4.33 SZS output start Proof for theBenchmark.p
% 4.14/4.33 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A B) (set_intersection2 B A)) True
% 4.14/4.33 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), subset A B → Eq (set_intersection2 A B) A) True
% 4.14/4.33 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (subset (unordered_pair A B) C) (And (in A C) (in B C))) True
% 4.14/4.33 Clause #9 (by assumption #[]): Eq (Not (∀ (A B C : Iota), And (in A B) (in C B) → Eq (set_intersection2 (unordered_pair A C) B) (unordered_pair A C)))
% 4.14/4.33 True
% 4.14/4.33 Clause #26 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a B → Eq (set_intersection2 a B) a) True
% 4.14/4.33 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (subset a a_1 → Eq (set_intersection2 a a_1) a) True
% 4.14/4.33 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (Eq (set_intersection2 a a_1) a) True)
% 4.14/4.33 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_intersection2 a a_1) a)
% 4.14/4.33 Clause #31 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a B) (set_intersection2 B a)) True
% 4.14/4.33 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)) True
% 4.14/4.33 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)
% 4.14/4.33 Clause #34 (by clausification #[9]): Eq (∀ (A B C : Iota), And (in A B) (in C B) → Eq (set_intersection2 (unordered_pair A C) B) (unordered_pair A C)) False
% 4.14/4.33 Clause #35 (by clausification #[34]): ∀ (a : Iota),
% 4.14/4.33 Eq
% 4.14/4.33 (Not
% 4.14/4.33 (∀ (B C : Iota),
% 4.14/4.33 And (in (skS.0 2 a) B) (in C B) →
% 4.14/4.33 Eq (set_intersection2 (unordered_pair (skS.0 2 a) C) B) (unordered_pair (skS.0 2 a) C)))
% 4.14/4.33 True
% 4.14/4.33 Clause #36 (by clausification #[35]): ∀ (a : Iota),
% 4.14/4.33 Eq
% 4.14/4.33 (∀ (B C : Iota),
% 4.14/4.33 And (in (skS.0 2 a) B) (in C B) →
% 4.14/4.33 Eq (set_intersection2 (unordered_pair (skS.0 2 a) C) B) (unordered_pair (skS.0 2 a) C))
% 4.14/4.33 False
% 4.14/4.33 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 4.14/4.33 Eq
% 4.14/4.33 (Not
% 4.14/4.33 (∀ (C : Iota),
% 4.14/4.33 And (in (skS.0 2 a) (skS.0 3 a a_1)) (in C (skS.0 3 a a_1)) →
% 4.14/4.33 Eq (set_intersection2 (unordered_pair (skS.0 2 a) C) (skS.0 3 a a_1)) (unordered_pair (skS.0 2 a) C)))
% 4.14/4.33 True
% 4.14/4.33 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 4.14/4.33 Eq
% 4.14/4.33 (∀ (C : Iota),
% 4.14/4.33 And (in (skS.0 2 a) (skS.0 3 a a_1)) (in C (skS.0 3 a a_1)) →
% 4.14/4.33 Eq (set_intersection2 (unordered_pair (skS.0 2 a) C) (skS.0 3 a a_1)) (unordered_pair (skS.0 2 a) C))
% 4.14/4.33 False
% 4.14/4.33 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 4.14/4.33 Eq
% 4.14/4.33 (Not
% 4.14/4.33 (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) →
% 4.14/4.33 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1))
% 4.14/4.33 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))))
% 4.14/4.33 True
% 4.14/4.33 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 4.14/4.33 Eq
% 4.14/4.33 (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) →
% 4.14/4.33 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1))
% 4.14/4.33 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 4.14/4.33 False
% 4.14/4.33 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1))) True
% 4.14/4.33 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 4.14/4.33 Eq
% 4.14/4.33 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1))
% 4.14/4.33 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 4.14/4.33 False
% 4.14/4.33 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) True
% 4.14/4.33 Clause #44 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True
% 4.14/4.33 Clause #47 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (subset (unordered_pair a B) C) (And (in a C) (in B C))) True
% 4.14/4.33 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Iff (subset (unordered_pair a a_1) C) (And (in a C) (in a_1 C))) True
% 4.19/4.34 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Eq (Iff (subset (unordered_pair a a_1) a_2) (And (in a a_2) (in a_1 a_2))) True
% 4.19/4.34 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) True) (Eq (And (in a a_2) (in a_1 a_2)) False)
% 4.19/4.34 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Or (Eq (subset (unordered_pair a a_1) a_2) True) (Or (Eq (in a a_2) False) (Eq (in a_1 a_2) False))
% 4.19/4.34 Clause #54 (by superposition #[52, 44]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Or (Eq (subset (unordered_pair (skS.0 2 a) a_1) (skS.0 3 a a_2)) True)
% 4.19/4.34 (Or (Eq (in a_1 (skS.0 3 a a_2)) False) (Eq False True))
% 4.19/4.34 Clause #66 (by clausification #[42]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Ne (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1))
% 4.19/4.34 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 4.19/4.34 Clause #67 (by forward demodulation #[66, 33]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Ne (set_intersection2 (skS.0 3 a a_1) (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 4.19/4.34 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 4.19/4.34 Clause #97 (by clausification #[54]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Or (Eq (subset (unordered_pair (skS.0 2 a) a_1) (skS.0 3 a a_2)) True) (Eq (in a_1 (skS.0 3 a a_2)) False)
% 4.19/4.34 Clause #98 (by superposition #[97, 43]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Or (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) True) (Eq False True)
% 4.19/4.34 Clause #108 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) True
% 4.19/4.34 Clause #110 (by superposition #[108, 29]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Or (Eq True False)
% 4.19/4.34 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1))
% 4.19/4.34 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 4.19/4.34 Clause #118 (by clausification #[110]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1))
% 4.19/4.34 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 4.19/4.34 Clause #119 (by superposition #[118, 33]): ∀ (a a_1 a_2 : Iota),
% 4.19/4.34 Eq (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 4.19/4.34 (set_intersection2 (skS.0 3 a a_1) (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 4.19/4.34 Clause #121 (by forward contextual literal cutting #[119, 67]): False
% 4.19/4.34 SZS output end Proof for theBenchmark.p
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