TSTP Solution File: SET907+1 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SET907+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 14:47:59 EDT 2023
% Result : Theorem 4.21s 4.42s
% Output : Proof 4.26s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:38:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.21/4.42 SZS status Theorem for theBenchmark.p
% 4.21/4.42 SZS output start Proof for theBenchmark.p
% 4.21/4.42 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True
% 4.21/4.42 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True
% 4.21/4.42 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), subset A B → Eq (set_union2 A B) B) True
% 4.21/4.42 Clause #10 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (subset (unordered_pair A B) C) (And (in A C) (in B C))) True
% 4.21/4.42 Clause #11 (by assumption #[]): Eq (Not (∀ (A B C : Iota), And (in A B) (in C B) → Eq (set_union2 (unordered_pair A C) B) B)) True
% 4.21/4.42 Clause #25 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True
% 4.21/4.42 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True
% 4.21/4.42 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a)
% 4.21/4.42 Clause #39 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a B → Eq (set_union2 a B) B) True
% 4.21/4.42 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (subset a a_1 → Eq (set_union2 a a_1) a_1) True
% 4.21/4.42 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (Eq (set_union2 a a_1) a_1) True)
% 4.21/4.42 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_union2 a a_1) a_1)
% 4.21/4.42 Clause #44 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True
% 4.21/4.42 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True
% 4.21/4.42 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a)
% 4.21/4.42 Clause #47 (by clausification #[11]): Eq (∀ (A B C : Iota), And (in A B) (in C B) → Eq (set_union2 (unordered_pair A C) B) B) False
% 4.21/4.42 Clause #48 (by clausification #[47]): ∀ (a : Iota),
% 4.21/4.42 Eq (Not (∀ (B C : Iota), And (in (skS.0 2 a) B) (in C B) → Eq (set_union2 (unordered_pair (skS.0 2 a) C) B) B)) True
% 4.21/4.42 Clause #49 (by clausification #[48]): ∀ (a : Iota),
% 4.21/4.42 Eq (∀ (B C : Iota), And (in (skS.0 2 a) B) (in C B) → Eq (set_union2 (unordered_pair (skS.0 2 a) C) B) B) False
% 4.21/4.42 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 4.21/4.42 Eq
% 4.21/4.42 (Not
% 4.21/4.42 (∀ (C : Iota),
% 4.21/4.42 And (in (skS.0 2 a) (skS.0 3 a a_1)) (in C (skS.0 3 a a_1)) →
% 4.21/4.42 Eq (set_union2 (unordered_pair (skS.0 2 a) C) (skS.0 3 a a_1)) (skS.0 3 a a_1)))
% 4.21/4.42 True
% 4.21/4.42 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota),
% 4.21/4.42 Eq
% 4.21/4.42 (∀ (C : Iota),
% 4.21/4.42 And (in (skS.0 2 a) (skS.0 3 a a_1)) (in C (skS.0 3 a a_1)) →
% 4.21/4.42 Eq (set_union2 (unordered_pair (skS.0 2 a) C) (skS.0 3 a a_1)) (skS.0 3 a a_1))
% 4.21/4.42 False
% 4.21/4.42 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 4.21/4.42 Eq
% 4.21/4.42 (Not
% 4.21/4.42 (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)) →
% 4.21/4.42 Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1)))
% 4.21/4.42 True
% 4.21/4.42 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota),
% 4.21/4.42 Eq
% 4.21/4.42 (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)) →
% 4.21/4.42 Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1))
% 4.21/4.42 False
% 4.21/4.42 Clause #54 (by clausification #[53]): ∀ (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
% 4.21/4.42 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 4.21/4.42 Eq (Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1)) False
% 4.21/4.42 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) True
% 4.21/4.42 Clause #57 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True
% 4.21/4.42 Clause #60 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (subset (unordered_pair a B) C) (And (in a C) (in B C))) True
% 4.21/4.42 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Iff (subset (unordered_pair a a_1) C) (And (in a C) (in a_1 C))) True
% 4.26/4.43 Clause #62 (by clausification #[61]): ∀ (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
% 4.26/4.43 Clause #63 (by clausification #[62]): ∀ (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)
% 4.26/4.43 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 4.26/4.43 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))
% 4.26/4.43 Clause #66 (by superposition #[65, 56]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.26/4.43 Or (Eq (subset (unordered_pair (skS.0 4 a a_1 a_2) a_3) (skS.0 3 a a_1)) True)
% 4.26/4.43 (Or (Eq (in a_3 (skS.0 3 a a_1)) False) (Eq False True))
% 4.26/4.43 Clause #75 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Ne (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1)
% 4.26/4.43 Clause #76 (by forward demodulation #[75, 46]): ∀ (a a_1 a_2 : Iota), Ne (set_union2 (skS.0 3 a a_1) (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) (skS.0 3 a a_1)
% 4.26/4.43 Clause #103 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.26/4.43 Or (Eq (subset (unordered_pair (skS.0 4 a a_1 a_2) a_3) (skS.0 3 a a_1)) True) (Eq (in a_3 (skS.0 3 a a_1)) False)
% 4.26/4.43 Clause #105 (by superposition #[103, 57]): ∀ (a a_1 a_2 : Iota),
% 4.26/4.43 Or (Eq (subset (unordered_pair (skS.0 4 a a_1 a_2) (skS.0 2 a)) (skS.0 3 a a_1)) True) (Eq False True)
% 4.26/4.43 Clause #128 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 4 a a_1 a_2) (skS.0 2 a)) (skS.0 3 a a_1)) True
% 4.26/4.43 Clause #129 (by forward demodulation #[128, 27]): ∀ (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
% 4.26/4.43 Clause #130 (by superposition #[129, 42]): ∀ (a a_1 a_2 : Iota),
% 4.26/4.43 Or (Eq True False) (Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1))
% 4.26/4.43 Clause #141 (by clausification #[130]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1)
% 4.26/4.43 Clause #144 (by superposition #[141, 46]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 (skS.0 3 a a_1) (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) (skS.0 3 a a_1)
% 4.26/4.43 Clause #145 (by forward contextual literal cutting #[144, 76]): False
% 4.26/4.43 SZS output end Proof for theBenchmark.p
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