TSTP Solution File: SET902+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 14:47:58 EDT 2023
% Result : Theorem 4.00s 4.18s
% Output : Proof 4.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n002.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 10:30:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.00/4.18 SZS status Theorem for theBenchmark.p
% 4.00/4.18 SZS output start Proof for theBenchmark.p
% 4.00/4.18 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True
% 4.00/4.18 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), Iota → Eq (set_union2 A A) A) True
% 4.00/4.18 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Ne (singleton A) empty_set) True
% 4.00/4.18 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) True
% 4.00/4.18 Clause #10 (by assumption #[]): Eq
% 4.00/4.18 (Not
% 4.00/4.18 (∀ (A B C : Iota),
% 4.00/4.18 Not
% 4.00/4.18 (And
% 4.00/4.18 (And (And (Eq (singleton A) (set_union2 B C)) (Not (And (Eq B (singleton A)) (Eq C (singleton A)))))
% 4.00/4.18 (Not (And (Eq B empty_set) (Eq C (singleton A)))))
% 4.00/4.18 (Not (And (Eq B (singleton A)) (Eq C empty_set))))))
% 4.00/4.18 True
% 4.00/4.18 Clause #11 (by assumption #[]): Eq (∀ (A B : Iota), subset A (set_union2 A B)) True
% 4.00/4.18 Clause #18 (by clausification #[5]): ∀ (a : Iota), Eq (Ne (singleton a) empty_set) True
% 4.00/4.18 Clause #19 (by clausification #[18]): ∀ (a : Iota), Ne (singleton a) empty_set
% 4.00/4.18 Clause #20 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True
% 4.00/4.18 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True
% 4.00/4.18 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a)
% 4.00/4.18 Clause #23 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a (set_union2 a B)) True
% 4.00/4.18 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (subset a (set_union2 a a_1)) True
% 4.00/4.18 Clause #25 (by superposition #[24, 22]): ∀ (a a_1 : Iota), Eq (subset a (set_union2 a_1 a)) True
% 4.00/4.18 Clause #26 (by clausification #[4]): ∀ (a : Iota), Eq (Iota → Eq (set_union2 a a) a) True
% 4.00/4.18 Clause #27 (by clausification #[26]): ∀ (a : Iota), Iota → Eq (Eq (set_union2 a a) a) True
% 4.00/4.18 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (set_union2 a a) a
% 4.00/4.18 Clause #41 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a (singleton B)) (Or (Eq a empty_set) (Eq a (singleton B)))) True
% 4.00/4.18 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (Iff (subset a (singleton a_1)) (Or (Eq a empty_set) (Eq a (singleton a_1)))) True
% 4.00/4.18 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) True)
% 4.00/4.18 Clause #51 (by clausification #[44]): ∀ (a a_1 : Iota),
% 4.00/4.18 Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq a (singleton a_1)) True))
% 4.00/4.18 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a (singleton a_1)) True) (Eq a empty_set))
% 4.00/4.18 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq a empty_set) (Eq a (singleton a_1)))
% 4.00/4.18 Clause #56 (by clausification #[10]): Eq
% 4.00/4.18 (∀ (A B C : Iota),
% 4.00/4.18 Not
% 4.00/4.18 (And
% 4.00/4.18 (And (And (Eq (singleton A) (set_union2 B C)) (Not (And (Eq B (singleton A)) (Eq C (singleton A)))))
% 4.00/4.18 (Not (And (Eq B empty_set) (Eq C (singleton A)))))
% 4.00/4.18 (Not (And (Eq B (singleton A)) (Eq C empty_set)))))
% 4.00/4.18 False
% 4.00/4.18 Clause #57 (by clausification #[56]): ∀ (a : Iota),
% 4.00/4.18 Eq
% 4.00/4.18 (Not
% 4.00/4.18 (∀ (B C : Iota),
% 4.00/4.18 Not
% 4.00/4.18 (And
% 4.00/4.18 (And
% 4.00/4.18 (And (Eq (singleton (skS.0 2 a)) (set_union2 B C))
% 4.00/4.18 (Not (And (Eq B (singleton (skS.0 2 a))) (Eq C (singleton (skS.0 2 a))))))
% 4.00/4.18 (Not (And (Eq B empty_set) (Eq C (singleton (skS.0 2 a))))))
% 4.00/4.18 (Not (And (Eq B (singleton (skS.0 2 a))) (Eq C empty_set))))))
% 4.00/4.18 True
% 4.00/4.18 Clause #58 (by clausification #[57]): ∀ (a : Iota),
% 4.00/4.18 Eq
% 4.00/4.18 (∀ (B C : Iota),
% 4.00/4.18 Not
% 4.00/4.18 (And
% 4.00/4.18 (And
% 4.00/4.18 (And (Eq (singleton (skS.0 2 a)) (set_union2 B C))
% 4.00/4.18 (Not (And (Eq B (singleton (skS.0 2 a))) (Eq C (singleton (skS.0 2 a))))))
% 4.00/4.18 (Not (And (Eq B empty_set) (Eq C (singleton (skS.0 2 a))))))
% 4.00/4.18 (Not (And (Eq B (singleton (skS.0 2 a))) (Eq C empty_set)))))
% 4.00/4.18 False
% 4.00/4.18 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota),
% 4.00/4.21 Eq
% 4.00/4.21 (Not
% 4.00/4.21 (∀ (C : Iota),
% 4.00/4.21 Not
% 4.00/4.21 (And
% 4.00/4.21 (And
% 4.00/4.21 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) C))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq C (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) empty_set) (Eq C (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq C empty_set))))))
% 4.00/4.21 True
% 4.00/4.21 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota),
% 4.00/4.21 Eq
% 4.00/4.21 (∀ (C : Iota),
% 4.00/4.21 Not
% 4.00/4.21 (And
% 4.00/4.21 (And
% 4.00/4.21 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) C))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq C (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) empty_set) (Eq C (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq C empty_set)))))
% 4.00/4.21 False
% 4.00/4.21 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 4.00/4.21 Eq
% 4.00/4.21 (Not
% 4.00/4.21 (Not
% 4.00/4.21 (And
% 4.00/4.21 (And
% 4.00/4.21 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) empty_set))))))
% 4.00/4.21 True
% 4.00/4.21 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 4.00/4.21 Eq
% 4.00/4.21 (Not
% 4.00/4.21 (And
% 4.00/4.21 (And
% 4.00/4.21 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) empty_set)))))
% 4.00/4.21 False
% 4.00/4.21 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota),
% 4.00/4.21 Eq
% 4.00/4.21 (And
% 4.00/4.21 (And
% 4.00/4.21 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) empty_set))))
% 4.00/4.21 True
% 4.00/4.21 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 4.00/4.21 Eq (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) empty_set))) True
% 4.00/4.21 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 4.00/4.21 Eq
% 4.00/4.21 (And
% 4.00/4.21 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.00/4.21 True
% 4.00/4.21 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), Eq (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) empty_set)) False
% 4.00/4.21 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota),
% 4.00/4.21 Or (Eq (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) False) (Eq (Eq (skS.0 4 a a_1 a_2) empty_set) False)
% 4.00/4.21 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq (skS.0 4 a a_1 a_2) empty_set) False) (Ne (skS.0 3 a a_1) (singleton (skS.0 2 a)))
% 4.00/4.21 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Or (Ne (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Ne (skS.0 4 a a_1 a_2) empty_set)
% 4.00/4.21 Clause #72 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 4.00/4.21 Eq (Not (And (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))) True
% 4.00/4.21 Clause #73 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 4.00/4.21 Eq
% 4.00/4.21 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.00/4.21 (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))))
% 4.06/4.23 True
% 4.06/4.23 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), Eq (And (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))) False
% 4.06/4.23 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.23 Or (Eq (Eq (skS.0 3 a a_1) empty_set) False) (Eq (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) False)
% 4.06/4.23 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) False) (Ne (skS.0 3 a a_1) empty_set)
% 4.06/4.23 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Or (Ne (skS.0 3 a a_1) empty_set) (Ne (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 4.06/4.23 Clause #78 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.23 Eq (Not (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))) True
% 4.06/4.23 Clause #79 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Eq (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True
% 4.06/4.23 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.23 Eq (And (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))) False
% 4.06/4.23 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.23 Or (Eq (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))) False) (Eq (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) False)
% 4.06/4.23 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.23 Or (Eq (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) False) (Ne (skS.0 3 a a_1) (singleton (skS.0 2 a)))
% 4.06/4.23 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Or (Ne (skS.0 3 a a_1) (singleton (skS.0 2 a))) (Ne (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 4.06/4.23 Clause #84 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))
% 4.06/4.23 Clause #85 (by superposition #[84, 24]): ∀ (a a_1 : Iota), Eq (subset (skS.0 3 a a_1) (singleton (skS.0 2 a))) True
% 4.06/4.23 Clause #86 (by superposition #[84, 25]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) True
% 4.06/4.23 Clause #89 (by superposition #[85, 53]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))))
% 4.06/4.23 Clause #90 (by superposition #[86, 53]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.23 Or (Eq True False) (Or (Eq (skS.0 4 a a_1 a_2) empty_set) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))
% 4.06/4.23 Clause #91 (by clausification #[89]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 3 a a_1) (singleton (skS.0 2 a)))
% 4.06/4.23 Clause #92 (by superposition #[91, 69]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.23 Or (Eq (skS.0 3 a a_1) empty_set)
% 4.06/4.23 (Or (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) (Ne (skS.0 4 a a_1 a_2) empty_set))
% 4.06/4.23 Clause #94 (by superposition #[91, 83]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.23 Or (Eq (skS.0 3 a a_1) empty_set)
% 4.06/4.23 (Or (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) (Ne (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))))
% 4.06/4.23 Clause #98 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 4 a a_1 a_2) empty_set) (Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 4.06/4.23 Clause #102 (by eliminate resolved literals #[92]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 3 a a_1) empty_set) (Ne (skS.0 4 a a_1 a_2) empty_set)
% 4.06/4.23 Clause #118 (by eliminate resolved literals #[94]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 3 a a_1) empty_set) (Ne (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)))
% 4.06/4.23 Clause #119 (by forward contextual literal cutting #[118, 77]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))
% 4.06/4.23 Clause #120 (by backward contextual literal cutting #[119, 98]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 4 a a_1 a_2) empty_set
% 4.06/4.23 Clause #123 (by backward demodulation #[120, 84]): ∀ (a a_1 : Iota), Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) empty_set)
% 4.06/4.23 Clause #129 (by backward contextual literal cutting #[120, 102]): ∀ (a a_1 : Iota), Eq (skS.0 3 a a_1) empty_set
% 4.06/4.23 Clause #134 (by forward demodulation #[123, 129]): ∀ (a : Iota), Eq (singleton (skS.0 2 a)) (set_union2 empty_set empty_set)
% 4.06/4.23 Clause #135 (by forward demodulation #[134, 28]): ∀ (a : Iota), Eq (singleton (skS.0 2 a)) empty_set
% 4.06/4.23 Clause #136 (by forward contextual literal cutting #[135, 19]): False
% 4.06/4.23 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------