TSTP Solution File: SET903+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET903+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 3.49s 3.71s
% Output : Proof 3.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET903+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n028.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 08:49:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.49/3.71 SZS status Theorem for theBenchmark.p
% 3.49/3.71 SZS output start Proof for theBenchmark.p
% 3.49/3.71 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True
% 3.49/3.71 Clause #7 (by assumption #[]): Eq
% 3.49/3.71 (∀ (A B C : Iota),
% 3.49/3.71 Not
% 3.49/3.71 (And
% 3.49/3.71 (And (And (Eq (singleton A) (set_union2 B C)) (Not (And (Eq B (singleton A)) (Eq C (singleton A)))))
% 3.49/3.71 (Not (And (Eq B empty_set) (Eq C (singleton A)))))
% 3.49/3.71 (Not (And (Eq B (singleton A)) (Eq C empty_set)))))
% 3.49/3.71 True
% 3.49/3.71 Clause #8 (by assumption #[]): Eq
% 3.49/3.71 (Not
% 3.49/3.71 (∀ (A B C : Iota),
% 3.49/3.71 Not (And (And (And (Eq (singleton A) (set_union2 B C)) (Ne B C)) (Ne B empty_set)) (Ne C empty_set))))
% 3.49/3.71 True
% 3.49/3.71 Clause #22 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True
% 3.49/3.71 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True
% 3.49/3.71 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a)
% 3.49/3.71 Clause #30 (by clausification #[8]): Eq
% 3.49/3.71 (∀ (A B C : Iota),
% 3.49/3.71 Not (And (And (And (Eq (singleton A) (set_union2 B C)) (Ne B C)) (Ne B empty_set)) (Ne C empty_set)))
% 3.49/3.71 False
% 3.49/3.71 Clause #31 (by clausification #[30]): ∀ (a : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (Not
% 3.49/3.71 (∀ (B C : Iota),
% 3.49/3.71 Not (And (And (And (Eq (singleton (skS.0 2 a)) (set_union2 B C)) (Ne B C)) (Ne B empty_set)) (Ne C empty_set))))
% 3.49/3.71 True
% 3.49/3.71 Clause #32 (by clausification #[31]): ∀ (a : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (∀ (B C : Iota),
% 3.49/3.71 Not (And (And (And (Eq (singleton (skS.0 2 a)) (set_union2 B C)) (Ne B C)) (Ne B empty_set)) (Ne C empty_set)))
% 3.49/3.71 False
% 3.49/3.71 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (Not
% 3.49/3.71 (∀ (C : Iota),
% 3.49/3.71 Not
% 3.49/3.71 (And
% 3.49/3.71 (And (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) C)) (Ne (skS.0 3 a a_1) C))
% 3.49/3.71 (Ne (skS.0 3 a a_1) empty_set))
% 3.49/3.71 (Ne C empty_set))))
% 3.49/3.71 True
% 3.49/3.71 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (∀ (C : Iota),
% 3.49/3.71 Not
% 3.49/3.71 (And
% 3.49/3.71 (And (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) C)) (Ne (skS.0 3 a a_1) C))
% 3.49/3.71 (Ne (skS.0 3 a a_1) empty_set))
% 3.49/3.71 (Ne C empty_set)))
% 3.49/3.71 False
% 3.49/3.71 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (Not
% 3.49/3.71 (Not
% 3.49/3.71 (And
% 3.49/3.71 (And
% 3.49/3.71 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.71 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.71 (Ne (skS.0 3 a a_1) empty_set))
% 3.49/3.71 (Ne (skS.0 4 a a_1 a_2) empty_set))))
% 3.49/3.71 True
% 3.49/3.71 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (Not
% 3.49/3.71 (And
% 3.49/3.71 (And
% 3.49/3.71 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.71 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.71 (Ne (skS.0 3 a a_1) empty_set))
% 3.49/3.71 (Ne (skS.0 4 a a_1 a_2) empty_set)))
% 3.49/3.71 False
% 3.49/3.71 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (And
% 3.49/3.71 (And
% 3.49/3.71 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.71 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.71 (Ne (skS.0 3 a a_1) empty_set))
% 3.49/3.71 (Ne (skS.0 4 a a_1 a_2) empty_set))
% 3.49/3.71 True
% 3.49/3.71 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Eq (Ne (skS.0 4 a a_1 a_2) empty_set) True
% 3.49/3.71 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (And
% 3.49/3.71 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.71 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.71 (Ne (skS.0 3 a a_1) empty_set))
% 3.49/3.71 True
% 3.49/3.71 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 4 a a_1 a_2) empty_set
% 3.49/3.71 Clause #41 (by clausification #[7]): ∀ (a : Iota),
% 3.49/3.71 Eq
% 3.49/3.71 (∀ (B C : Iota),
% 3.49/3.71 Not
% 3.49/3.71 (And
% 3.49/3.71 (And (And (Eq (singleton a) (set_union2 B C)) (Not (And (Eq B (singleton a)) (Eq C (singleton a)))))
% 3.49/3.71 (Not (And (Eq B empty_set) (Eq C (singleton a)))))
% 3.49/3.71 (Not (And (Eq B (singleton a)) (Eq C empty_set)))))
% 3.49/3.71 True
% 3.49/3.71 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 3.49/3.74 Eq
% 3.49/3.74 (∀ (C : Iota),
% 3.49/3.74 Not
% 3.49/3.74 (And
% 3.49/3.74 (And (And (Eq (singleton a) (set_union2 a_1 C)) (Not (And (Eq a_1 (singleton a)) (Eq C (singleton a)))))
% 3.49/3.74 (Not (And (Eq a_1 empty_set) (Eq C (singleton a)))))
% 3.49/3.74 (Not (And (Eq a_1 (singleton a)) (Eq C empty_set)))))
% 3.49/3.74 True
% 3.49/3.74 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Eq
% 3.49/3.74 (Not
% 3.49/3.74 (And
% 3.49/3.74 (And (And (Eq (singleton a) (set_union2 a_1 a_2)) (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a)))))
% 3.49/3.74 (Not (And (Eq a_1 empty_set) (Eq a_2 (singleton a)))))
% 3.49/3.74 (Not (And (Eq a_1 (singleton a)) (Eq a_2 empty_set)))))
% 3.49/3.74 True
% 3.49/3.74 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Eq
% 3.49/3.74 (And
% 3.49/3.74 (And (And (Eq (singleton a) (set_union2 a_1 a_2)) (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a)))))
% 3.49/3.74 (Not (And (Eq a_1 empty_set) (Eq a_2 (singleton a)))))
% 3.49/3.74 (Not (And (Eq a_1 (singleton a)) (Eq a_2 empty_set))))
% 3.49/3.74 False
% 3.49/3.74 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or
% 3.49/3.74 (Eq
% 3.49/3.74 (And (And (Eq (singleton a) (set_union2 a_1 a_2)) (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a)))))
% 3.49/3.74 (Not (And (Eq a_1 empty_set) (Eq a_2 (singleton a)))))
% 3.49/3.74 False)
% 3.49/3.74 (Eq (Not (And (Eq a_1 (singleton a)) (Eq a_2 empty_set))) False)
% 3.49/3.74 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Eq (Not (And (Eq a (singleton a_1)) (Eq a_2 empty_set))) False)
% 3.49/3.74 (Or
% 3.49/3.74 (Eq (And (Eq (singleton a_1) (set_union2 a a_2)) (Not (And (Eq a (singleton a_1)) (Eq a_2 (singleton a_1)))))
% 3.49/3.74 False)
% 3.49/3.74 (Eq (Not (And (Eq a empty_set) (Eq a_2 (singleton a_1)))) False))
% 3.49/3.74 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Eq (And (Eq (singleton a) (set_union2 a_1 a_2)) (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a))))) False)
% 3.49/3.74 (Or (Eq (Not (And (Eq a_1 empty_set) (Eq a_2 (singleton a)))) False)
% 3.49/3.74 (Eq (And (Eq a_1 (singleton a)) (Eq a_2 empty_set)) True))
% 3.49/3.74 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Eq (Not (And (Eq a empty_set) (Eq a_1 (singleton a_2)))) False)
% 3.49/3.74 (Or (Eq (And (Eq a (singleton a_2)) (Eq a_1 empty_set)) True)
% 3.49/3.74 (Or (Eq (Eq (singleton a_2) (set_union2 a a_1)) False)
% 3.49/3.74 (Eq (Not (And (Eq a (singleton a_2)) (Eq a_1 (singleton a_2)))) False)))
% 3.49/3.74 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Eq (And (Eq a (singleton a_1)) (Eq a_2 empty_set)) True)
% 3.49/3.74 (Or (Eq (Eq (singleton a_1) (set_union2 a a_2)) False)
% 3.49/3.74 (Or (Eq (Not (And (Eq a (singleton a_1)) (Eq a_2 (singleton a_1)))) False)
% 3.49/3.74 (Eq (And (Eq a empty_set) (Eq a_2 (singleton a_1))) True)))
% 3.49/3.74 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Eq (Eq (singleton a) (set_union2 a_1 a_2)) False)
% 3.49/3.74 (Or (Eq (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a)))) False)
% 3.49/3.74 (Or (Eq (And (Eq a_1 empty_set) (Eq a_2 (singleton a))) True) (Eq (Eq a_2 empty_set) True)))
% 3.49/3.74 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Eq (Not (And (Eq a (singleton a_1)) (Eq a_2 (singleton a_1)))) False)
% 3.49/3.74 (Or (Eq (And (Eq a empty_set) (Eq a_2 (singleton a_1))) True)
% 3.49/3.74 (Or (Eq (Eq a_2 empty_set) True) (Ne (singleton a_1) (set_union2 a a_2))))
% 3.49/3.74 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Eq (And (Eq a empty_set) (Eq a_1 (singleton a_2))) True)
% 3.49/3.74 (Or (Eq (Eq a_1 empty_set) True)
% 3.49/3.74 (Or (Ne (singleton a_2) (set_union2 a a_1)) (Eq (And (Eq a (singleton a_2)) (Eq a_1 (singleton a_2))) True)))
% 3.49/3.74 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Eq (Eq a empty_set) True)
% 3.49/3.74 (Or (Ne (singleton a_1) (set_union2 a_2 a))
% 3.49/3.74 (Or (Eq (And (Eq a_2 (singleton a_1)) (Eq a (singleton a_1))) True) (Eq (Eq a (singleton a_1)) True)))
% 3.49/3.74 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Ne (singleton a) (set_union2 a_1 a_2))
% 3.49/3.74 (Or (Eq (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a))) True)
% 3.49/3.74 (Or (Eq (Eq a_2 (singleton a)) True) (Eq a_2 empty_set)))
% 3.49/3.74 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.74 Or (Ne (singleton a) (set_union2 a_1 a_2))
% 3.49/3.75 (Or (Eq (Eq a_2 (singleton a)) True) (Or (Eq a_2 empty_set) (Eq (Eq a_2 (singleton a)) True)))
% 3.49/3.75 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.75 Or (Ne (singleton a) (set_union2 a_1 a_2))
% 3.49/3.75 (Or (Eq a_2 empty_set) (Or (Eq (Eq a_2 (singleton a)) True) (Eq a_2 (singleton a))))
% 3.49/3.75 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.75 Or (Ne (singleton a) (set_union2 a_1 a_2)) (Or (Eq a_2 empty_set) (Or (Eq a_2 (singleton a)) (Eq a_2 (singleton a))))
% 3.49/3.75 Clause #61 (by eliminate duplicate literals #[60]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (set_union2 a_1 a_2)) (Or (Eq a_2 empty_set) (Eq a_2 (singleton a)))
% 3.49/3.75 Clause #63 (by superposition #[61, 24]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (set_union2 a_1 a_2)) (Or (Eq a_1 empty_set) (Eq a_1 (singleton a)))
% 3.49/3.75 Clause #64 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 3 a a_1) empty_set) True
% 3.49/3.75 Clause #65 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.75 Eq
% 3.49/3.75 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.75 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 3.49/3.75 True
% 3.49/3.75 Clause #66 (by clausification #[64]): ∀ (a a_1 : Iota), Ne (skS.0 3 a a_1) empty_set
% 3.49/3.75 Clause #98 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Eq (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True
% 3.49/3.75 Clause #99 (by clausification #[65]): ∀ (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
% 3.49/3.75 Clause #100 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)
% 3.49/3.75 Clause #101 (by clausification #[99]): ∀ (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))
% 3.49/3.75 Clause #104 (by superposition #[101, 61]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.49/3.75 Or (Ne (singleton a) (singleton (skS.0 2 a_1)))
% 3.49/3.75 (Or (Eq (skS.0 4 a_1 a_2 a_3) empty_set) (Eq (skS.0 4 a_1 a_2 a_3) (singleton a)))
% 3.49/3.75 Clause #105 (by superposition #[101, 63]): ∀ (a a_1 a_2 : Iota),
% 3.49/3.75 Or (Ne (singleton a) (singleton (skS.0 2 a_1)))
% 3.49/3.75 (Or (Eq (skS.0 3 a_1 a_2) empty_set) (Eq (skS.0 3 a_1 a_2) (singleton a)))
% 3.49/3.75 Clause #106 (by forward contextual literal cutting #[105, 66]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (singleton (skS.0 2 a_1))) (Eq (skS.0 3 a_1 a_2) (singleton a))
% 3.49/3.75 Clause #107 (by equality resolution #[106]): ∀ (a a_1 : Iota), Eq (skS.0 3 a a_1) (singleton (skS.0 2 a))
% 3.49/3.75 Clause #109 (by backward demodulation #[107, 100]): ∀ (a a_1 a_2 : Iota), Ne (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)
% 3.49/3.75 Clause #113 (by forward contextual literal cutting #[104, 40]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (singleton a) (singleton (skS.0 2 a_1))) (Eq (skS.0 4 a_1 a_2 a_3) (singleton a))
% 3.49/3.75 Clause #114 (by equality resolution #[113]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))
% 3.49/3.75 Clause #115 (by forward contextual literal cutting #[114, 109]): False
% 3.49/3.75 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------