TSTP Solution File: SET046+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET046+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 14:45:18 EDT 2023
% Result : Theorem 4.63s 4.81s
% Output : Proof 4.63s
% 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 : SET046+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : duper %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 09:12:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 4.63/4.81 SZS status Theorem for theBenchmark.p
% 4.63/4.81 SZS output start Proof for theBenchmark.p
% 4.63/4.81 Clause #0 (by assumption #[]): Eq (Not (Not (Exists fun Y => ∀ (X : Iota), Iff (element X Y) (Not (Exists fun Z => And (element X Z) (element Z X))))))
% 4.63/4.81 True
% 4.63/4.81 Clause #1 (by clausification #[0]): Eq (Not (Exists fun Y => ∀ (X : Iota), Iff (element X Y) (Not (Exists fun Z => And (element X Z) (element Z X))))) False
% 4.63/4.81 Clause #2 (by clausification #[1]): Eq (Exists fun Y => ∀ (X : Iota), Iff (element X Y) (Not (Exists fun Z => And (element X Z) (element Z X)))) True
% 4.63/4.81 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 4.63/4.81 Eq (∀ (X : Iota), Iff (element X (skS.0 0 a)) (Not (Exists fun Z => And (element X Z) (element Z X)))) True
% 4.63/4.81 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), Eq (Iff (element a (skS.0 0 a_1)) (Not (Exists fun Z => And (element a Z) (element Z a)))) True
% 4.63/4.81 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota),
% 4.63/4.81 Or (Eq (element a (skS.0 0 a_1)) True) (Eq (Not (Exists fun Z => And (element a Z) (element Z a))) False)
% 4.63/4.81 Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota),
% 4.63/4.81 Or (Eq (element a (skS.0 0 a_1)) False) (Eq (Not (Exists fun Z => And (element a Z) (element Z a))) True)
% 4.63/4.81 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (Exists fun Z => And (element a Z) (element Z a)) True)
% 4.63/4.81 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota),
% 4.63/4.81 Or (Eq (element a (skS.0 0 a_1)) True) (Eq (And (element a (skS.0 1 a a_2)) (element (skS.0 1 a a_2) a)) True)
% 4.63/4.81 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element (skS.0 1 a a_2) a) True)
% 4.63/4.81 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element a (skS.0 1 a a_2)) True)
% 4.63/4.81 Clause #11 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Eq (Exists fun Z => And (element a Z) (element Z a)) False)
% 4.63/4.81 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Eq (And (element a a_2) (element a_2 a)) False)
% 4.63/4.81 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Or (Eq (element a a_2) False) (Eq (element a_2 a) False))
% 4.63/4.81 Clause #16 (by superposition #[13, 9]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.63/4.81 Or (Eq (element (skS.0 1 (skS.0 0 a) a_1) a_2) False)
% 4.63/4.81 (Or (Eq (element a_2 (skS.0 1 (skS.0 0 a) a_1)) False)
% 4.63/4.81 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True)))
% 4.63/4.81 Clause #27 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.63/4.81 Or (Eq (element (skS.0 1 (skS.0 0 a) a_1) a_2) False)
% 4.63/4.81 (Or (Eq (element a_2 (skS.0 1 (skS.0 0 a) a_1)) False) (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True))
% 4.63/4.81 Clause #31 (by superposition #[27, 9]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.63/4.81 Or (Eq (element (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) False)
% 4.63/4.81 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True)
% 4.63/4.81 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True)))
% 4.63/4.81 Clause #156 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.63/4.81 Or (Eq (element (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) False)
% 4.63/4.81 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True))
% 4.63/4.81 Clause #157 (by superposition #[156, 10]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.63/4.81 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True)
% 4.63/4.81 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True)
% 4.63/4.81 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True)))
% 4.63/4.81 Clause #158 (by clausification #[157]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.63/4.81 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True)
% 4.63/4.81 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True))
% 4.63/4.81 Clause #171 (by equality factoring #[158]): ∀ (a a_1 a_2 : Iota),
% 4.63/4.81 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True))
% 4.63/4.81 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 : Iota),
% 4.63/4.81 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True)
% 4.63/4.81 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) (Or (Eq True False) (Eq True False)))
% 4.63/4.82 Clause #174 (by clausification #[172]): ∀ (a a_1 a_2 : Iota),
% 4.63/4.82 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) (Eq True False))
% 4.63/4.82 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 : Iota), Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True)
% 4.63/4.82 Clause #188 (by equality factoring #[175]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True)
% 4.63/4.82 Clause #189 (by clausification #[188]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Eq True False) (Eq True False))
% 4.63/4.82 Clause #191 (by clausification #[189]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Eq True False)
% 4.63/4.82 Clause #192 (by clausification #[191]): ∀ (a a_1 : Iota), Eq (element (skS.0 0 a) (skS.0 0 a_1)) True
% 4.63/4.82 Clause #193 (by superposition #[192, 13]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (element (skS.0 0 a) a_1) False) (Eq (element a_1 (skS.0 0 a)) False))
% 4.63/4.82 Clause #218 (by clausification #[193]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 0 a) a_1) False) (Eq (element a_1 (skS.0 0 a)) False)
% 4.63/4.82 Clause #219 (by superposition #[218, 192]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) False) (Eq False True)
% 4.63/4.82 Clause #225 (by clausification #[219]): ∀ (a a_1 : Iota), Eq (element (skS.0 0 a) (skS.0 0 a_1)) False
% 4.63/4.82 Clause #226 (by superposition #[225, 192]): Eq False True
% 4.63/4.82 Clause #231 (by clausification #[226]): False
% 4.63/4.82 SZS output end Proof for theBenchmark.p
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