TSTP Solution File: SEU619^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU619^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n015.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 16:43:02 EDT 2023
% Result : Theorem 3.73s 3.90s
% Output : Proof 3.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU619^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15 % Command : duper %s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 16:16:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.73/3.90 SZS status Theorem for theBenchmark.p
% 3.73/3.90 SZS output start Proof for theBenchmark.p
% 3.73/3.90 Clause #0 (by assumption #[]): Eq
% 3.73/3.90 (Eq iskpair fun A =>
% 3.73/3.90 Exists fun Xx =>
% 3.73/3.90 And (in Xx (setunion A))
% 3.73/3.90 (Exists fun Xy =>
% 3.73/3.90 And (in Xy (setunion A))
% 3.73/3.90 (Eq A (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))))
% 3.73/3.90 True
% 3.73/3.90 Clause #1 (by assumption #[]): Eq
% 3.73/3.90 (Eq setukpairIL
% 3.73/3.90 (∀ (Xx Xy : Iota),
% 3.73/3.90 in Xx (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))))
% 3.73/3.90 True
% 3.73/3.90 Clause #2 (by assumption #[]): Eq
% 3.73/3.90 (Eq setukpairIR
% 3.73/3.90 (∀ (Xx Xy : Iota),
% 3.73/3.90 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))))
% 3.73/3.90 True
% 3.73/3.90 Clause #3 (by assumption #[]): Eq
% 3.73/3.90 (Not
% 3.73/3.90 (setukpairIL →
% 3.73/3.90 setukpairIR →
% 3.73/3.90 ∀ (Xx Xy : Iota),
% 3.73/3.90 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.90 True
% 3.73/3.90 Clause #4 (by clausification #[3]): Eq
% 3.73/3.90 (setukpairIL →
% 3.73/3.90 setukpairIR →
% 3.73/3.90 ∀ (Xx Xy : Iota),
% 3.73/3.90 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))
% 3.73/3.90 False
% 3.73/3.90 Clause #5 (by clausification #[4]): Eq setukpairIL True
% 3.73/3.90 Clause #6 (by clausification #[4]): Eq
% 3.73/3.90 (setukpairIR →
% 3.73/3.90 ∀ (Xx Xy : Iota),
% 3.73/3.90 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))
% 3.73/3.90 False
% 3.73/3.90 Clause #7 (by clausification #[6]): Eq setukpairIR True
% 3.73/3.90 Clause #8 (by clausification #[6]): Eq
% 3.73/3.90 (∀ (Xx Xy : Iota),
% 3.73/3.90 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))
% 3.73/3.90 False
% 3.73/3.90 Clause #9 (by clausification #[8]): ∀ (a : Iota),
% 3.73/3.90 Eq
% 3.73/3.90 (Not
% 3.73/3.90 (∀ (Xy : Iota),
% 3.73/3.90 iskpair
% 3.73/3.90 (setadjoin (setadjoin (skS.0 0 a) emptyset)
% 3.73/3.90 (setadjoin (setadjoin (skS.0 0 a) (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.90 True
% 3.73/3.90 Clause #10 (by clausification #[9]): ∀ (a : Iota),
% 3.73/3.90 Eq
% 3.73/3.90 (∀ (Xy : Iota),
% 3.73/3.90 iskpair
% 3.73/3.90 (setadjoin (setadjoin (skS.0 0 a) emptyset)
% 3.73/3.90 (setadjoin (setadjoin (skS.0 0 a) (setadjoin Xy emptyset)) emptyset)))
% 3.73/3.90 False
% 3.73/3.90 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota),
% 3.73/3.90 Eq
% 3.73/3.90 (Not
% 3.73/3.90 (iskpair
% 3.73/3.90 (setadjoin (setadjoin (skS.0 0 a) emptyset)
% 3.73/3.90 (setadjoin (setadjoin (skS.0 0 a) (setadjoin (skS.0 1 a a_1) emptyset)) emptyset))))
% 3.73/3.90 True
% 3.73/3.90 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota),
% 3.73/3.90 Eq
% 3.73/3.90 (iskpair
% 3.73/3.90 (setadjoin (setadjoin (skS.0 0 a) emptyset)
% 3.73/3.90 (setadjoin (setadjoin (skS.0 0 a) (setadjoin (skS.0 1 a a_1) emptyset)) emptyset)))
% 3.73/3.90 False
% 3.73/3.90 Clause #13 (by clausification #[2]): Eq setukpairIR
% 3.73/3.90 (∀ (Xx Xy : Iota),
% 3.73/3.90 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.90 Clause #14 (by forward demodulation #[13, 7]): Eq True
% 3.73/3.90 (∀ (Xx Xy : Iota),
% 3.73/3.90 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.90 Clause #15 (by clausification #[14]): ∀ (a : Iota),
% 3.73/3.90 Eq
% 3.73/3.90 (∀ (Xy : Iota),
% 3.73/3.90 in Xy (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.90 True
% 3.73/3.90 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota),
% 3.73/3.90 Eq (in a (setunion (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a emptyset)) emptyset))))
% 3.73/3.90 True
% 3.73/3.90 Clause #17 (by clausification #[1]): Eq setukpairIL
% 3.73/3.90 (∀ (Xx Xy : Iota),
% 3.73/3.90 in Xx (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.90 Clause #18 (by forward demodulation #[17, 5]): Eq True
% 3.73/3.90 (∀ (Xx Xy : Iota),
% 3.73/3.90 in Xx (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.90 Clause #19 (by clausification #[18]): ∀ (a : Iota),
% 3.73/3.90 Eq
% 3.73/3.90 (∀ (Xy : Iota),
% 3.73/3.90 in a (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.90 True
% 3.73/3.90 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 3.73/3.92 Eq (in a (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))))
% 3.73/3.92 True
% 3.73/3.92 Clause #21 (by clausification #[0]): Eq iskpair fun A =>
% 3.73/3.92 Exists fun Xx =>
% 3.73/3.92 And (in Xx (setunion A))
% 3.73/3.92 (Exists fun Xy =>
% 3.73/3.92 And (in Xy (setunion A))
% 3.73/3.92 (Eq A (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.92 Clause #22 (by argument congruence #[21]): ∀ (a : Iota),
% 3.73/3.92 Eq (iskpair a)
% 3.73/3.92 ((fun A =>
% 3.73/3.92 Exists fun Xx =>
% 3.73/3.92 And (in Xx (setunion A))
% 3.73/3.92 (Exists fun Xy =>
% 3.73/3.92 And (in Xy (setunion A))
% 3.73/3.92 (Eq A (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))))
% 3.73/3.92 a)
% 3.73/3.92 Clause #23 (by betaEtaReduce #[22]): ∀ (a : Iota),
% 3.73/3.92 Eq (iskpair a)
% 3.73/3.92 (Exists fun Xx =>
% 3.73/3.92 And (in Xx (setunion a))
% 3.73/3.92 (Exists fun Xy =>
% 3.73/3.92 And (in Xy (setunion a))
% 3.73/3.92 (Eq a (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))))
% 3.73/3.92 Clause #26 (by existsHoist #[23]): ∀ (a a_1 : Iota),
% 3.73/3.92 Or (Eq (iskpair a) True)
% 3.73/3.92 (Eq
% 3.73/3.92 ((fun Xx =>
% 3.73/3.92 And (in Xx (setunion a))
% 3.73/3.92 (Exists fun Xy =>
% 3.73/3.92 And (in Xy (setunion a))
% 3.73/3.92 (Eq a (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))))
% 3.73/3.92 a_1)
% 3.73/3.92 False)
% 3.73/3.92 Clause #27 (by betaEtaReduce #[26]): ∀ (a a_1 : Iota),
% 3.73/3.92 Or (Eq (iskpair a) True)
% 3.73/3.92 (Eq
% 3.73/3.92 (And (in a_1 (setunion a))
% 3.73/3.92 (Exists fun Xy =>
% 3.73/3.92 And (in Xy (setunion a))
% 3.73/3.92 (Eq a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin Xy emptyset)) emptyset)))))
% 3.73/3.92 False)
% 3.73/3.92 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota),
% 3.73/3.92 Or (Eq (iskpair a) True)
% 3.73/3.92 (Or (Eq (in a_1 (setunion a)) False)
% 3.73/3.92 (Eq
% 3.73/3.92 (Exists fun Xy =>
% 3.73/3.92 And (in Xy (setunion a))
% 3.73/3.92 (Eq a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin Xy emptyset)) emptyset))))
% 3.73/3.92 False))
% 3.73/3.92 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota),
% 3.73/3.92 Or (Eq (iskpair a) True)
% 3.73/3.92 (Or (Eq (in a_1 (setunion a)) False)
% 3.73/3.92 (Eq
% 3.73/3.92 (And (in a_2 (setunion a))
% 3.73/3.92 (Eq a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset))))
% 3.73/3.92 False))
% 3.73/3.92 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota),
% 3.73/3.92 Or (Eq (iskpair a) True)
% 3.73/3.92 (Or (Eq (in a_1 (setunion a)) False)
% 3.73/3.92 (Or (Eq (in a_2 (setunion a)) False)
% 3.73/3.92 (Eq (Eq a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset)))
% 3.73/3.92 False)))
% 3.73/3.92 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota),
% 3.73/3.92 Or (Eq (iskpair a) True)
% 3.73/3.92 (Or (Eq (in a_1 (setunion a)) False)
% 3.73/3.92 (Or (Eq (in a_2 (setunion a)) False)
% 3.73/3.92 (Ne a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset)))))
% 3.73/3.92 Clause #32 (by destructive equality resolution #[31]): ∀ (a a_1 : Iota),
% 3.73/3.92 Or (Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True)
% 3.73/3.92 (Or
% 3.73/3.92 (Eq
% 3.73/3.92 (in a (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))))
% 3.73/3.92 False)
% 3.73/3.92 (Eq
% 3.73/3.92 (in a_1
% 3.73/3.92 (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))))
% 3.73/3.92 False))
% 3.73/3.92 Clause #34 (by superposition #[32, 20]): ∀ (a a_1 : Iota),
% 3.73/3.92 Or (Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True)
% 3.73/3.92 (Or
% 3.73/3.92 (Eq
% 3.73/3.92 (in a_1
% 3.73/3.92 (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))))
% 3.73/3.92 False)
% 3.73/3.92 (Eq False True))
% 3.73/3.92 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 3.73/3.92 Or (Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True)
% 3.73/3.92 (Eq
% 3.73/3.92 (in a_1 (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))))
% 3.73/3.92 False)
% 3.73/3.92 Clause #36 (by superposition #[35, 16]): ∀ (a a_1 : Iota),
% 3.73/3.92 Or (Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True)
% 3.73/3.92 (Eq False True)
% 3.73/3.92 Clause #39 (by clausification #[36]): ∀ (a a_1 : Iota),
% 3.73/3.92 Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True
% 3.73/3.92 Clause #41 (by superposition #[39, 12]): Eq True False
% 3.73/3.92 Clause #42 (by clausification #[41]): False
% 3.73/3.92 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------