TSTP Solution File: SEU618^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU618^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 16:43:01 EDT 2023
% Result : Theorem 3.44s 3.63s
% Output : Proof 3.44s
% 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 : SEU618^2 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:33:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.44/3.63 SZS status Theorem for theBenchmark.p
% 3.44/3.63 SZS output start Proof for theBenchmark.p
% 3.44/3.63 Clause #0 (by assumption #[]): Eq (Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))) True
% 3.44/3.63 Clause #1 (by assumption #[]): Eq (Eq secondinupair (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))) True
% 3.44/3.63 Clause #2 (by assumption #[]): Eq
% 3.44/3.63 (Not
% 3.44/3.63 (setunionI →
% 3.44/3.63 secondinupair →
% 3.44/3.63 ∀ (Xx Xy : Iota),
% 3.44/3.63 in Xy
% 3.44/3.63 (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))))
% 3.44/3.63 True
% 3.44/3.63 Clause #3 (by clausification #[1]): Eq secondinupair (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))
% 3.44/3.63 Clause #5 (by clausify Prop equality #[3]): Or (Eq secondinupair False) (Eq (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) True)
% 3.44/3.63 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq secondinupair False) (Eq (∀ (Xy : Iota), in Xy (setadjoin a (setadjoin Xy emptyset))) True)
% 3.44/3.63 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq secondinupair False) (Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True)
% 3.44/3.63 Clause #13 (by clausification #[0]): Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))
% 3.44/3.63 Clause #22 (by clausification #[2]): Eq
% 3.44/3.63 (setunionI →
% 3.44/3.63 secondinupair →
% 3.44/3.63 ∀ (Xx Xy : Iota),
% 3.44/3.63 in Xy
% 3.44/3.63 (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.44/3.63 False
% 3.44/3.63 Clause #23 (by clausification #[22]): Eq setunionI True
% 3.44/3.63 Clause #24 (by clausification #[22]): Eq
% 3.44/3.63 (secondinupair →
% 3.44/3.63 ∀ (Xx Xy : Iota),
% 3.44/3.63 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.44/3.63 False
% 3.44/3.63 Clause #25 (by backward demodulation #[23, 13]): Eq True (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))
% 3.44/3.63 Clause #27 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Xx B : Iota), in Xx B → in B a → in Xx (setunion a)) True
% 3.44/3.63 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (B : Iota), in a B → in B a_1 → in a (setunion a_1)) True
% 3.44/3.63 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a_1 a_2 → in a (setunion a_2)) True
% 3.44/3.63 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a_1 a_2 → in a (setunion a_2)) True)
% 3.44/3.63 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_1 a_2) False) (Eq (in a (setunion a_2)) True))
% 3.44/3.63 Clause #41 (by clausification #[24]): Eq secondinupair True
% 3.44/3.63 Clause #42 (by clausification #[24]): Eq
% 3.44/3.63 (∀ (Xx Xy : Iota),
% 3.44/3.63 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.44/3.63 False
% 3.44/3.63 Clause #44 (by backward demodulation #[41, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True)
% 3.44/3.63 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True
% 3.44/3.63 Clause #47 (by superposition #[46, 31]): ∀ (a a_1 a_2 : Iota),
% 3.44/3.63 Or (Eq True False) (Or (Eq (in (setadjoin a (setadjoin a_1 emptyset)) a_2) False) (Eq (in a_1 (setunion a_2)) True))
% 3.44/3.63 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (setadjoin a (setadjoin a_1 emptyset)) a_2) False) (Eq (in a_1 (setunion a_2)) True)
% 3.44/3.63 Clause #50 (by superposition #[49, 46]): ∀ (a a_1 a_2 : Iota),
% 3.44/3.63 Or (Eq (in a (setunion (setadjoin a_1 (setadjoin (setadjoin a_2 (setadjoin a emptyset)) emptyset)))) True)
% 3.44/3.63 (Eq False True)
% 3.44/3.63 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 3.44/3.63 Eq (in a (setunion (setadjoin a_1 (setadjoin (setadjoin a_2 (setadjoin a emptyset)) emptyset)))) True
% 3.44/3.63 Clause #54 (by clausification #[42]): ∀ (a : Iota),
% 3.44/3.63 Eq
% 3.44/3.63 (Not
% 3.44/3.63 (∀ (Xy : Iota),
% 3.44/3.63 in Xy
% 3.44/3.63 (setunion
% 3.44/3.63 (setadjoin (setadjoin (skS.0 5 a) emptyset)
% 3.44/3.63 (setadjoin (setadjoin (skS.0 5 a) (setadjoin Xy emptyset)) emptyset)))))
% 3.44/3.63 True
% 3.44/3.63 Clause #55 (by clausification #[54]): ∀ (a : Iota),
% 3.44/3.63 Eq
% 3.44/3.63 (∀ (Xy : Iota),
% 3.44/3.63 in Xy
% 3.44/3.63 (setunion
% 3.44/3.63 (setadjoin (setadjoin (skS.0 5 a) emptyset)
% 3.44/3.63 (setadjoin (setadjoin (skS.0 5 a) (setadjoin Xy emptyset)) emptyset))))
% 3.44/3.63 False
% 3.44/3.63 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota),
% 3.44/3.63 Eq
% 3.44/3.63 (Not
% 3.44/3.63 (in (skS.0 6 a a_1)
% 3.44/3.63 (setunion
% 3.44/3.63 (setadjoin (setadjoin (skS.0 5 a) emptyset)
% 3.44/3.63 (setadjoin (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_1) emptyset)) emptyset)))))
% 3.44/3.63 True
% 3.44/3.63 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota),
% 3.44/3.63 Eq
% 3.44/3.63 (in (skS.0 6 a a_1)
% 3.44/3.63 (setunion
% 3.44/3.63 (setadjoin (setadjoin (skS.0 5 a) emptyset)
% 3.44/3.63 (setadjoin (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_1) emptyset)) emptyset))))
% 3.44/3.63 False
% 3.44/3.63 Clause #58 (by superposition #[57, 51]): Eq False True
% 3.44/3.63 Clause #62 (by clausification #[58]): False
% 3.44/3.63 SZS output end Proof for theBenchmark.p
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