TSTP Solution File: SYO261^5 by Duper---1.0
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% File : Duper---1.0
% Problem : SYO261^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n013.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 : Fri Sep 1 04:21:59 EDT 2023
% Result : Theorem 4.20s 4.43s
% Output : Proof 4.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO261^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 06:40:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.20/4.43 SZS status Theorem for theBenchmark.p
% 4.20/4.43 SZS output start Proof for theBenchmark.p
% 4.20/4.43 Clause #0 (by assumption #[]): Eq
% 4.20/4.43 (Not
% 4.20/4.43 (And (And (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) (cP cO))
% 4.20/4.43 (∀ (Xx : Iota), cP Xx → cP (c1_plus Xx)) →
% 4.20/4.43 cP n))
% 4.20/4.43 True
% 4.20/4.43 Clause #1 (by clausification #[0]): Eq
% 4.20/4.43 (And (And (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) (cP cO))
% 4.20/4.43 (∀ (Xx : Iota), cP Xx → cP (c1_plus Xx)) →
% 4.20/4.43 cP n)
% 4.20/4.43 False
% 4.20/4.43 Clause #2 (by clausification #[1]): Eq
% 4.20/4.43 (And (And (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) (cP cO))
% 4.20/4.43 (∀ (Xx : Iota), cP Xx → cP (c1_plus Xx)))
% 4.20/4.43 True
% 4.20/4.43 Clause #3 (by clausification #[1]): Eq (cP n) False
% 4.20/4.43 Clause #4 (by clausification #[2]): Eq (∀ (Xx : Iota), cP Xx → cP (c1_plus Xx)) True
% 4.20/4.43 Clause #5 (by clausification #[2]): Eq (And (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) (cP cO)) True
% 4.20/4.43 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (cP a → cP (c1_plus a)) True
% 4.20/4.43 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (cP (c1_plus a)) True)
% 4.20/4.43 Clause #8 (by clausification #[5]): Eq (cP cO) True
% 4.20/4.43 Clause #9 (by clausification #[5]): Eq (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) True
% 4.20/4.43 Clause #11 (by clausification #[9]): ∀ (a : Iota → Prop), Eq (And (a cO) (∀ (Xx : Iota), a Xx → a (c1_plus Xx)) → a n) True
% 4.20/4.43 Clause #12 (by clausification #[11]): ∀ (a : Iota → Prop), Or (Eq (And (a cO) (∀ (Xx : Iota), a Xx → a (c1_plus Xx))) False) (Eq (a n) True)
% 4.20/4.43 Clause #13 (by clausification #[12]): ∀ (a : Iota → Prop), Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (∀ (Xx : Iota), a Xx → a (c1_plus Xx)) False))
% 4.20/4.43 Clause #14 (by clausification #[13]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.20/4.43 Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (Not (a (skS.0 0 a a_1) → a (c1_plus (skS.0 0 a a_1)))) True))
% 4.20/4.43 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.20/4.43 Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (a (skS.0 0 a a_1) → a (c1_plus (skS.0 0 a a_1))) False))
% 4.20/4.43 Clause #16 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (a (skS.0 0 a a_1)) True))
% 4.20/4.43 Clause #17 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (a (c1_plus (skS.0 0 a a_1))) False))
% 4.20/4.43 Clause #26 (by superposition #[16, 8]): ∀ (a : Iota),
% 4.20/4.43 Or (Eq ((fun x => cP x) n) True) (Or (Eq ((fun x => cP x) (skS.0 0 (fun x => cP x) a)) True) (Eq False True))
% 4.20/4.43 Clause #39 (by fluidLoobHoist #[17]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.20/4.43 Or (Eq (a n) True) (Or (Eq (a (c1_plus (skS.0 0 a a_1))) False) (Or (Eq True False) (Eq (a cO) False)))
% 4.20/4.43 Clause #111 (by clausification #[39]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a n) True) (Or (Eq (a (c1_plus (skS.0 0 a a_1))) False) (Eq (a cO) False))
% 4.20/4.43 Clause #128 (by fluidSup #[111, 8]): ∀ (a : Iota → Prop) (a_1 : Prop → Iota),
% 4.20/4.43 Or (Eq (a n) True) (Or (Eq (a (c1_plus (skS.0 0 a (a_1 True)))) False) (Eq (a cO) False))
% 4.20/4.43 Clause #242 (by betaEtaReduce #[26]): ∀ (a : Iota), Or (Eq (cP n) True) (Or (Eq (cP (skS.0 0 cP a)) True) (Eq False True))
% 4.20/4.43 Clause #243 (by clausification #[242]): ∀ (a : Iota), Or (Eq (cP n) True) (Eq (cP (skS.0 0 cP a)) True)
% 4.20/4.43 Clause #244 (by forward demodulation #[243, 3]): ∀ (a : Iota), Or (Eq False True) (Eq (cP (skS.0 0 cP a)) True)
% 4.20/4.43 Clause #245 (by clausification #[244]): ∀ (a : Iota), Eq (cP (skS.0 0 cP a)) True
% 4.20/4.43 Clause #246 (by superposition #[245, 7]): ∀ (a : Iota), Or (Eq True False) (Eq (cP (c1_plus (skS.0 0 cP a))) True)
% 4.20/4.43 Clause #251 (by clausification #[246]): ∀ (a : Iota), Eq (cP (c1_plus (skS.0 0 cP a))) True
% 4.20/4.43 Clause #255 (by fluidSup #[251, 128]): Or (Eq ((fun x => cP x) n) True) (Or (Eq ((fun _ => _) True) False) (Eq ((fun x => cP x) cO) False))
% 4.20/4.43 Clause #258 (by betaEtaReduce #[255]): Or (Eq (cP n) True) (Or (Eq True False) (Eq (cP cO) False))
% 4.20/4.43 Clause #259 (by clausification #[258]): Or (Eq (cP n) True) (Eq (cP cO) False)
% 4.20/4.44 Clause #260 (by forward demodulation #[259, 8]): Or (Eq (cP n) True) (Eq True False)
% 4.20/4.44 Clause #261 (by clausification #[260]): Eq (cP n) True
% 4.20/4.44 Clause #262 (by superposition #[261, 3]): Eq True False
% 4.20/4.44 Clause #276 (by clausification #[262]): False
% 4.20/4.44 SZS output end Proof for theBenchmark.p
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