TSTP Solution File: PUZ102^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : PUZ102^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 13:14:44 EDT 2023
% Result : Theorem 4.35s 4.52s
% Output : Proof 4.35s
% 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 : PUZ102^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.13 % Command : duper %s
% 0.16/0.35 % Computer : n019.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sat Aug 26 22:29:28 EDT 2023
% 0.16/0.35 % CPUTime :
% 4.35/4.52 SZS status Theorem for theBenchmark.p
% 4.35/4.52 SZS output start Proof for theBenchmark.p
% 4.35/4.52 Clause #0 (by assumption #[]): Eq (Eq cCKB_E2 fun Xx Xy => ∀ (Xp : Iota → Prop), And (Xp Xx) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy) True
% 4.35/4.52 Clause #1 (by assumption #[]): Eq (Not (∀ (Xx : Iota), cCKB_E2 Xx (s (s Xx)))) True
% 4.35/4.52 Clause #2 (by clausification #[1]): Eq (∀ (Xx : Iota), cCKB_E2 Xx (s (s Xx))) False
% 4.35/4.52 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (cCKB_E2 (skS.0 0 a) (s (s (skS.0 0 a))))) True
% 4.35/4.52 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (cCKB_E2 (skS.0 0 a) (s (s (skS.0 0 a)))) False
% 4.35/4.52 Clause #5 (by clausification #[0]): Eq cCKB_E2 fun Xx Xy => ∀ (Xp : Iota → Prop), And (Xp Xx) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy
% 4.35/4.52 Clause #6 (by argument congruence #[5]): ∀ (a : Iota),
% 4.35/4.52 Eq (cCKB_E2 a) ((fun Xx Xy => ∀ (Xp : Iota → Prop), And (Xp Xx) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy) a)
% 4.35/4.52 Clause #8 (by betaEtaReduce #[6]): ∀ (a : Iota), Eq (cCKB_E2 a) fun Xy => ∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy
% 4.35/4.52 Clause #9 (by argument congruence #[8]): ∀ (a a_1 : Iota),
% 4.35/4.52 Eq (cCKB_E2 a a_1) ((fun Xy => ∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy) a_1)
% 4.35/4.52 Clause #12 (by betaEtaReduce #[9]): ∀ (a a_1 : Iota), Eq (cCKB_E2 a a_1) (∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp a_1)
% 4.35/4.52 Clause #13 (by clausify Prop equality #[12]): ∀ (a a_1 : Iota),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True)
% 4.35/4.52 (Eq (∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp a_1) False)
% 4.35/4.52 Clause #27 (by clausification #[13]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True)
% 4.35/4.52 (Eq
% 4.35/4.52 (Not
% 4.35/4.52 (And (skS.0 2 a a_1 a_2 a) (∀ (Xu : Iota), skS.0 2 a a_1 a_2 Xu → skS.0 2 a a_1 a_2 (s (s Xu))) →
% 4.35/4.52 skS.0 2 a a_1 a_2 a_1))
% 4.35/4.52 True)
% 4.35/4.52 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True)
% 4.35/4.52 (Eq
% 4.35/4.52 (And (skS.0 2 a a_1 a_2 a) (∀ (Xu : Iota), skS.0 2 a a_1 a_2 Xu → skS.0 2 a a_1 a_2 (s (s Xu))) →
% 4.35/4.52 skS.0 2 a a_1 a_2 a_1)
% 4.35/4.52 False)
% 4.35/4.52 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True)
% 4.35/4.52 (Eq (And (skS.0 2 a a_1 a_2 a) (∀ (Xu : Iota), skS.0 2 a a_1 a_2 Xu → skS.0 2 a a_1 a_2 (s (s Xu)))) True)
% 4.35/4.52 Clause #30 (by clausification #[28]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (cCKB_E2 a a_1) True) (Eq (skS.0 2 a a_1 a_2 a_1) False)
% 4.35/4.52 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True) (Eq (∀ (Xu : Iota), skS.0 2 a a_1 a_2 Xu → skS.0 2 a a_1 a_2 (s (s Xu))) True)
% 4.35/4.52 Clause #32 (by clausification #[29]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (cCKB_E2 a a_1) True) (Eq (skS.0 2 a a_1 a_2 a) True)
% 4.35/4.52 Clause #33 (by clausification #[31]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop) (a_3 : Iota),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True) (Eq (skS.0 2 a a_1 a_2 a_3 → skS.0 2 a a_1 a_2 (s (s a_3))) True)
% 4.35/4.52 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop) (a_3 : Iota),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True) (Or (Eq (skS.0 2 a a_1 a_2 a_3) False) (Eq (skS.0 2 a a_1 a_2 (s (s a_3))) True))
% 4.35/4.52 Clause #36 (by superposition #[32, 34]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True)
% 4.35/4.52 (Or (Eq (skS.0 2 a a_1 (fun x => a_2 x) (s (s a))) True) (Or (Eq (cCKB_E2 a a_1) True) (Eq False True)))
% 4.35/4.52 Clause #181 (by betaEtaReduce #[36]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True)
% 4.35/4.52 (Or (Eq (skS.0 2 a a_1 a_2 (s (s a))) True) (Or (Eq (cCKB_E2 a a_1) True) (Eq False True)))
% 4.35/4.52 Clause #182 (by clausification #[181]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop),
% 4.35/4.52 Or (Eq (cCKB_E2 a a_1) True) (Or (Eq (skS.0 2 a a_1 a_2 (s (s a))) True) (Eq (cCKB_E2 a a_1) True))
% 4.35/4.52 Clause #183 (by eliminate duplicate literals #[182]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (cCKB_E2 a a_1) True) (Eq (skS.0 2 a a_1 a_2 (s (s a))) True)
% 4.35/4.53 Clause #185 (by superposition #[183, 30]): ∀ (a : Iota), Or (Eq (cCKB_E2 a (s (s a))) True) (Or (Eq (cCKB_E2 a (s (s a))) True) (Eq True False))
% 4.35/4.53 Clause #204 (by clausification #[185]): ∀ (a : Iota), Or (Eq (cCKB_E2 a (s (s a))) True) (Eq (cCKB_E2 a (s (s a))) True)
% 4.35/4.53 Clause #205 (by eliminate duplicate literals #[204]): ∀ (a : Iota), Eq (cCKB_E2 a (s (s a))) True
% 4.35/4.53 Clause #206 (by superposition #[205, 4]): Eq True False
% 4.35/4.53 Clause #226 (by clausification #[206]): False
% 4.35/4.53 SZS output end Proof for theBenchmark.p
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