TSTP Solution File: SEV282^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV282^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 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 19:24:39 EDT 2023
% Result : Theorem 9.05s 9.25s
% Output : Proof 9.05s
% 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 : SEV282^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n016.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 : Thu Aug 24 03:46:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 9.05/9.25 SZS status Theorem for theBenchmark.p
% 9.05/9.25 SZS output start Proof for theBenchmark.p
% 9.05/9.25 Clause #2 (by assumption #[]): Eq
% 9.05/9.25 (Eq cNAT fun Xn =>
% 9.05/9.25 ∀ (Xp : ((Iota → Prop) → Prop) → Prop),
% 9.05/9.25 And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp Xn)
% 9.05/9.25 True
% 9.05/9.25 Clause #3 (by assumption #[]): Eq (Not (cNAT cZERO)) True
% 9.05/9.25 Clause #4 (by clausification #[3]): Eq (cNAT cZERO) False
% 9.05/9.25 Clause #5 (by clausification #[2]): Eq cNAT fun Xn =>
% 9.05/9.25 ∀ (Xp : ((Iota → Prop) → Prop) → Prop), And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp Xn
% 9.05/9.25 Clause #6 (by argument congruence #[5]): ∀ (a : (Iota → Prop) → Prop),
% 9.05/9.25 Eq (cNAT a)
% 9.05/9.25 ((fun Xn =>
% 9.05/9.25 ∀ (Xp : ((Iota → Prop) → Prop) → Prop),
% 9.05/9.25 And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp Xn)
% 9.05/9.25 a)
% 9.05/9.25 Clause #7 (by betaEtaReduce #[6]): ∀ (a : (Iota → Prop) → Prop),
% 9.05/9.25 Eq (cNAT a)
% 9.05/9.25 (∀ (Xp : ((Iota → Prop) → Prop) → Prop),
% 9.05/9.25 And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp a)
% 9.05/9.25 Clause #8 (by clausify Prop equality #[7]): ∀ (a : (Iota → Prop) → Prop),
% 9.05/9.25 Or (Eq (cNAT a) True)
% 9.05/9.25 (Eq
% 9.05/9.25 (∀ (Xp : ((Iota → Prop) → Prop) → Prop),
% 9.05/9.25 And (Xp cZERO) (∀ (Xx : (Iota → Prop) → Prop), Xp Xx → Xp (cSUCC Xx)) → Xp a)
% 9.05/9.25 False)
% 9.05/9.25 Clause #19 (by clausification #[8]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop),
% 9.05/9.25 Or (Eq (cNAT a) True)
% 9.05/9.25 (Eq
% 9.05/9.25 (Not
% 9.05/9.25 (And (skS.0 1 a a_1 cZERO) (∀ (Xx : (Iota → Prop) → Prop), skS.0 1 a a_1 Xx → skS.0 1 a a_1 (cSUCC Xx)) →
% 9.05/9.25 skS.0 1 a a_1 a))
% 9.05/9.25 True)
% 9.05/9.25 Clause #20 (by clausification #[19]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop),
% 9.05/9.25 Or (Eq (cNAT a) True)
% 9.05/9.25 (Eq
% 9.05/9.25 (And (skS.0 1 a a_1 cZERO) (∀ (Xx : (Iota → Prop) → Prop), skS.0 1 a a_1 Xx → skS.0 1 a a_1 (cSUCC Xx)) →
% 9.05/9.25 skS.0 1 a a_1 a)
% 9.05/9.25 False)
% 9.05/9.25 Clause #21 (by clausification #[20]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop),
% 9.05/9.25 Or (Eq (cNAT a) True)
% 9.05/9.25 (Eq (And (skS.0 1 a a_1 cZERO) (∀ (Xx : (Iota → Prop) → Prop), skS.0 1 a a_1 Xx → skS.0 1 a a_1 (cSUCC Xx))) True)
% 9.05/9.25 Clause #22 (by clausification #[20]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop), Or (Eq (cNAT a) True) (Eq (skS.0 1 a a_1 a) False)
% 9.05/9.25 Clause #24 (by clausification #[21]): ∀ (a : (Iota → Prop) → Prop) (a_1 : ((Iota → Prop) → Prop) → Prop),
% 9.05/9.25 Or (Eq (cNAT a) True) (Eq (skS.0 1 a a_1 cZERO) True)
% 9.05/9.25 Clause #293 (by superposition #[24, 22]): Or (Eq (cNAT fun x => cZERO x) True) (Or (Eq (cNAT cZERO) True) (Eq True False))
% 9.05/9.25 Clause #1531 (by betaEtaReduce #[293]): Or (Eq (cNAT cZERO) True) (Or (Eq (cNAT cZERO) True) (Eq True False))
% 9.05/9.25 Clause #1532 (by clausification #[1531]): Or (Eq (cNAT cZERO) True) (Eq (cNAT cZERO) True)
% 9.05/9.25 Clause #1533 (by eliminate duplicate literals #[1532]): Eq (cNAT cZERO) True
% 9.05/9.25 Clause #1534 (by superposition #[1533, 4]): Eq True False
% 9.05/9.25 Clause #1558 (by clausification #[1534]): False
% 9.05/9.25 SZS output end Proof for theBenchmark.p
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