TSTP Solution File: ANA068^1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : ANA068^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n017.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 : Wed Aug 30 17:15:46 EDT 2023
% Result : Theorem 3.23s 3.43s
% Output : Proof 3.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : ANA068^1 : TPTP v8.1.2. Released v7.0.0.
% 0.00/0.07 % Command : duper %s
% 0.07/0.26 % Computer : n017.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Fri Aug 25 18:19:55 EDT 2023
% 0.07/0.26 % CPUTime :
% 3.23/3.43 SZS status Theorem for theBenchmark.p
% 3.23/3.43 SZS output start Proof for theBenchmark.p
% 3.23/3.43 Clause #0 (by assumption #[]): Eq
% 3.23/3.43 (∀ (A : «type/realax/real»),
% 3.23/3.43 Not
% 3.23/3.43 («const/sets/FINITE» «type/realax/real»
% 3.23/3.43 («const/sets/GSPEC» «type/realax/real» fun A0 =>
% 3.23/3.43 Exists fun A1 => «const/sets/SETSPEC» «type/realax/real» A0 («const/realax/real_le» A A1) A1)))
% 3.23/3.43 True
% 3.23/3.43 Clause #1 (by assumption #[]): Eq (∀ (A : Type) (A0 : A → Prop), «const/sets/SUBSET» A A0 («const/sets/UNIV» A)) True
% 3.23/3.43 Clause #2 (by assumption #[]): Eq
% 3.23/3.43 (∀ (A : Type) (A0 A1 : A → Prop),
% 3.23/3.43 And («const/sets/FINITE» A A1) («const/sets/SUBSET» A A0 A1) → «const/sets/FINITE» A A0)
% 3.23/3.43 True
% 3.23/3.43 Clause #3 (by assumption #[]): Eq (∀ (A : Type) (A0 : A → Prop), Eq («const/sets/INFINITE» A A0) (Not («const/sets/FINITE» A A0))) True
% 3.23/3.43 Clause #4 (by assumption #[]): Eq (Not («const/sets/INFINITE» «type/realax/real» («const/sets/UNIV» «type/realax/real»))) True
% 3.23/3.43 Clause #5 (by clausification #[4]): Eq («const/sets/INFINITE» «type/realax/real» («const/sets/UNIV» «type/realax/real»)) False
% 3.23/3.43 Clause #6 (by clausification #[2]): ∀ (a : Type),
% 3.23/3.43 Eq (∀ (A0 A1 : a → Prop), And («const/sets/FINITE» a A1) («const/sets/SUBSET» a A0 A1) → «const/sets/FINITE» a A0)
% 3.23/3.43 True
% 3.23/3.43 Clause #7 (by clausification #[6]): ∀ (a : Type) (a_1 : a → Prop),
% 3.23/3.43 Eq (∀ (A1 : a → Prop), And («const/sets/FINITE» a A1) («const/sets/SUBSET» a a_1 A1) → «const/sets/FINITE» a a_1) True
% 3.23/3.43 Clause #8 (by clausification #[7]): ∀ (a : Type) (a_1 a_2 : a → Prop),
% 3.23/3.43 Eq (And («const/sets/FINITE» a a_1) («const/sets/SUBSET» a a_2 a_1) → «const/sets/FINITE» a a_2) True
% 3.23/3.43 Clause #9 (by clausification #[8]): ∀ (a : Type) (a_1 a_2 : a → Prop),
% 3.23/3.43 Or (Eq (And («const/sets/FINITE» a a_1) («const/sets/SUBSET» a a_2 a_1)) False) (Eq («const/sets/FINITE» a a_2) True)
% 3.23/3.43 Clause #10 (by clausification #[9]): ∀ (a : Type) (a_1 a_2 : a → Prop),
% 3.23/3.43 Or (Eq («const/sets/FINITE» a a_1) True)
% 3.23/3.43 (Or (Eq («const/sets/FINITE» a a_2) False) (Eq («const/sets/SUBSET» a a_1 a_2) False))
% 3.23/3.43 Clause #11 (by clausification #[1]): ∀ (a : Type), Eq (∀ (A0 : a → Prop), «const/sets/SUBSET» a A0 («const/sets/UNIV» a)) True
% 3.23/3.43 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : a → Prop), Eq («const/sets/SUBSET» a a_1 («const/sets/UNIV» a)) True
% 3.23/3.43 Clause #13 (by clausification #[3]): ∀ (a : Type), Eq (∀ (A0 : a → Prop), Eq («const/sets/INFINITE» a A0) (Not («const/sets/FINITE» a A0))) True
% 3.23/3.43 Clause #14 (by clausification #[13]): ∀ (a : Type) (a_1 : a → Prop), Eq (Eq («const/sets/INFINITE» a a_1) (Not («const/sets/FINITE» a a_1))) True
% 3.23/3.43 Clause #15 (by clausification #[14]): ∀ (a : Type) (a_1 : a → Prop), Eq («const/sets/INFINITE» a a_1) (Not («const/sets/FINITE» a a_1))
% 3.23/3.43 Clause #17 (by identity boolHoist #[15]): ∀ (a : Type) (a_1 : a → Prop), Or (Eq («const/sets/INFINITE» a a_1) (Not False)) (Eq («const/sets/FINITE» a a_1) True)
% 3.23/3.43 Clause #19 (by bool simp #[17]): ∀ (a : Type) (a_1 : a → Prop), Or (Eq («const/sets/INFINITE» a a_1) True) (Eq («const/sets/FINITE» a a_1) True)
% 3.23/3.43 Clause #20 (by superposition #[19, 5]): Or (Eq («const/sets/FINITE» «type/realax/real» fun x => «const/sets/UNIV» «type/realax/real» x) True) (Eq True False)
% 3.23/3.43 Clause #22 (by clausification #[0]): ∀ (a : «type/realax/real»),
% 3.23/3.43 Eq
% 3.23/3.43 (Not
% 3.23/3.43 («const/sets/FINITE» «type/realax/real»
% 3.23/3.43 («const/sets/GSPEC» «type/realax/real» fun A0 =>
% 3.23/3.43 Exists fun A1 => «const/sets/SETSPEC» «type/realax/real» A0 («const/realax/real_le» a A1) A1)))
% 3.23/3.43 True
% 3.23/3.43 Clause #23 (by clausification #[22]): ∀ (a : «type/realax/real»),
% 3.23/3.43 Eq
% 3.23/3.43 («const/sets/FINITE» «type/realax/real»
% 3.23/3.43 («const/sets/GSPEC» «type/realax/real» fun A0 =>
% 3.23/3.43 Exists fun A1 => «const/sets/SETSPEC» «type/realax/real» A0 («const/realax/real_le» a A1) A1))
% 3.23/3.43 False
% 3.23/3.43 Clause #24 (by betaEtaReduce #[20]): Or (Eq («const/sets/FINITE» «type/realax/real» («const/sets/UNIV» «type/realax/real»)) True) (Eq True False)
% 3.23/3.43 Clause #25 (by clausification #[24]): Eq («const/sets/FINITE» «type/realax/real» («const/sets/UNIV» «type/realax/real»)) True
% 3.23/3.43 Clause #26 (by superposition #[25, 10]): ∀ (a : «type/realax/real» → Prop),
% 3.23/3.43 Or (Eq («const/sets/FINITE» «type/realax/real» a) True)
% 3.23/3.43 (Or (Eq True False) (Eq («const/sets/SUBSET» «type/realax/real» a («const/sets/UNIV» «type/realax/real»)) False))
% 3.23/3.43 Clause #29 (by clausification #[26]): ∀ (a : «type/realax/real» → Prop),
% 3.23/3.43 Or (Eq («const/sets/FINITE» «type/realax/real» a) True)
% 3.23/3.43 (Eq («const/sets/SUBSET» «type/realax/real» a («const/sets/UNIV» «type/realax/real»)) False)
% 3.23/3.43 Clause #30 (by superposition #[29, 12]): ∀ (a : «type/realax/real» → Prop), Or (Eq («const/sets/FINITE» «type/realax/real» fun x => a x) True) (Eq False True)
% 3.23/3.43 Clause #31 (by betaEtaReduce #[30]): ∀ (a : «type/realax/real» → Prop), Or (Eq («const/sets/FINITE» «type/realax/real» a) True) (Eq False True)
% 3.23/3.43 Clause #32 (by clausification #[31]): ∀ (a : «type/realax/real» → Prop), Eq («const/sets/FINITE» «type/realax/real» a) True
% 3.23/3.43 Clause #34 (by superposition #[32, 23]): Eq True False
% 3.23/3.43 Clause #36 (by clausification #[34]): False
% 3.23/3.43 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------