%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SYO253^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n027.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 04:21:58 EDT 2023

% Result   : Theorem 3.68s 3.85s
% Output   : Proof 3.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SYO253^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command    : duper %s
% 0.16/0.36  % Computer : n027.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Sat Aug 26 05:20:04 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 3.68/3.85  SZS status Theorem for theBenchmark.p
% 3.68/3.85  SZS output start Proof for theBenchmark.p
% 3.68/3.85  Clause #0 (by assumption #[]): Eq (Not (Exists fun Xf => And (Xf (And p (Not p))) (Not (Xf (Or p (Not p)))))) True
% 3.68/3.85  Clause #1 (by clausification #[0]): Eq (Exists fun Xf => And (Xf (And p (Not p))) (Not (Xf (Or p (Not p))))) False
% 3.68/3.85  Clause #2 (by clausification #[1]): ∀ (a : Prop → Prop), Eq (And (a (And p (Not p))) (Not (a (Or p (Not p))))) False
% 3.68/3.85  Clause #3 (by clausification #[2]): ∀ (a : Prop → Prop), Or (Eq (a (And p (Not p))) False) (Eq (Not (a (Or p (Not p)))) False)
% 3.68/3.85  Clause #4 (by clausification #[3]): ∀ (a : Prop → Prop), Or (Eq (a (And p (Not p))) False) (Eq (a (Or p (Not p))) True)
% 3.68/3.85  Clause #5 (by bool simp #[4]): ∀ (a : Prop → Prop), Or (Eq (a False) False) (Eq (a (Or p (Not p))) True)
% 3.68/3.85  Clause #6 (by bool simp #[5]): ∀ (a : Prop → Prop), Or (Eq (a False) False) (Eq (a True) True)
% 3.68/3.85  Clause #8 (by neHoist #[6]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.68/3.85    Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) True) True) (Or (Eq True False) (Eq (a_1 False) (a_2 False)))
% 3.68/3.85  Clause #31 (by betaEtaReduce #[8]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.68/3.85    Or (Eq (Ne (a_1 True) (a_2 True)) True) (Or (Eq True False) (Eq (a_1 False) (a_2 False)))
% 3.68/3.85  Clause #32 (by clausification #[31]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.68/3.85    Or (Eq True False) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True)))
% 3.68/3.85  Clause #33 (by clausification #[32]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True))
% 3.68/3.85  Clause #34 (by equality resolution #[33]): Eq ((fun x => x) False) ((fun x => True) False)
% 3.68/3.85  Clause #37 (by betaEtaReduce #[34]): Eq False True
% 3.68/3.85  Clause #38 (by clausification #[37]): False
% 3.68/3.85  SZS output end Proof for theBenchmark.p
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