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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SYN082+1 : TPTP v9.2.0. Released v2.0.0.
% 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 Oct  3 08:07:09 PM UTC 2025

% Result   : Theorem 3.66s 3.82s
% Output   : Proof 3.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SYN082+1 : TPTP v9.2.0. Released v2.0.0.
% 0.06/0.13  % Command    : duper %s
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Thu Oct  2 15:30:23 EDT 2025
% 0.14/0.35  % CPUTime    : 
% 3.66/3.82  SZS status Theorem for theBenchmark.p
% 3.66/3.82  SZS output start Proof for theBenchmark.p
% 3.66/3.82  Clause #0 (by assumption #[]): Eq (Not (∀ (X : Iota), Iff (big_f X (f X)) (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f X)) (big_f X Y))))
% 3.66/3.82    True
% 3.66/3.82  Clause #1 (by clausification #[0]): Eq (∀ (X : Iota), Iff (big_f X (f X)) (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f X)) (big_f X Y))) False
% 3.66/3.82  Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 3.66/3.82    Eq
% 3.66/3.82      (Not
% 3.66/3.82        (Iff (big_f (skS.0 0 a) (f (skS.0 0 a)))
% 3.66/3.82          (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) Y))))
% 3.66/3.82      True
% 3.66/3.82  Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 3.66/3.82    Eq
% 3.66/3.82      (Iff (big_f (skS.0 0 a) (f (skS.0 0 a)))
% 3.66/3.82        (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) Y)))
% 3.66/3.82      False
% 3.66/3.82  Clause #4 (by clausification #[3]): ∀ (a : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.66/3.82      (Eq (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) Y)) False)
% 3.66/3.82  Clause #5 (by clausification #[3]): ∀ (a : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.66/3.82      (Eq (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) Y)) True)
% 3.66/3.82  Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.66/3.82      (Eq (And (∀ (Z : Iota), big_f Z a_1 → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) a_1)) False)
% 3.66/3.82  Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.66/3.82      (Or (Eq (∀ (Z : Iota), big_f Z a_1 → big_f Z (f (skS.0 0 a))) False) (Eq (big_f (skS.0 0 a) a_1) False))
% 3.66/3.82  Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.66/3.82      (Or (Eq (big_f (skS.0 0 a) a_1) False)
% 3.66/3.82        (Eq (Not (big_f (skS.0 1 a_1 a a_2) a_1 → big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a)))) True))
% 3.66/3.82  Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.66/3.82      (Or (Eq (big_f (skS.0 0 a) a_1) False)
% 3.66/3.82        (Eq (big_f (skS.0 1 a_1 a a_2) a_1 → big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a))) False))
% 3.66/3.82  Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.66/3.82      (Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) True))
% 3.66/3.82  Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.66/3.82      (Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a))) False))
% 3.66/3.82  Clause #12 (by clausification #[5]): ∀ (a a_1 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.66/3.82      (Eq (And (∀ (Z : Iota), big_f Z (skS.0 2 a a_1) → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) (skS.0 2 a a_1)))
% 3.66/3.82        True)
% 3.66/3.82  Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True) (Eq (big_f (skS.0 0 a) (skS.0 2 a a_1)) True)
% 3.66/3.82  Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.66/3.82      (Eq (∀ (Z : Iota), big_f Z (skS.0 2 a a_1) → big_f Z (f (skS.0 0 a))) True)
% 3.66/3.82  Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True) (Eq (big_f a_1 (skS.0 2 a a_2) → big_f a_1 (f (skS.0 0 a))) True)
% 3.66/3.82  Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.66/3.82      (Or (Eq (big_f a_1 (skS.0 2 a a_2)) False) (Eq (big_f a_1 (f (skS.0 0 a))) True))
% 3.66/3.82  Clause #17 (by superposition #[16, 13]): ∀ (a : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.66/3.82      (Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.66/3.82        (Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True) (Eq False True)))
% 3.66/3.82  Clause #18 (by clausification #[17]): ∀ (a : Iota),
% 3.66/3.82    Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.66/3.82      (Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True) (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True))
% 3.66/3.82  Clause #19 (by eliminate duplicate literals #[18]): ∀ (a : Iota), Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True
% 3.66/3.83  Clause #21 (by backward demodulation #[19, 11]): ∀ (a a_1 a_2 : Iota),
% 3.66/3.83    Or (Eq True False) (Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a))) False))
% 3.66/3.83  Clause #22 (by superposition #[19, 10]): ∀ (a a_1 a_2 : Iota),
% 3.66/3.83    Or (Eq True False) (Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) True))
% 3.66/3.83  Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) True)
% 3.66/3.83  Clause #24 (by superposition #[23, 19]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 1 (f (skS.0 0 a)) a a_1) (f (skS.0 0 a))) True) (Eq False True)
% 3.66/3.83  Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 1 (f (skS.0 0 a)) a a_1) (f (skS.0 0 a))) True
% 3.66/3.83  Clause #26 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a))) False)
% 3.66/3.83  Clause #27 (by superposition #[26, 19]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 1 (f (skS.0 0 a)) a a_1) (f (skS.0 0 a))) False) (Eq False True)
% 3.66/3.83  Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 1 (f (skS.0 0 a)) a a_1) (f (skS.0 0 a))) False
% 3.66/3.83  Clause #29 (by superposition #[28, 25]): Eq False True
% 3.66/3.83  Clause #30 (by clausification #[29]): False
% 3.66/3.83  SZS output end Proof for theBenchmark.p
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