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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SYN386^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n003.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 08:07:33 PM UTC 2025

% Result   : Theorem 3.56s 3.75s
% Output   : Proof 3.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN386^5 : TPTP v9.2.0. Released v4.0.0.
% 0.13/0.13  % Command    : duper %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Oct  2 15:41:38 EDT 2025
% 0.13/0.35  % CPUTime    : 
% 3.56/3.75  SZS status Theorem for theBenchmark.p
% 3.56/3.75  SZS output start Proof for theBenchmark.p
% 3.56/3.75  Clause #0 (by assumption #[]): Eq
% 3.56/3.75    (Not
% 3.56/3.75      (And
% 3.56/3.75          (And (∀ (Xx : Iota), Exists fun Xy => cF Xx Xy)
% 3.56/3.75            (Exists fun Xx => ∀ (Xe : Iota), Exists fun Xn => ∀ (Xw : Iota), cS Xn Xw → cD Xw Xx Xe))
% 3.56/3.75          (∀ (Xe : Iota),
% 3.56/3.75            Exists fun Xd => ∀ (Xa Xb : Iota), cD Xa Xb Xd → ∀ (Xy Xz : Iota), And (cF Xa Xy) (cF Xb Xz) → cD Xy Xz Xe) →
% 3.56/3.75        Exists fun Xy => ∀ (Xe : Iota), Exists fun Xm => ∀ (Xw : Iota), cS Xm Xw → ∀ (Xz : Iota), cF Xw Xz → cD Xz Xy Xe))
% 3.56/3.75    True
% 3.56/3.75  Clause #1 (by betaEtaReduce #[0]): Eq
% 3.56/3.75    (Not
% 3.56/3.75      (And
% 3.56/3.75          (And (∀ (Xx : Iota), Exists (cF Xx))
% 3.56/3.75            (Exists fun Xx => ∀ (Xe : Iota), Exists fun Xn => ∀ (Xw : Iota), cS Xn Xw → cD Xw Xx Xe))
% 3.56/3.75          (∀ (Xe : Iota),
% 3.56/3.75            Exists fun Xd => ∀ (Xa Xb : Iota), cD Xa Xb Xd → ∀ (Xy Xz : Iota), And (cF Xa Xy) (cF Xb Xz) → cD Xy Xz Xe) →
% 3.56/3.75        Exists fun Xy => ∀ (Xe : Iota), Exists fun Xm => ∀ (Xw : Iota), cS Xm Xw → ∀ (Xz : Iota), cF Xw Xz → cD Xz Xy Xe))
% 3.56/3.75    True
% 3.56/3.75  Clause #2 (by clausification #[1]): Eq
% 3.56/3.75    (And
% 3.56/3.75        (And (∀ (Xx : Iota), Exists (cF Xx))
% 3.56/3.75          (Exists fun Xx => ∀ (Xe : Iota), Exists fun Xn => ∀ (Xw : Iota), cS Xn Xw → cD Xw Xx Xe))
% 3.56/3.75        (∀ (Xe : Iota),
% 3.56/3.75          Exists fun Xd => ∀ (Xa Xb : Iota), cD Xa Xb Xd → ∀ (Xy Xz : Iota), And (cF Xa Xy) (cF Xb Xz) → cD Xy Xz Xe) →
% 3.56/3.75      Exists fun Xy => ∀ (Xe : Iota), Exists fun Xm => ∀ (Xw : Iota), cS Xm Xw → ∀ (Xz : Iota), cF Xw Xz → cD Xz Xy Xe)
% 3.56/3.75    False
% 3.56/3.75  Clause #3 (by clausification #[2]): Eq
% 3.56/3.75    (And
% 3.56/3.75      (And (∀ (Xx : Iota), Exists (cF Xx))
% 3.56/3.75        (Exists fun Xx => ∀ (Xe : Iota), Exists fun Xn => ∀ (Xw : Iota), cS Xn Xw → cD Xw Xx Xe))
% 3.56/3.75      (∀ (Xe : Iota),
% 3.56/3.75        Exists fun Xd => ∀ (Xa Xb : Iota), cD Xa Xb Xd → ∀ (Xy Xz : Iota), And (cF Xa Xy) (cF Xb Xz) → cD Xy Xz Xe))
% 3.56/3.75    True
% 3.56/3.75  Clause #4 (by clausification #[2]): Eq (Exists fun Xy => ∀ (Xe : Iota), Exists fun Xm => ∀ (Xw : Iota), cS Xm Xw → ∀ (Xz : Iota), cF Xw Xz → cD Xz Xy Xe)
% 3.56/3.75    False
% 3.56/3.75  Clause #5 (by clausification #[3]): Eq
% 3.56/3.75    (∀ (Xe : Iota),
% 3.56/3.75      Exists fun Xd => ∀ (Xa Xb : Iota), cD Xa Xb Xd → ∀ (Xy Xz : Iota), And (cF Xa Xy) (cF Xb Xz) → cD Xy Xz Xe)
% 3.56/3.75    True
% 3.56/3.75  Clause #6 (by clausification #[3]): Eq
% 3.56/3.75    (And (∀ (Xx : Iota), Exists (cF Xx))
% 3.56/3.75      (Exists fun Xx => ∀ (Xe : Iota), Exists fun Xn => ∀ (Xw : Iota), cS Xn Xw → cD Xw Xx Xe))
% 3.56/3.75    True
% 3.56/3.75  Clause #7 (by clausification #[5]): ∀ (a : Iota),
% 3.56/3.75    Eq (Exists fun Xd => ∀ (Xa Xb : Iota), cD Xa Xb Xd → ∀ (Xy Xz : Iota), And (cF Xa Xy) (cF Xb Xz) → cD Xy Xz a) True
% 3.56/3.75  Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 3.56/3.75    Eq (∀ (Xa Xb : Iota), cD Xa Xb (skS.0 0 a a_1) → ∀ (Xy Xz : Iota), And (cF Xa Xy) (cF Xb Xz) → cD Xy Xz a) True
% 3.56/3.75  Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.75    Eq (∀ (Xb : Iota), cD a Xb (skS.0 0 a_1 a_2) → ∀ (Xy Xz : Iota), And (cF a Xy) (cF Xb Xz) → cD Xy Xz a_1) True
% 3.56/3.75  Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.75    Eq (cD a a_1 (skS.0 0 a_2 a_3) → ∀ (Xy Xz : Iota), And (cF a Xy) (cF a_1 Xz) → cD Xy Xz a_2) True
% 3.56/3.75  Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.75    Or (Eq (cD a a_1 (skS.0 0 a_2 a_3)) False) (Eq (∀ (Xy Xz : Iota), And (cF a Xy) (cF a_1 Xz) → cD Xy Xz a_2) True)
% 3.56/3.75  Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.56/3.75    Or (Eq (cD a a_1 (skS.0 0 a_2 a_3)) False) (Eq (∀ (Xz : Iota), And (cF a a_4) (cF a_1 Xz) → cD a_4 Xz a_2) True)
% 3.56/3.75  Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.56/3.75    Or (Eq (cD a a_1 (skS.0 0 a_2 a_3)) False) (Eq (And (cF a a_4) (cF a_1 a_5) → cD a_4 a_5 a_2) True)
% 3.56/3.75  Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.56/3.75    Or (Eq (cD a a_1 (skS.0 0 a_2 a_3)) False) (Or (Eq (And (cF a a_4) (cF a_1 a_5)) False) (Eq (cD a_4 a_5 a_2) True))
% 3.56/3.75  Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.56/3.75    Or (Eq (cD a a_1 (skS.0 0 a_2 a_3)) False)
% 3.56/3.75      (Or (Eq (cD a_4 a_5 a_2) True) (Or (Eq (cF a a_4) False) (Eq (cF a_1 a_5) False)))
% 3.56/3.78  Clause #16 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Xe : Iota), Exists fun Xm => ∀ (Xw : Iota), cS Xm Xw → ∀ (Xz : Iota), cF Xw Xz → cD Xz a Xe) False
% 3.56/3.78  Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota),
% 3.56/3.78    Eq (Not (Exists fun Xm => ∀ (Xw : Iota), cS Xm Xw → ∀ (Xz : Iota), cF Xw Xz → cD Xz a (skS.0 1 a a_1))) True
% 3.56/3.78  Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 3.56/3.78    Eq (Exists fun Xm => ∀ (Xw : Iota), cS Xm Xw → ∀ (Xz : Iota), cF Xw Xz → cD Xz a (skS.0 1 a a_1)) False
% 3.56/3.78  Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xw : Iota), cS a Xw → ∀ (Xz : Iota), cF Xw Xz → cD Xz a_1 (skS.0 1 a_1 a_2)) False
% 3.56/3.78  Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.78    Eq (Not (cS a (skS.0 2 a a_1 a_2 a_3) → ∀ (Xz : Iota), cF (skS.0 2 a a_1 a_2 a_3) Xz → cD Xz a_1 (skS.0 1 a_1 a_2)))
% 3.56/3.78      True
% 3.56/3.78  Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.56/3.78    Eq (cS a (skS.0 2 a a_1 a_2 a_3) → ∀ (Xz : Iota), cF (skS.0 2 a a_1 a_2 a_3) Xz → cD Xz a_1 (skS.0 1 a_1 a_2)) False
% 3.56/3.78  Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Eq (cS a (skS.0 2 a a_1 a_2 a_3)) True
% 3.56/3.78  Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (Xz : Iota), cF (skS.0 2 a a_1 a_2 a_3) Xz → cD Xz a_1 (skS.0 1 a_1 a_2)) False
% 3.56/3.78  Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.56/3.78    Eq
% 3.56/3.78      (Not
% 3.56/3.78        (cF (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4) → cD (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2)))
% 3.56/3.78      True
% 3.56/3.78  Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.56/3.78    Eq (cF (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4) → cD (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2))
% 3.56/3.78      False
% 3.56/3.78  Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (cF (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4)) True
% 3.56/3.78  Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (cD (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2)) False
% 3.56/3.78  Clause #28 (by clausification #[6]): Eq (Exists fun Xx => ∀ (Xe : Iota), Exists fun Xn => ∀ (Xw : Iota), cS Xn Xw → cD Xw Xx Xe) True
% 3.56/3.78  Clause #29 (by clausification #[6]): Eq (∀ (Xx : Iota), Exists (cF Xx)) True
% 3.56/3.78  Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Xe : Iota), Exists fun Xn => ∀ (Xw : Iota), cS Xn Xw → cD Xw (skS.0 4 a) Xe) True
% 3.56/3.78  Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Exists fun Xn => ∀ (Xw : Iota), cS Xn Xw → cD Xw (skS.0 4 a) a_1) True
% 3.56/3.78  Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xw : Iota), cS (skS.0 5 a a_1 a_2) Xw → cD Xw (skS.0 4 a) a_1) True
% 3.56/3.78  Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), Eq (cS (skS.0 5 a a_1 a_2) a_3 → cD a_3 (skS.0 4 a) a_1) True
% 3.56/3.78  Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cS (skS.0 5 a a_1 a_2) a_3) False) (Eq (cD a_3 (skS.0 4 a) a_1) True)
% 3.56/3.78  Clause #35 (by superposition #[34, 22]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.56/3.78    Or (Eq (cD (skS.0 2 (skS.0 5 a a_1 a_2) a_3 a_4 a_5) (skS.0 4 a) a_1) True) (Eq False True)
% 3.56/3.78  Clause #36 (by clausification #[29]): ∀ (a : Iota), Eq (Exists (cF a)) True
% 3.56/3.78  Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (cF a (skS.0 6 a a_1)) True
% 3.56/3.78  Clause #38 (by clausification #[35]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (cD (skS.0 2 (skS.0 5 a a_1 a_2) a_3 a_4 a_5) (skS.0 4 a) a_1) True
% 3.56/3.78  Clause #39 (by superposition #[38, 15]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.56/3.78    Or (Eq True False)
% 3.56/3.78      (Or (Eq (cD a a_1 a_2) True)
% 3.56/3.78        (Or (Eq (cF (skS.0 2 (skS.0 5 a_3 (skS.0 0 a_2 a_4) a_5) a_6 a_7 a_8) a) False)
% 3.56/3.78          (Eq (cF (skS.0 4 a_3) a_1) False)))
% 3.56/3.78  Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.56/3.78    Or (Eq (cD a a_1 a_2) True)
% 3.56/3.78      (Or (Eq (cF (skS.0 2 (skS.0 5 a_3 (skS.0 0 a_2 a_4) a_5) a_6 a_7 a_8) a) False) (Eq (cF (skS.0 4 a_3) a_1) False))
% 3.56/3.78  Clause #41 (by superposition #[40, 26]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.56/3.78    Or (Eq (cD (skS.0 3 (skS.0 5 a (skS.0 0 a_1 a_2) a_3) a_4 a_5 a_6 a_7) a_8 a_1) True)
% 3.61/3.78      (Or (Eq (cF (skS.0 4 a) a_8) False) (Eq False True))
% 3.61/3.78  Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.61/3.78    Or (Eq (cD (skS.0 3 (skS.0 5 a (skS.0 0 a_1 a_2) a_3) a_4 a_5 a_6 a_7) a_8 a_1) True) (Eq (cF (skS.0 4 a) a_8) False)
% 3.61/3.78  Clause #44 (by superposition #[43, 37]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.61/3.78    Or (Eq (cD (skS.0 3 (skS.0 5 a (skS.0 0 a_1 a_2) a_3) a_4 a_5 a_6 a_7) (skS.0 6 (skS.0 4 a) a_8) a_1) True)
% 3.61/3.78      (Eq False True)
% 3.61/3.78  Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.61/3.78    Eq (cD (skS.0 3 (skS.0 5 a (skS.0 0 a_1 a_2) a_3) a_4 a_5 a_6 a_7) (skS.0 6 (skS.0 4 a) a_8) a_1) True
% 3.61/3.78  Clause #47 (by superposition #[45, 27]): Eq True False
% 3.61/3.78  Clause #48 (by clausification #[47]): False
% 3.61/3.78  SZS output end Proof for theBenchmark.p
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