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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SYN386+1 : TPTP v9.2.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n006.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 4.18s 4.39s
% Output   : Proof 4.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SYN386+1 : TPTP v9.2.0. Released v2.0.0.
% 0.12/0.14  % Command    : duper %s
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Thu Oct  2 15:13:08 EDT 2025
% 0.14/0.36  % CPUTime    : 
% 4.18/4.39  SZS status Theorem for theBenchmark.p
% 4.18/4.39  SZS output start Proof for theBenchmark.p
% 4.18/4.39  Clause #0 (by assumption #[]): Eq
% 4.18/4.39    (Not
% 4.18/4.39      (And
% 4.18/4.39          (And (∀ (X : Iota), Exists fun Y => big_f X Y)
% 4.18/4.39            (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 4.18/4.39          (∀ (E : Iota),
% 4.18/4.39            Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E) →
% 4.18/4.39        Exists fun Y => ∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z Y E))
% 4.18/4.39    True
% 4.18/4.39  Clause #1 (by betaEtaReduce #[0]): Eq
% 4.18/4.39    (Not
% 4.18/4.39      (And
% 4.18/4.39          (And (∀ (X : Iota), Exists (big_f X))
% 4.18/4.39            (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 4.18/4.39          (∀ (E : Iota),
% 4.18/4.39            Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E) →
% 4.18/4.39        Exists fun Y => ∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z Y E))
% 4.18/4.39    True
% 4.18/4.39  Clause #2 (by clausification #[1]): Eq
% 4.18/4.39    (And
% 4.18/4.39        (And (∀ (X : Iota), Exists (big_f X))
% 4.18/4.39          (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 4.18/4.39        (∀ (E : Iota),
% 4.18/4.39          Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E) →
% 4.18/4.39      Exists fun Y => ∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z Y E)
% 4.18/4.39    False
% 4.18/4.39  Clause #3 (by clausification #[2]): Eq
% 4.18/4.39    (And
% 4.18/4.39      (And (∀ (X : Iota), Exists (big_f X))
% 4.18/4.39        (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 4.18/4.39      (∀ (E : Iota),
% 4.18/4.39        Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E))
% 4.18/4.39    True
% 4.18/4.39  Clause #4 (by clausification #[2]): Eq (Exists fun Y => ∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z Y E) False
% 4.18/4.39  Clause #5 (by clausification #[3]): Eq
% 4.18/4.39    (∀ (E : Iota),
% 4.18/4.39      Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E)
% 4.18/4.39    True
% 4.18/4.39  Clause #6 (by clausification #[3]): Eq
% 4.18/4.39    (And (∀ (X : Iota), Exists (big_f X))
% 4.18/4.39      (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 4.18/4.39    True
% 4.18/4.39  Clause #7 (by clausification #[5]): ∀ (a : Iota),
% 4.18/4.39    Eq (Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z a) True
% 4.18/4.39  Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 4.18/4.39    Eq (∀ (A B : Iota), big_d A B (skS.0 0 a a_1) → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z a) True
% 4.18/4.39  Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 4.18/4.39    Eq (∀ (B : Iota), big_d a B (skS.0 0 a_1 a_2) → ∀ (Y Z : Iota), And (big_f a Y) (big_f B Z) → big_d Y Z a_1) True
% 4.18/4.39  Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.18/4.39    Eq (big_d a a_1 (skS.0 0 a_2 a_3) → ∀ (Y Z : Iota), And (big_f a Y) (big_f a_1 Z) → big_d Y Z a_2) True
% 4.18/4.39  Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.18/4.39    Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False)
% 4.18/4.39      (Eq (∀ (Y Z : Iota), And (big_f a Y) (big_f a_1 Z) → big_d Y Z a_2) True)
% 4.18/4.39  Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.18/4.39    Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False)
% 4.18/4.39      (Eq (∀ (Z : Iota), And (big_f a a_4) (big_f a_1 Z) → big_d a_4 Z a_2) True)
% 4.18/4.39  Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.18/4.39    Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False) (Eq (And (big_f a a_4) (big_f a_1 a_5) → big_d a_4 a_5 a_2) True)
% 4.18/4.39  Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.18/4.39    Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False)
% 4.18/4.39      (Or (Eq (And (big_f a a_4) (big_f a_1 a_5)) False) (Eq (big_d a_4 a_5 a_2) True))
% 4.18/4.39  Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.18/4.39    Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False)
% 4.18/4.39      (Or (Eq (big_d a_4 a_5 a_2) True) (Or (Eq (big_f a a_4) False) (Eq (big_f a_1 a_5) False)))
% 4.18/4.42  Clause #16 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z a E) False
% 4.18/4.42  Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota),
% 4.18/4.42    Eq (Not (Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z a (skS.0 1 a a_1))) True
% 4.18/4.42  Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 4.18/4.42    Eq (Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z a (skS.0 1 a a_1)) False
% 4.18/4.42  Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Eq (∀ (W : Iota), big_s a W → ∀ (Z : Iota), big_f W Z → big_d Z a_1 (skS.0 1 a_1 a_2)) False
% 4.18/4.42  Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.18/4.42    Eq
% 4.18/4.42      (Not
% 4.18/4.42        (big_s a (skS.0 2 a a_1 a_2 a_3) → ∀ (Z : Iota), big_f (skS.0 2 a a_1 a_2 a_3) Z → big_d Z a_1 (skS.0 1 a_1 a_2)))
% 4.18/4.42      True
% 4.18/4.42  Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.18/4.42    Eq (big_s a (skS.0 2 a a_1 a_2 a_3) → ∀ (Z : Iota), big_f (skS.0 2 a a_1 a_2 a_3) Z → big_d Z a_1 (skS.0 1 a_1 a_2))
% 4.18/4.42      False
% 4.18/4.42  Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_s a (skS.0 2 a a_1 a_2 a_3)) True
% 4.18/4.42  Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (Z : Iota), big_f (skS.0 2 a a_1 a_2 a_3) Z → big_d Z a_1 (skS.0 1 a_1 a_2)) False
% 4.18/4.42  Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.18/4.42    Eq
% 4.18/4.42      (Not
% 4.18/4.42        (big_f (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4) →
% 4.18/4.42          big_d (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2)))
% 4.18/4.42      True
% 4.18/4.42  Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.18/4.42    Eq
% 4.18/4.42      (big_f (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4) →
% 4.18/4.42        big_d (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2))
% 4.18/4.42      False
% 4.18/4.42  Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4)) True
% 4.18/4.42  Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_d (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2)) False
% 4.18/4.42  Clause #28 (by clausification #[6]): Eq (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E) True
% 4.18/4.42  Clause #29 (by clausification #[6]): Eq (∀ (X : Iota), Exists (big_f X)) True
% 4.18/4.42  Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W (skS.0 4 a) E) True
% 4.18/4.42  Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Exists fun N => ∀ (W : Iota), big_s N W → big_d W (skS.0 4 a) a_1) True
% 4.18/4.42  Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (∀ (W : Iota), big_s (skS.0 5 a a_1 a_2) W → big_d W (skS.0 4 a) a_1) True
% 4.18/4.42  Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_s (skS.0 5 a a_1 a_2) a_3 → big_d a_3 (skS.0 4 a) a_1) True
% 4.18/4.42  Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_s (skS.0 5 a a_1 a_2) a_3) False) (Eq (big_d a_3 (skS.0 4 a) a_1) True)
% 4.18/4.42  Clause #35 (by superposition #[34, 22]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.18/4.42    Or (Eq (big_d (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)
% 4.18/4.42  Clause #36 (by clausification #[29]): ∀ (a : Iota), Eq (Exists (big_f a)) True
% 4.18/4.42  Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (big_f a (skS.0 6 a a_1)) True
% 4.18/4.42  Clause #38 (by clausification #[35]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (big_d (skS.0 2 (skS.0 5 a a_1 a_2) a_3 a_4 a_5) (skS.0 4 a) a_1) True
% 4.18/4.42  Clause #39 (by superposition #[38, 15]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 4.18/4.42    Or (Eq True False)
% 4.18/4.42      (Or (Eq (big_d a a_1 a_2) True)
% 4.18/4.42        (Or (Eq (big_f (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)
% 4.18/4.42          (Eq (big_f (skS.0 4 a_3) a_1) False)))
% 4.18/4.42  Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 4.18/4.42    Or (Eq (big_d a a_1 a_2) True)
% 4.18/4.42      (Or (Eq (big_f (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)
% 4.18/4.42        (Eq (big_f (skS.0 4 a_3) a_1) False))
% 4.18/4.42  Clause #41 (by superposition #[40, 26]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 4.18/4.43    Or (Eq (big_d (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)
% 4.18/4.43      (Or (Eq (big_f (skS.0 4 a) a_8) False) (Eq False True))
% 4.18/4.43  Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 4.18/4.43    Or (Eq (big_d (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)
% 4.18/4.43      (Eq (big_f (skS.0 4 a) a_8) False)
% 4.18/4.43  Clause #44 (by superposition #[43, 37]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 4.18/4.43    Or (Eq (big_d (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)
% 4.18/4.43      (Eq False True)
% 4.18/4.43  Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 4.18/4.43    Eq (big_d (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
% 4.18/4.43  Clause #47 (by superposition #[45, 27]): Eq True False
% 4.18/4.43  Clause #48 (by clausification #[47]): False
% 4.18/4.43  SZS output end Proof for theBenchmark.p
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