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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SEU167+1 : TPTP v9.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n009.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 08:01:02 PM UTC 2025

% Result   : Theorem 6.25s 6.46s
% Output   : Proof 6.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU167+1 : TPTP v9.2.0. Released v3.3.0.
% 0.07/0.13  % Command    : duper %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Oct  3 05:07:38 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 6.25/6.46  SZS status Theorem for theBenchmark.p
% 6.25/6.46  SZS output start Proof for theBenchmark.p
% 6.25/6.46  Clause #2 (by assumption #[]): Eq
% 6.25/6.46    (∀ (A B C : Iota),
% 6.25/6.46      subset A B →
% 6.25/6.46        And (subset (cartesian_product2 A C) (cartesian_product2 B C))
% 6.25/6.46          (subset (cartesian_product2 C A) (cartesian_product2 C B)))
% 6.25/6.46    True
% 6.25/6.46  Clause #3 (by assumption #[]): Eq (Not (∀ (A B C D : Iota), And (subset A B) (subset C D) → subset (cartesian_product2 A C) (cartesian_product2 B D)))
% 6.25/6.46    True
% 6.25/6.46  Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C) True
% 6.25/6.46  Clause #7 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset a B) (subset B C) → subset a C) True
% 6.25/6.46  Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (subset a a_1) (subset a_1 C) → subset a C) True
% 6.25/6.46  Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True
% 6.25/6.46  Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a_2)) False) (Eq (subset a a_2) True)
% 6.25/6.46  Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Or (Eq (subset a a_2) False) (Eq (subset a_2 a_1) False))
% 6.25/6.46  Clause #14 (by clausification #[3]): Eq (∀ (A B C D : Iota), And (subset A B) (subset C D) → subset (cartesian_product2 A C) (cartesian_product2 B D)) False
% 6.25/6.46  Clause #15 (by clausification #[14]): ∀ (a : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (Not
% 6.25/6.46        (∀ (B C D : Iota),
% 6.25/6.46          And (subset (skS.0 0 a) B) (subset C D) → subset (cartesian_product2 (skS.0 0 a) C) (cartesian_product2 B D)))
% 6.25/6.46      True
% 6.25/6.46  Clause #16 (by clausification #[15]): ∀ (a : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (∀ (B C D : Iota),
% 6.25/6.46        And (subset (skS.0 0 a) B) (subset C D) → subset (cartesian_product2 (skS.0 0 a) C) (cartesian_product2 B D))
% 6.25/6.46      False
% 6.25/6.46  Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (Not
% 6.25/6.46        (∀ (C D : Iota),
% 6.25/6.46          And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset C D) →
% 6.25/6.46            subset (cartesian_product2 (skS.0 0 a) C) (cartesian_product2 (skS.0 1 a a_1) D)))
% 6.25/6.46      True
% 6.25/6.46  Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (∀ (C D : Iota),
% 6.25/6.46        And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset C D) →
% 6.25/6.46          subset (cartesian_product2 (skS.0 0 a) C) (cartesian_product2 (skS.0 1 a a_1) D))
% 6.25/6.46      False
% 6.25/6.46  Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (Not
% 6.25/6.46        (∀ (D : Iota),
% 6.25/6.46          And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 2 a a_1 a_2) D) →
% 6.25/6.46            subset (cartesian_product2 (skS.0 0 a) (skS.0 2 a a_1 a_2)) (cartesian_product2 (skS.0 1 a a_1) D)))
% 6.25/6.46      True
% 6.25/6.46  Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (∀ (D : Iota),
% 6.25/6.46        And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 2 a a_1 a_2) D) →
% 6.25/6.46          subset (cartesian_product2 (skS.0 0 a) (skS.0 2 a a_1 a_2)) (cartesian_product2 (skS.0 1 a a_1) D))
% 6.25/6.46      False
% 6.25/6.46  Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (Not
% 6.25/6.46        (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) →
% 6.25/6.46          subset (cartesian_product2 (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 6.25/6.46            (cartesian_product2 (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3))))
% 6.25/6.46      True
% 6.25/6.46  Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) →
% 6.25/6.46        subset (cartesian_product2 (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 6.25/6.46          (cartesian_product2 (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)))
% 6.25/6.46      False
% 6.25/6.46  Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.25/6.46    Eq (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True
% 6.25/6.46  Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.25/6.46    Eq
% 6.25/6.46      (subset (cartesian_product2 (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 6.25/6.46        (cartesian_product2 (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)))
% 6.25/6.46      False
% 6.25/6.46  Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) True
% 6.25/6.48  Clause #26 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True
% 6.25/6.48  Clause #28 (by clausification #[2]): ∀ (a : Iota),
% 6.25/6.48    Eq
% 6.25/6.48      (∀ (B C : Iota),
% 6.25/6.48        subset a B →
% 6.25/6.48          And (subset (cartesian_product2 a C) (cartesian_product2 B C))
% 6.25/6.48            (subset (cartesian_product2 C a) (cartesian_product2 C B)))
% 6.25/6.48      True
% 6.25/6.48  Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota),
% 6.25/6.48    Eq
% 6.25/6.48      (∀ (C : Iota),
% 6.25/6.48        subset a a_1 →
% 6.25/6.48          And (subset (cartesian_product2 a C) (cartesian_product2 a_1 C))
% 6.25/6.48            (subset (cartesian_product2 C a) (cartesian_product2 C a_1)))
% 6.25/6.48      True
% 6.25/6.48  Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota),
% 6.25/6.48    Eq
% 6.25/6.48      (subset a a_1 →
% 6.25/6.48        And (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2))
% 6.25/6.48          (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1)))
% 6.25/6.48      True
% 6.25/6.48  Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota),
% 6.25/6.48    Or (Eq (subset a a_1) False)
% 6.25/6.48      (Eq
% 6.25/6.48        (And (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2))
% 6.25/6.48          (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1)))
% 6.25/6.48        True)
% 6.25/6.48  Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota),
% 6.25/6.48    Or (Eq (subset a a_1) False) (Eq (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1)) True)
% 6.25/6.48  Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Iota),
% 6.25/6.48    Or (Eq (subset a a_1) False) (Eq (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)) True)
% 6.25/6.48  Clause #34 (by superposition #[32, 25]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.25/6.48    Or (Eq (subset (cartesian_product2 a (skS.0 2 a_1 a_2 a_3)) (cartesian_product2 a (skS.0 3 a_1 a_2 a_3 a_4))) True)
% 6.25/6.48      (Eq False True)
% 6.25/6.48  Clause #40 (by superposition #[26, 33]): ∀ (a a_1 a_2 : Iota),
% 6.25/6.48    Or (Eq (subset (cartesian_product2 (skS.0 0 a) a_1) (cartesian_product2 (skS.0 1 a a_2) a_1)) True) (Eq False True)
% 6.25/6.48  Clause #47 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (subset (cartesian_product2 (skS.0 0 a) a_1) (cartesian_product2 (skS.0 1 a a_2) a_1)) True
% 6.25/6.48  Clause #48 (by superposition #[47, 11]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.25/6.48    Or (Eq (subset (cartesian_product2 (skS.0 0 a) a_1) a_2) True)
% 6.25/6.48      (Or (Eq True False) (Eq (subset (cartesian_product2 (skS.0 1 a a_3) a_1) a_2) False))
% 6.25/6.48  Clause #69 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.25/6.48    Or (Eq (subset (cartesian_product2 (skS.0 0 a) a_1) a_2) True)
% 6.25/6.48      (Eq (subset (cartesian_product2 (skS.0 1 a a_3) a_1) a_2) False)
% 6.25/6.48  Clause #81 (by clausification #[34]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.25/6.48    Eq (subset (cartesian_product2 a (skS.0 2 a_1 a_2 a_3)) (cartesian_product2 a (skS.0 3 a_1 a_2 a_3 a_4))) True
% 6.25/6.48  Clause #82 (by superposition #[81, 69]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 6.25/6.48    Or
% 6.25/6.48      (Eq
% 6.25/6.48        (subset (cartesian_product2 (skS.0 0 a) (skS.0 2 a_1 a_2 a_3))
% 6.25/6.48          (cartesian_product2 (skS.0 1 a a_4) (skS.0 3 a_1 a_2 a_3 a_5)))
% 6.25/6.48        True)
% 6.25/6.48      (Eq True False)
% 6.25/6.48  Clause #509 (by clausification #[82]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 6.25/6.48    Eq
% 6.25/6.48      (subset (cartesian_product2 (skS.0 0 a) (skS.0 2 a_1 a_2 a_3))
% 6.25/6.48        (cartesian_product2 (skS.0 1 a a_4) (skS.0 3 a_1 a_2 a_3 a_5)))
% 6.25/6.48      True
% 6.25/6.48  Clause #510 (by superposition #[509, 24]): Eq True False
% 6.25/6.48  Clause #514 (by clausification #[510]): False
% 6.25/6.48  SZS output end Proof for theBenchmark.p
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