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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SYO892_15 : TPTP v9.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n002.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 08:09:43 PM UTC 2025

% Result   : Theorem 3.58s 3.74s
% Output   : Proof 3.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYO892_15 : TPTP v9.2.0. Released v8.2.0.
% 0.12/0.13  % Command    : duper %s
% 0.13/0.34  % Computer : n002.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   : Fri Oct  3 13:09:38 EDT 2025
% 0.13/0.35  % CPUTime    : 
% 3.58/3.74  SZS status Theorem for theBenchmark.p
% 3.58/3.74  SZS output start Proof for theBenchmark.p
% 3.58/3.74  Clause #1 (by assumption #[]): Eq
% 3.58/3.74    (∀ (W V : «$ki_world») (X : Iota),
% 3.58/3.74      And («$ki_exists_in_world_$i» W X) («$ki_accessible» W V) → «$ki_exists_in_world_$i» V X)
% 3.58/3.74    True
% 3.58/3.74  Clause #3 (by assumption #[]): Eq
% 3.58/3.74    (Not
% 3.58/3.74      ((Exists fun W => And («$ki_accessible» «$ki_local_world» W) (∀ (X : Iota), «$ki_exists_in_world_$i» W X → f W X)) →
% 3.58/3.74        ∀ (X : Iota),
% 3.58/3.74          «$ki_exists_in_world_$i» «$ki_local_world» X →
% 3.58/3.74            Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W X)))
% 3.58/3.74    True
% 3.58/3.74  Clause #7 (by clausification #[1]): ∀ (a : «$ki_world»),
% 3.58/3.74    Eq
% 3.58/3.74      (∀ (V : «$ki_world») (X : Iota),
% 3.58/3.74        And («$ki_exists_in_world_$i» a X) («$ki_accessible» a V) → «$ki_exists_in_world_$i» V X)
% 3.58/3.74      True
% 3.58/3.74  Clause #8 (by clausification #[7]): ∀ (a a_1 : «$ki_world»),
% 3.58/3.74    Eq (∀ (X : Iota), And («$ki_exists_in_world_$i» a X) («$ki_accessible» a a_1) → «$ki_exists_in_world_$i» a_1 X) True
% 3.58/3.74  Clause #9 (by clausification #[8]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.58/3.74    Eq (And («$ki_exists_in_world_$i» a a_1) («$ki_accessible» a a_2) → «$ki_exists_in_world_$i» a_2 a_1) True
% 3.58/3.74  Clause #10 (by clausification #[9]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.58/3.74    Or (Eq (And («$ki_exists_in_world_$i» a a_1) («$ki_accessible» a a_2)) False)
% 3.58/3.74      (Eq («$ki_exists_in_world_$i» a_2 a_1) True)
% 3.58/3.74  Clause #11 (by clausification #[10]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.58/3.74    Or (Eq («$ki_exists_in_world_$i» a a_1) True)
% 3.58/3.74      (Or (Eq («$ki_exists_in_world_$i» a_2 a_1) False) (Eq («$ki_accessible» a_2 a) False))
% 3.58/3.74  Clause #16 (by clausification #[3]): Eq
% 3.58/3.74    ((Exists fun W => And («$ki_accessible» «$ki_local_world» W) (∀ (X : Iota), «$ki_exists_in_world_$i» W X → f W X)) →
% 3.58/3.74      ∀ (X : Iota),
% 3.58/3.74        «$ki_exists_in_world_$i» «$ki_local_world» X → Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W X))
% 3.58/3.74    False
% 3.58/3.74  Clause #17 (by clausification #[16]): Eq (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (∀ (X : Iota), «$ki_exists_in_world_$i» W X → f W X))
% 3.58/3.74    True
% 3.58/3.74  Clause #18 (by clausification #[16]): Eq
% 3.58/3.74    (∀ (X : Iota),
% 3.58/3.74      «$ki_exists_in_world_$i» «$ki_local_world» X → Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W X))
% 3.58/3.74    False
% 3.58/3.74  Clause #19 (by clausification #[17]): ∀ (a : «$ki_world»),
% 3.58/3.74    Eq
% 3.58/3.74      (And («$ki_accessible» «$ki_local_world» (skS.0 2 a))
% 3.58/3.74        (∀ (X : Iota), «$ki_exists_in_world_$i» (skS.0 2 a) X → f (skS.0 2 a) X))
% 3.58/3.74      True
% 3.58/3.74  Clause #20 (by clausification #[19]): ∀ (a : «$ki_world»), Eq (∀ (X : Iota), «$ki_exists_in_world_$i» (skS.0 2 a) X → f (skS.0 2 a) X) True
% 3.58/3.74  Clause #21 (by clausification #[19]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 2 a)) True
% 3.58/3.74  Clause #22 (by clausification #[20]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1 → f (skS.0 2 a) a_1) True
% 3.58/3.74  Clause #23 (by clausification #[22]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) (Eq (f (skS.0 2 a) a_1) True)
% 3.58/3.74  Clause #28 (by clausification #[18]): ∀ (a : Iota),
% 3.58/3.74    Eq
% 3.58/3.74      (Not
% 3.58/3.74        («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 3 a) →
% 3.58/3.74          Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W (skS.0 3 a))))
% 3.58/3.74      True
% 3.58/3.74  Clause #29 (by clausification #[28]): ∀ (a : Iota),
% 3.58/3.74    Eq
% 3.58/3.74      («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 3 a) →
% 3.58/3.74        Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W (skS.0 3 a)))
% 3.58/3.74      False
% 3.58/3.74  Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 3 a)) True
% 3.58/3.74  Clause #31 (by clausification #[29]): ∀ (a : Iota), Eq (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W (skS.0 3 a))) False
% 3.58/3.74  Clause #32 (by superposition #[30, 11]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.58/3.74    Or (Eq («$ki_exists_in_world_$i» a (skS.0 3 a_1)) True)
% 3.58/3.75      (Or (Eq True False) (Eq («$ki_accessible» «$ki_local_world» a) False))
% 3.58/3.75  Clause #33 (by clausification #[32]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.58/3.75    Or (Eq («$ki_exists_in_world_$i» a (skS.0 3 a_1)) True) (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.58/3.75  Clause #34 (by superposition #[33, 21]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) (skS.0 3 a_1)) True) (Eq False True)
% 3.58/3.75  Clause #36 (by clausification #[34]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» (skS.0 2 a) (skS.0 3 a_1)) True
% 3.58/3.75  Clause #37 (by superposition #[36, 23]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (f (skS.0 2 a) (skS.0 3 a_1)) True)
% 3.58/3.75  Clause #39 (by clausification #[37]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (f (skS.0 2 a) (skS.0 3 a_1)) True
% 3.58/3.75  Clause #40 (by clausification #[31]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (And («$ki_accessible» «$ki_local_world» a) (f a (skS.0 3 a_1))) False
% 3.58/3.75  Clause #41 (by clausification #[40]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (f a (skS.0 3 a_1)) False)
% 3.58/3.75  Clause #42 (by superposition #[41, 21]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (f (skS.0 2 a) (skS.0 3 a_1)) False) (Eq False True)
% 3.58/3.75  Clause #45 (by clausification #[42]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (f (skS.0 2 a) (skS.0 3 a_1)) False
% 3.58/3.75  Clause #46 (by superposition #[45, 39]): Eq False True
% 3.58/3.75  Clause #47 (by clausification #[46]): False
% 3.58/3.75  SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------