TSTP Solution File: SEU303+3 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU303+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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  : 600s
% DateTime : Tue Jul 19 12:40:10 EDT 2022

% Result   : Theorem 6.20s 6.39s
% Output   : CNFRefutation 6.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   32 (  12 unt;   0 def)
%            Number of atoms       :   74 (   7 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   70 (  28   ~;  23   |;  13   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   19 (   0 sgn  12   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fc13_finset_1,axiom,
    ! [A,B] :
      ( ( relation(A)
        & function(A)
        & finite(B) )
     => finite(relation_image(A,B)) ) ).

fof(t146_relat_1,axiom,
    ! [A] :
      ( relation(A)
     => relation_image(A,relation_dom(A)) = relation_rng(A) ) ).

fof(t26_finset_1,conjecture,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( finite(relation_dom(A))
       => finite(relation_rng(A)) ) ) ).

fof(subgoal_0,plain,
    ! [A] :
      ( ( relation(A)
        & function(A)
        & finite(relation_dom(A)) )
     => finite(relation_rng(A)) ),
    inference(strip,[],[t26_finset_1]) ).

fof(negate_0_0,plain,
    ~ ! [A] :
        ( ( relation(A)
          & function(A)
          & finite(relation_dom(A)) )
       => finite(relation_rng(A)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A] :
      ( ~ finite(relation_rng(A))
      & finite(relation_dom(A))
      & function(A)
      & relation(A) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ finite(relation_rng(skolemFOFtoCNF_A_21))
    & finite(relation_dom(skolemFOFtoCNF_A_21))
    & function(skolemFOFtoCNF_A_21)
    & relation(skolemFOFtoCNF_A_21) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    finite(relation_dom(skolemFOFtoCNF_A_21)),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    relation(skolemFOFtoCNF_A_21),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_4,plain,
    ! [A,B] :
      ( ~ finite(B)
      | ~ function(A)
      | ~ relation(A)
      | finite(relation_image(A,B)) ),
    inference(canonicalize,[],[fc13_finset_1]) ).

fof(normalize_0_5,plain,
    ! [A,B] :
      ( ~ finite(B)
      | ~ function(A)
      | ~ relation(A)
      | finite(relation_image(A,B)) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    function(skolemFOFtoCNF_A_21),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_7,plain,
    ! [A] :
      ( ~ relation(A)
      | relation_image(A,relation_dom(A)) = relation_rng(A) ),
    inference(canonicalize,[],[t146_relat_1]) ).

fof(normalize_0_8,plain,
    ! [A] :
      ( ~ relation(A)
      | relation_image(A,relation_dom(A)) = relation_rng(A) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ~ finite(relation_rng(skolemFOFtoCNF_A_21)),
    inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
    finite(relation_dom(skolemFOFtoCNF_A_21)),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    relation(skolemFOFtoCNF_A_21),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    ( ~ finite(B)
    | ~ function(A)
    | ~ relation(A)
    | finite(relation_image(A,B)) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ( ~ finite(X_187)
    | ~ function(skolemFOFtoCNF_A_21)
    | ~ relation(skolemFOFtoCNF_A_21)
    | finite(relation_image(skolemFOFtoCNF_A_21,X_187)) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_21)),bind(B,$fot(X_187))]]) ).

cnf(refute_0_4,plain,
    ( ~ finite(X_187)
    | ~ function(skolemFOFtoCNF_A_21)
    | finite(relation_image(skolemFOFtoCNF_A_21,X_187)) ),
    inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_21) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    function(skolemFOFtoCNF_A_21),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_6,plain,
    ( ~ finite(X_187)
    | finite(relation_image(skolemFOFtoCNF_A_21,X_187)) ),
    inference(resolve,[$cnf( function(skolemFOFtoCNF_A_21) )],[refute_0_5,refute_0_4]) ).

cnf(refute_0_7,plain,
    ( ~ finite(relation_dom(skolemFOFtoCNF_A_21))
    | finite(relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21))) ),
    inference(subst,[],[refute_0_6:[bind(X_187,$fot(relation_dom(skolemFOFtoCNF_A_21)))]]) ).

cnf(refute_0_8,plain,
    finite(relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21))),
    inference(resolve,[$cnf( finite(relation_dom(skolemFOFtoCNF_A_21)) )],[refute_0_0,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ relation(A)
    | relation_image(A,relation_dom(A)) = relation_rng(A) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ relation(skolemFOFtoCNF_A_21)
    | relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21)) = relation_rng(skolemFOFtoCNF_A_21) ),
    inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_A_21))]]) ).

cnf(refute_0_11,plain,
    relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21)) = relation_rng(skolemFOFtoCNF_A_21),
    inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_21) )],[refute_0_1,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21)) != relation_rng(skolemFOFtoCNF_A_21)
    | ~ finite(relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21)))
    | finite(relation_rng(skolemFOFtoCNF_A_21)) ),
    introduced(tautology,[equality,[$cnf( finite(relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21))) ),[0],$fot(relation_rng(skolemFOFtoCNF_A_21))]]) ).

cnf(refute_0_13,plain,
    ( ~ finite(relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21)))
    | finite(relation_rng(skolemFOFtoCNF_A_21)) ),
    inference(resolve,[$cnf( $equal(relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21)),relation_rng(skolemFOFtoCNF_A_21)) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    finite(relation_rng(skolemFOFtoCNF_A_21)),
    inference(resolve,[$cnf( finite(relation_image(skolemFOFtoCNF_A_21,relation_dom(skolemFOFtoCNF_A_21))) )],[refute_0_8,refute_0_13]) ).

cnf(refute_0_15,plain,
    ~ finite(relation_rng(skolemFOFtoCNF_A_21)),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( finite(relation_rng(skolemFOFtoCNF_A_21)) )],[refute_0_14,refute_0_15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU303+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jun 19 06:49:44 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.20/6.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.20/6.39  
% 6.20/6.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.20/6.39  
%------------------------------------------------------------------------------