%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU303+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n024.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 : Thu Aug 31 16:24:16 EDT 2023

% Result   : Theorem 0.46s 1.56s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   23 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :   39 (   3 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   38 (  14   ~;  11   |;   7   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   6   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   12 (   0 sgn;   8   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    relation: $i > $o ).

tff(decl_23,type,
    function: $i > $o ).

tff(decl_24,type,
    finite: $i > $o ).

tff(decl_25,type,
    relation_image: ( $i * $i ) > $i ).

tff(decl_26,type,
    relation_dom: $i > $i ).

tff(decl_27,type,
    relation_rng: $i > $i ).

tff(decl_28,type,
    esk1_0: $i ).

tff(decl_29,type,
    esk2_0: $i ).

fof(t26_finset_1,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( finite(relation_dom(X1))
       => finite(relation_rng(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).

fof(fc13_finset_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1)
        & finite(X2) )
     => finite(relation_image(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).

fof(t146_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ( finite(relation_dom(X1))
         => finite(relation_rng(X1)) ) ),
    inference(assume_negation,[status(cth)],[t26_finset_1]) ).

fof(c_0_4,plain,
    ! [X3,X4] :
      ( ~ relation(X3)
      | ~ function(X3)
      | ~ finite(X4)
      | finite(relation_image(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_finset_1])]) ).

fof(c_0_5,plain,
    ! [X6] :
      ( ~ relation(X6)
      | relation_image(X6,relation_dom(X6)) = relation_rng(X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t146_relat_1])]) ).

fof(c_0_6,negated_conjecture,
    ( relation(esk2_0)
    & function(esk2_0)
    & finite(relation_dom(esk2_0))
    & ~ finite(relation_rng(esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_7,plain,
    ( finite(relation_image(X1,X2))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ finite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    ( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ~ finite(relation_rng(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( finite(relation_rng(X1))
    | ~ finite(relation_dom(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    finite(relation_dom(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,negated_conjecture,
    function(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,negated_conjecture,
    relation(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.84  % Problem    : SEU303+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.84  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/1.31  % Computer : n024.cluster.edu
% 0.14/1.31  % Model    : x86_64 x86_64
% 0.14/1.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/1.31  % Memory   : 8042.1875MB
% 0.14/1.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/1.31  % CPULimit   : 300
% 0.14/1.31  % WCLimit    : 300
% 0.14/1.31  % DateTime   : Wed Aug 23 12:12:11 EDT 2023
% 0.14/1.31  % CPUTime  : 
% 0.46/1.54  start to proof: theBenchmark
% 0.46/1.56  % Version  : CSE_E---1.5
% 0.46/1.56  % Problem  : theBenchmark.p
% 0.46/1.56  % Proof found
% 0.46/1.56  % SZS status Theorem for theBenchmark.p
% 0.46/1.56  % SZS output start Proof
% See solution above
% 0.46/1.56  % Total time : 0.005000 s
% 0.46/1.56  % SZS output end Proof
% 0.46/1.56  % Total time : 0.008000 s
%------------------------------------------------------------------------------