%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN068+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n023.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 Sep  1 01:49:54 EDT 2023

% Result   : Theorem 0.18s 0.58s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   23 (   4 unt;   7 typ;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   44 (  18   ~;  10   |;  13   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   6   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   17 (   0 sgn;   6   !;   7   ?;   0   :)

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

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

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

tff(decl_25,type,
    big_j: $i > $o ).

tff(decl_26,type,
    esk1_1: $i > $i ).

tff(decl_27,type,
    esk2_1: $i > $i ).

tff(decl_28,type,
    esk3_0: $i ).

fof(pel44,conjecture,
    ? [X1] :
      ( big_j(X1)
      & ~ big_f(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel44) ).

fof(pel44_1,axiom,
    ! [X1] :
      ( big_f(X1)
     => ( ? [X2] :
            ( big_g(X2)
            & big_h(X1,X2) )
        & ? [X3] :
            ( big_g(X3)
            & ~ big_h(X1,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel44_1) ).

fof(pel44_2,axiom,
    ? [X1] :
      ( big_j(X1)
      & ! [X2] :
          ( big_g(X2)
         => big_h(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel44_2) ).

fof(c_0_3,negated_conjecture,
    ~ ? [X1] :
        ( big_j(X1)
        & ~ big_f(X1) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[pel44])]) ).

fof(c_0_4,plain,
    ! [X1] :
      ( big_f(X1)
     => ( ? [X2] :
            ( big_g(X2)
            & big_h(X1,X2) )
        & ? [X3] :
            ( big_g(X3)
            & ~ big_h(X1,X3) ) ) ),
    inference(fof_simplification,[status(thm)],[pel44_1]) ).

fof(c_0_5,negated_conjecture,
    ! [X9] :
      ( ~ big_j(X9)
      | big_f(X9) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])]) ).

fof(c_0_6,plain,
    ! [X8] :
      ( big_j(esk3_0)
      & ( ~ big_g(X8)
        | big_h(esk3_0,X8) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel44_2])])])]) ).

fof(c_0_7,plain,
    ! [X4] :
      ( ( big_g(esk1_1(X4))
        | ~ big_f(X4) )
      & ( big_h(X4,esk1_1(X4))
        | ~ big_f(X4) )
      & ( big_g(esk2_1(X4))
        | ~ big_f(X4) )
      & ( ~ big_h(X4,esk2_1(X4))
        | ~ big_f(X4) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

cnf(c_0_8,negated_conjecture,
    ( big_f(X1)
    | ~ big_j(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    big_j(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( ~ big_h(X1,esk2_1(X1))
    | ~ big_f(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( big_h(esk3_0,X1)
    | ~ big_g(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,negated_conjecture,
    big_f(esk3_0),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    ~ big_g(esk2_1(esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).

cnf(c_0_14,plain,
    ( big_g(esk2_1(X1))
    | ~ big_f(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_15,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SYN068+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n023.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    : 300
% 0.12/0.33  % DateTime   : Sat Aug 26 20:10:56 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.57  start to proof: theBenchmark
% 0.18/0.58  % Version  : CSE_E---1.5
% 0.18/0.58  % Problem  : theBenchmark.p
% 0.18/0.58  % Proof found
% 0.18/0.58  % SZS status Theorem for theBenchmark.p
% 0.18/0.58  % SZS output start Proof
% See solution above
% 0.18/0.58  % Total time : 0.004000 s
% 0.18/0.58  % SZS output end Proof
% 0.18/0.58  % Total time : 0.007000 s
%------------------------------------------------------------------------------