%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN317+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 : n001.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 01:51:04 EDT 2023

% Result   : Theorem 0.21s 0.61s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   15 (   3 unt;   5 typ;   0 def)
%            Number of atoms       :   33 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :   35 (  12   ~;  13   |;   4   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   15 (   6 sgn;   3   !;   6   ?;   0   :)

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

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

tff(decl_24,type,
    esk1_0: $i ).

tff(decl_25,type,
    esk2_0: $i ).

tff(decl_26,type,
    esk3_0: $i ).

fof(church_46_2_3,conjecture,
    ( ? [X1] :
        ( big_f(X1)
       => big_g(X1) )
  <=> ? [X1,X2] :
        ( big_f(X1)
       => big_g(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_2_3) ).

fof(c_0_1,negated_conjecture,
    ~ ( ? [X1] :
          ( big_f(X1)
         => big_g(X1) )
    <=> ? [X1,X2] :
          ( big_f(X1)
         => big_g(X2) ) ),
    inference(assume_negation,[status(cth)],[church_46_2_3]) ).

fof(c_0_2,negated_conjecture,
    ! [X3,X4,X5] :
      ( ( big_f(X4)
        | big_f(X3) )
      & ( ~ big_g(X5)
        | big_f(X3) )
      & ( big_f(X4)
        | ~ big_g(X3) )
      & ( ~ big_g(X5)
        | ~ big_g(X3) )
      & ( ~ big_f(esk1_0)
        | big_g(esk1_0)
        | ~ big_f(esk2_0)
        | big_g(esk3_0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])]) ).

cnf(c_0_3,negated_conjecture,
    ( big_f(X1)
    | big_f(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
    ( big_g(esk1_0)
    | big_g(esk3_0)
    | ~ big_f(esk1_0)
    | ~ big_f(esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_5,negated_conjecture,
    big_f(X1),
    inference(ef,[status(thm)],[c_0_3]) ).

cnf(c_0_6,negated_conjecture,
    ( ~ big_g(X1)
    | ~ big_g(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_7,negated_conjecture,
    ( big_g(esk1_0)
    | big_g(esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_5]),c_0_5])]) ).

cnf(c_0_8,negated_conjecture,
    ~ big_g(X1),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_7,c_0_8]),c_0_8]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SYN317+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n001.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat Aug 26 21:29:31 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 0.21/0.61  % Version  : CSE_E---1.5
% 0.21/0.61  % Problem  : theBenchmark.p
% 0.21/0.61  % Proof found
% 0.21/0.61  % SZS status Theorem for theBenchmark.p
% 0.21/0.61  % SZS output start Proof
% See solution above
% 0.21/0.61  % Total time : 0.004000 s
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  % Total time : 0.006000 s
%------------------------------------------------------------------------------