%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN333+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 : n017.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 01:51:11 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   14 (   3 unt;   6 typ;   0 def)
%            Number of atoms       :   35 (   0 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :   42 (  15   ~;  12   |;  11   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 2-2 aty)
%            Number of variables   :   18 (   4 sgn;   6   !;   4   ?;   0   :)

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

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

tff(decl_24,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_25,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_26,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk4_2: ( $i * $i ) > $i ).

fof(church_46_14_5,conjecture,
    ? [X1,X2] :
    ! [X3] :
      ( big_f(X1,X2)
     => ( big_f(X2,X3)
        & big_f(X3,X3)
        & ( ( big_f(X1,X2)
            & big_g(X1,X2) )
         => ( big_g(X1,X3)
            & big_g(X3,X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_14_5) ).

fof(c_0_1,negated_conjecture,
    ~ ? [X1,X2] :
      ! [X3] :
        ( big_f(X1,X2)
       => ( big_f(X2,X3)
          & big_f(X3,X3)
          & ( ( big_f(X1,X2)
              & big_g(X1,X2) )
           => ( big_g(X1,X3)
              & big_g(X3,X3) ) ) ) ),
    inference(assume_negation,[status(cth)],[church_46_14_5]) ).

fof(c_0_2,negated_conjecture,
    ! [X4,X5,X6,X7] :
      ( big_f(X4,X5)
      & ( big_f(X6,X7)
        | ~ big_f(X7,esk1_2(X6,X7))
        | ~ big_f(esk2_2(X6,X7),esk2_2(X6,X7)) )
      & ( big_g(X6,X7)
        | ~ big_f(X7,esk1_2(X6,X7))
        | ~ big_f(esk2_2(X6,X7),esk2_2(X6,X7)) )
      & ( ~ big_g(X6,esk3_2(X6,X7))
        | ~ big_g(esk4_2(X6,X7),esk4_2(X6,X7))
        | ~ big_f(X7,esk1_2(X6,X7))
        | ~ big_f(esk2_2(X6,X7),esk2_2(X6,X7)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])])]) ).

cnf(c_0_3,negated_conjecture,
    ( big_g(X1,X2)
    | ~ big_f(X2,esk1_2(X1,X2))
    | ~ big_f(esk2_2(X1,X2),esk2_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
    big_f(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_5,negated_conjecture,
    ( ~ big_g(X1,esk3_2(X1,X2))
    | ~ big_g(esk4_2(X1,X2),esk4_2(X1,X2))
    | ~ big_f(X2,esk1_2(X1,X2))
    | ~ big_f(esk2_2(X1,X2),esk2_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_6,negated_conjecture,
    big_g(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_4]),c_0_4])]) ).

cnf(c_0_7,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_4]),c_0_4])]),c_0_6]),c_0_6])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN333+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n017.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   : Sat Aug 26 17:55:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.003000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.006000 s
%------------------------------------------------------------------------------