%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN365+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n031.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 01:51:25 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   19 (   5 unt;   6 typ;   0 def)
%            Number of atoms       :   44 (   0 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :   47 (  16   ~;  10   |;  13   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   5   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :   18 (   0 sgn;   9   !;   4   ?;   0   :)

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

tff(decl_23,type,
    h: $i > $i ).

tff(decl_24,type,
    g: $i > $i ).

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

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

tff(decl_27,type,
    esk2_0: $i ).

fof(x2116,conjecture,
    ( ( ! [X1] :
        ? [X2] :
          ( big_p(X1)
         => ( big_r(X1,g(h(X2)))
            & big_p(X2) ) )
      & ! [X3] :
          ( big_p(X3)
         => ( big_p(g(X3))
            & big_p(h(X3)) ) ) )
   => ! [X1] :
        ( big_p(X1)
       => ? [X2] :
            ( big_r(X1,X2)
            & big_p(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2116) ).

fof(c_0_1,negated_conjecture,
    ~ ( ( ! [X1] :
          ? [X2] :
            ( big_p(X1)
           => ( big_r(X1,g(h(X2)))
              & big_p(X2) ) )
        & ! [X3] :
            ( big_p(X3)
           => ( big_p(g(X3))
              & big_p(h(X3)) ) ) )
     => ! [X1] :
          ( big_p(X1)
         => ? [X2] :
              ( big_r(X1,X2)
              & big_p(X2) ) ) ),
    inference(assume_negation,[status(cth)],[x2116]) ).

fof(c_0_2,negated_conjecture,
    ! [X4,X6,X8] :
      ( ( big_r(X4,g(h(esk1_1(X4))))
        | ~ big_p(X4) )
      & ( big_p(esk1_1(X4))
        | ~ big_p(X4) )
      & ( big_p(g(X6))
        | ~ big_p(X6) )
      & ( big_p(h(X6))
        | ~ big_p(X6) )
      & big_p(esk2_0)
      & ( ~ big_r(esk2_0,X8)
        | ~ big_p(X8) ) ),
    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_r(esk2_0,X1)
    | ~ big_p(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
    ( big_r(X1,g(h(esk1_1(X1))))
    | ~ big_p(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_5,negated_conjecture,
    big_p(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_6,negated_conjecture,
    ~ big_p(g(h(esk1_1(esk2_0)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_5])]) ).

cnf(c_0_7,negated_conjecture,
    ( big_p(g(X1))
    | ~ big_p(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_8,negated_conjecture,
    ~ big_p(h(esk1_1(esk2_0))),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,negated_conjecture,
    ( big_p(h(X1))
    | ~ big_p(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_10,negated_conjecture,
    ~ big_p(esk1_1(esk2_0)),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,negated_conjecture,
    ( big_p(esk1_1(X1))
    | ~ big_p(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_5])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SYN365+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 18:32:08 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.004000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.006000 s
%------------------------------------------------------------------------------