%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN362+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 : n004.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 01:51:24 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   12 (   4 unt;   4 typ;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   20 (  10   ~;   2   |;   4   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   17 (   2 sgn;   7   !;   6   ?;   0   :)

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

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

tff(decl_24,type,
    esk1_1: $i > $i ).

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

fof(x2113,conjecture,
    ( ( ! [X1] :
        ? [X2] : big_r(X1,X2)
      & ? [X3] :
        ! [X4] :
          ( big_p(X4)
         => ~ big_r(X3,X4) ) )
   => ? [X4] : ~ big_p(X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2113) ).

fof(c_0_1,negated_conjecture,
    ~ ( ( ! [X1] :
          ? [X2] : big_r(X1,X2)
        & ? [X3] :
          ! [X4] :
            ( big_p(X4)
           => ~ big_r(X3,X4) ) )
     => ? [X4] : ~ big_p(X4) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[x2113])]) ).

fof(c_0_2,negated_conjecture,
    ! [X5,X8,X9] :
      ( big_r(X5,esk1_1(X5))
      & ( ~ big_p(X8)
        | ~ big_r(esk2_0,X8) )
      & big_p(X9) ),
    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_p(X1)
    | ~ big_r(esk2_0,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

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

cnf(c_0_5,negated_conjecture,
    ~ big_r(esk2_0,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_4])]) ).

cnf(c_0_6,negated_conjecture,
    big_r(X1,esk1_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SYN362+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n004.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 19:20:22 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  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 : 0.004000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.006000 s
%------------------------------------------------------------------------------