%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN065+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 : n009.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 01:49:27 EDT 2023

% Result   : Theorem 0.53s 0.58s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   19 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :   31 (   0 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   32 (  14   ~;  13   |;   3   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   22 (   1 sgn;  11   !;   3   ?;   0   :)

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

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

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

tff(decl_25,type,
    esk1_1: $i > $i ).

tff(decl_26,type,
    esk2_1: $i > $i ).

tff(decl_27,type,
    esk3_0: $i ).

fof(pel36_3,axiom,
    ! [X1,X2] :
      ( ( big_f(X1,X2)
        | big_g(X1,X2) )
     => ! [X3] :
          ( ( big_f(X2,X3)
            | big_g(X2,X3) )
         => big_h(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel36_3) ).

fof(pel36_1,axiom,
    ! [X1] :
    ? [X2] : big_f(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel36_1) ).

fof(pel36,conjecture,
    ! [X1] :
    ? [X2] : big_h(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel36) ).

fof(c_0_3,plain,
    ! [X8,X9,X10] :
      ( ( ~ big_f(X9,X10)
        | big_h(X8,X10)
        | ~ big_f(X8,X9) )
      & ( ~ big_g(X9,X10)
        | big_h(X8,X10)
        | ~ big_f(X8,X9) )
      & ( ~ big_f(X9,X10)
        | big_h(X8,X10)
        | ~ big_g(X8,X9) )
      & ( ~ big_g(X9,X10)
        | big_h(X8,X10)
        | ~ big_g(X8,X9) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel36_3])])])]) ).

fof(c_0_4,plain,
    ! [X4] : big_f(X4,esk1_1(X4)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[pel36_1])]) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1] :
      ? [X2] : big_h(X1,X2),
    inference(assume_negation,[status(cth)],[pel36]) ).

cnf(c_0_6,plain,
    ( big_h(X3,X2)
    | ~ big_f(X1,X2)
    | ~ big_f(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_7,plain,
    big_f(X1,esk1_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_8,negated_conjecture,
    ! [X12] : ~ big_h(esk3_0,X12),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_9,plain,
    ( big_h(X1,X2)
    | ~ big_f(esk1_1(X1),X2) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    ~ big_h(esk3_0,X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,plain,
    big_h(X1,esk1_1(esk1_1(X1))),
    inference(spm,[status(thm)],[c_0_9,c_0_7]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN065+1 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n009.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 21:49:50 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.49/0.57  start to proof: theBenchmark
% 0.53/0.58  % Version  : CSE_E---1.5
% 0.53/0.58  % Problem  : theBenchmark.p
% 0.53/0.58  % Proof found
% 0.53/0.58  % SZS status Theorem for theBenchmark.p
% 0.53/0.58  % SZS output start Proof
% See solution above
% 0.53/0.58  % Total time : 0.004000 s
% 0.53/0.58  % SZS output end Proof
% 0.53/0.58  % Total time : 0.007000 s
%------------------------------------------------------------------------------