%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL678+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 : Thu Aug 31 06:59:02 EDT 2023

% Result   : Theorem 0.18s 0.56s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   16 (   5 unt;   5 typ;   0 def)
%            Number of atoms       :   35 (   0 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :   57 (  33   ~;  21   |;   3   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   4   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   20 (   1 sgn;  12   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    r1: ( $i * $i ) > $o ).

tff(decl_23,type,
    p1: $i > $o ).

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

tff(decl_25,type,
    esk2_1: $i > $i ).

tff(decl_26,type,
    esk3_1: $i > $i ).

fof(main,conjecture,
    ~ ? [X1] :
        ~ ( ~ $true
          | ~ ! [X2] :
                ( ~ r1(X1,X2)
                | ~ $true
                | ~ ! [X1] :
                      ( ~ r1(X2,X1)
                      | ! [X2] :
                          ( ~ r1(X1,X2)
                          | p1(X2) )
                      | ~ ! [X2] :
                            ( ~ r1(X1,X2)
                            | p1(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).

fof(reflexivity,axiom,
    ! [X1] : r1(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

fof(c_0_2,negated_conjecture,
    ~ ~ ? [X1] :
          ~ ~ ! [X2] :
                ( ~ r1(X1,X2)
                | ~ ! [X1] :
                      ( ~ r1(X2,X1)
                      | ! [X2] :
                          ( ~ r1(X1,X2)
                          | p1(X2) )
                      | ~ ! [X2] :
                            ( ~ r1(X1,X2)
                            | p1(X2) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[main])]) ).

fof(c_0_3,negated_conjecture,
    ! [X9,X12] :
      ( ( r1(X9,esk2_1(X9))
        | ~ r1(esk1_0,X9) )
      & ( r1(esk2_1(X9),esk3_1(X9))
        | ~ r1(esk1_0,X9) )
      & ( ~ p1(esk3_1(X9))
        | ~ r1(esk1_0,X9) )
      & ( ~ r1(esk2_1(X9),X12)
        | p1(X12)
        | ~ r1(esk1_0,X9) ) ),
    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_2])])])])]) ).

cnf(c_0_4,negated_conjecture,
    ( p1(X2)
    | ~ r1(esk2_1(X1),X2)
    | ~ r1(esk1_0,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_5,negated_conjecture,
    ( r1(esk2_1(X1),esk3_1(X1))
    | ~ r1(esk1_0,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,negated_conjecture,
    ( ~ p1(esk3_1(X1))
    | ~ r1(esk1_0,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

fof(c_0_7,plain,
    ! [X4] : r1(X4,X4),
    inference(variable_rename,[status(thm)],[reflexivity]) ).

cnf(c_0_8,negated_conjecture,
    ~ r1(esk1_0,X1),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).

cnf(c_0_9,plain,
    r1(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_8,c_0_9]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL678+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Thu Aug 24 20:33:21 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.55  start to proof: theBenchmark
% 0.18/0.56  % Version  : CSE_E---1.5
% 0.18/0.56  % Problem  : theBenchmark.p
% 0.18/0.56  % Proof found
% 0.18/0.56  % SZS status Theorem for theBenchmark.p
% 0.18/0.56  % SZS output start Proof
% See solution above
% 0.18/0.57  % Total time : 0.004000 s
% 0.18/0.57  % SZS output end Proof
% 0.18/0.57  % Total time : 0.007000 s
%------------------------------------------------------------------------------