%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUN069+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 : Wed May 31 12:31:15 EDT 2023

% Result   : Theorem 0.29s 0.59s
% Output   : CNFRefutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   21 (   7 unt;   0 def)
%            Number of atoms       :   49 (  14 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   48 (  20   ~;  11   |;  16   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 1-1 aty)
%            Number of variables   :   41 (;  32   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( ~ r2(X11,X12)
        & X12 != Y21 )
      | ( r2(X11,X12)
        & X12 = Y21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X5] :
    ? [Y8] :
      ( ? [Y17] :
          ( r1(Y17)
          & r4(X5,Y17,Y8) )
      & ? [Y18] :
          ( r1(Y18)
          & Y8 = Y18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ? [Y1] :
      ( Y1 = Y1
      & ? [Y2] :
          ( r1(Y2)
          & r2(Y2,Y1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ? [Y1] :
        ( Y1 = Y1
        & ? [Y2] :
            ( r1(Y2)
            & r2(Y2,Y1) ) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f19,plain,
    ! [X11,Y21,X12] :
      ( pd0_1(X12,Y21,X11)
     => ( ~ r2(X11,X12)
        & X12 != Y21 ) ),
    introduced(predicate_definition,[f2]) ).

fof(f20,plain,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( pd0_1(X12,Y21,X11)
      | ( r2(X11,X12)
        & X12 = Y21 ) ),
    inference(formula_renaming,[status(thm)],[f2,f19]) ).

fof(f21,plain,
    ! [X11,X12] :
      ( pd0_1(X12,sk0_1(X11),X11)
      | ( r2(X11,X12)
        & X12 = sk0_1(X11) ) ),
    inference(skolemization,[status(esa)],[f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( pd0_1(X0,sk0_1(X1),X1)
      | r2(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f51,plain,
    ! [X5] :
      ( r1(sk0_15(X5))
      & r4(X5,sk0_15(X5),sk0_14(X5))
      & r1(sk0_16(X5))
      & sk0_14(X5) = sk0_16(X5) ),
    inference(skolemization,[status(esa)],[f9]) ).

fof(f54,plain,
    ! [X0] : r1(sk0_16(X0)),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f55,plain,
    ! [X0] : sk0_14(X0) = sk0_16(X0),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f64,plain,
    ! [Y1] :
      ( Y1 != Y1
      | ! [Y2] :
          ( ~ r1(Y2)
          | ~ r2(Y2,Y1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( X0 != X0
      | ~ r1(X1)
      | ~ r2(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f69,plain,
    ! [X11,Y21,X12] :
      ( ~ pd0_1(X12,Y21,X11)
      | ( ~ r2(X11,X12)
        & X12 != Y21 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ r1(X0)
      | ~ r2(X0,X1) ),
    inference(trivial_equality_resolution,[status(esa)],[f65]) ).

fof(f85,plain,
    ! [X0,X1] : ~ pd0_1(X0,X0,X1),
    inference(destructive_equality_resolution,[status(esa)],[f71]) ).

fof(f89,plain,
    ! [X0] : r1(sk0_14(X0)),
    inference(backward_demodulation,[status(thm)],[f55,f54]) ).

fof(f90,plain,
    ! [X0] : r2(X0,sk0_1(X0)),
    inference(resolution,[status(thm)],[f22,f85]) ).

fof(f93,plain,
    ! [X0] : ~ r1(X0),
    inference(resolution,[status(thm)],[f90,f83]) ).

fof(f94,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f89,f93]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUN069+2 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue May 30 10:43:22 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.5.1
% 0.29/0.59  % Refutation found
% 0.29/0.59  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.29/0.59  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.29/0.59  % Elapsed time: 0.022661 seconds
% 0.29/0.59  % CPU time: 0.031050 seconds
% 0.29/0.59  % Memory used: 14.456 MB
%------------------------------------------------------------------------------