%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM303+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 12:24:49 EDT 2023

% Result   : Theorem 0.20s 0.40s
% Output   : CNFRefutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   36 (  14 unt;   0 def)
%            Number of atoms       :   77 (   9 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   77 (  36   ~;  29   |;   7   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   48 (;  48   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f22,axiom,
    rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f268,axiom,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f276,axiom,
    ! [Ds,Os,Db,Ob] :
      ( rdn_positive_less(Os,Ob)
     => rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f281,axiom,
    ! [X,Y,RDN_X,RDN_Y] :
      ( ( rdn_translate(X,rdn_pos(RDN_X))
        & rdn_translate(Y,rdn_pos(RDN_Y))
        & rdn_positive_less(RDN_X,RDN_Y) )
     => less(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f284,axiom,
    ! [X,Y] :
      ( less(X,Y)
    <=> ( ~ less(Y,X)
        & Y != X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f402,conjecture,
    n31 != n21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f403,negated_conjecture,
    ~ ( n31 != n21 ),
    inference(negated_conjecture,[status(cth)],[f402]) ).

fof(f425,plain,
    rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f435,plain,
    rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f671,plain,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    inference(cnf_transformation,[status(esa)],[f268]) ).

fof(f681,plain,
    ! [Ds,Os,Db,Ob] :
      ( ~ rdn_positive_less(Os,Ob)
      | rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
    inference(pre_NNF_transformation,[status(esa)],[f276]) ).

fof(f682,plain,
    ! [Os,Ob] :
      ( ~ rdn_positive_less(Os,Ob)
      | ! [Ds,Db] : rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
    inference(miniscoping,[status(esa)],[f681]) ).

fof(f683,plain,
    ! [X0,X1,X2,X3] :
      ( ~ rdn_positive_less(X0,X1)
      | rdn_positive_less(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1)) ),
    inference(cnf_transformation,[status(esa)],[f682]) ).

fof(f694,plain,
    ! [X,Y,RDN_X,RDN_Y] :
      ( ~ rdn_translate(X,rdn_pos(RDN_X))
      | ~ rdn_translate(Y,rdn_pos(RDN_Y))
      | ~ rdn_positive_less(RDN_X,RDN_Y)
      | less(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f281]) ).

fof(f695,plain,
    ! [X,Y] :
      ( ! [RDN_X,RDN_Y] :
          ( ~ rdn_translate(X,rdn_pos(RDN_X))
          | ~ rdn_translate(Y,rdn_pos(RDN_Y))
          | ~ rdn_positive_less(RDN_X,RDN_Y) )
      | less(X,Y) ),
    inference(miniscoping,[status(esa)],[f694]) ).

fof(f696,plain,
    ! [X0,X1,X2,X3] :
      ( ~ rdn_translate(X0,rdn_pos(X1))
      | ~ rdn_translate(X2,rdn_pos(X3))
      | ~ rdn_positive_less(X1,X3)
      | less(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f695]) ).

fof(f703,plain,
    ! [X,Y] :
      ( ( ~ less(X,Y)
        | ( ~ less(Y,X)
          & Y != X ) )
      & ( less(X,Y)
        | less(Y,X)
        | Y = X ) ),
    inference(NNF_transformation,[status(esa)],[f284]) ).

fof(f704,plain,
    ( ! [X,Y] :
        ( ~ less(X,Y)
        | ( ~ less(Y,X)
          & Y != X ) )
    & ! [X,Y] :
        ( less(X,Y)
        | less(Y,X)
        | Y = X ) ),
    inference(miniscoping,[status(esa)],[f703]) ).

fof(f706,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | X1 != X0 ),
    inference(cnf_transformation,[status(esa)],[f704]) ).

fof(f861,plain,
    n31 = n21,
    inference(cnf_transformation,[status(esa)],[f403]) ).

fof(f862,plain,
    ! [X0] : ~ less(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f706]) ).

fof(f864,plain,
    rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
    inference(forward_demodulation,[status(thm)],[f861,f435]) ).

fof(f1966,plain,
    ! [X0,X1] :
      ( ~ rdn_translate(X0,rdn_pos(X1))
      | ~ rdn_positive_less(X1,rdn(rdnn(n1),rdnn(n3)))
      | less(X0,n21) ),
    inference(resolution,[status(thm)],[f696,f864]) ).

fof(f1976,plain,
    ! [X0,X1,X2] :
      ( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2)))
      | less(X0,n21)
      | ~ rdn_positive_less(X2,rdnn(n3)) ),
    inference(resolution,[status(thm)],[f1966,f683]) ).

fof(f2268,plain,
    ( spl0_123
  <=> less(n21,n21) ),
    introduced(split_symbol_definition) ).

fof(f2269,plain,
    ( less(n21,n21)
    | ~ spl0_123 ),
    inference(component_clause,[status(thm)],[f2268]) ).

fof(f2873,plain,
    ( spl0_242
  <=> rdn_positive_less(rdnn(n2),rdnn(n3)) ),
    introduced(split_symbol_definition) ).

fof(f2875,plain,
    ( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
    | spl0_242 ),
    inference(component_clause,[status(thm)],[f2873]) ).

fof(f2973,plain,
    ( less(n21,n21)
    | ~ rdn_positive_less(rdnn(n2),rdnn(n3)) ),
    inference(resolution,[status(thm)],[f1976,f425]) ).

fof(f2974,plain,
    ( spl0_123
    | ~ spl0_242 ),
    inference(split_clause,[status(thm)],[f2973,f2268,f2873]) ).

fof(f2975,plain,
    ( $false
    | spl0_242 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2875,f671]) ).

fof(f2976,plain,
    spl0_242,
    inference(contradiction_clause,[status(thm)],[f2975]) ).

fof(f2977,plain,
    ( $false
    | ~ spl0_123 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2269,f862]) ).

fof(f2978,plain,
    ~ spl0_123,
    inference(contradiction_clause,[status(thm)],[f2977]) ).

fof(f2979,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f2974,f2976,f2978]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM303+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n029.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue May 30 10:12:37 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.20/0.36  % Drodi V3.5.1
% 0.20/0.40  % Refutation found
% 0.20/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.41/0.64  % Elapsed time: 0.090397 seconds
% 0.41/0.64  % CPU time: 0.123122 seconds
% 0.41/0.64  % Memory used: 19.772 MB
%------------------------------------------------------------------------------