%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE001+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 12:15:25 EDT 2023

% Result   : Theorem 0.22s 0.57s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   15 (   6 unt;   0 def)
%            Number of atoms       :   28 (  10 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   25 (  12   ~;   5   |;   5   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   24 (;  18   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A] : addition(A,A) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> addition(A,B) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,conjecture,
    ! [X0,X1,X2] :
      ( leq(X0,X1)
     => leq(addition(X0,X2),addition(X0,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( leq(X0,X1)
       => leq(addition(X0,X2),addition(X0,X2)) ),
    inference(negated_conjecture,[status(cth)],[f13]) ).

fof(f18,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f26,plain,
    ! [A,B] :
      ( ( ~ leq(A,B)
        | addition(A,B) = B )
      & ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(NNF_transformation,[status(esa)],[f12]) ).

fof(f27,plain,
    ( ! [A,B] :
        ( ~ leq(A,B)
        | addition(A,B) = B )
    & ! [A,B] :
        ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(miniscoping,[status(esa)],[f26]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( leq(X0,X1)
      & ~ leq(addition(X0,X2),addition(X0,X2)) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f31,plain,
    ? [X0] :
      ( ? [X1] : leq(X0,X1)
      & ? [X2] : ~ leq(addition(X0,X2),addition(X0,X2)) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f32,plain,
    ( leq(sk0_0,sk0_1)
    & ~ leq(addition(sk0_0,sk0_2),addition(sk0_0,sk0_2)) ),
    inference(skolemization,[status(esa)],[f31]) ).

fof(f34,plain,
    ~ leq(addition(sk0_0,sk0_2),addition(sk0_0,sk0_2)),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f36,plain,
    addition(addition(sk0_0,sk0_2),addition(sk0_0,sk0_2)) != addition(sk0_0,sk0_2),
    inference(resolution,[status(thm)],[f29,f34]) ).

fof(f37,plain,
    addition(sk0_0,sk0_2) != addition(sk0_0,sk0_2),
    inference(forward_demodulation,[status(thm)],[f18,f36]) ).

fof(f38,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE001+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.33  % Computer : n002.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Tue May 30 12:02:13 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  % Drodi V3.5.1
% 0.22/0.57  % Refutation found
% 0.22/0.57  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.57  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.57  % Elapsed time: 0.012212 seconds
% 0.22/0.57  % CPU time: 0.027198 seconds
% 0.22/0.57  % Memory used: 9.037 MB
%------------------------------------------------------------------------------