%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : FLD070-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : Tue Apr 30 20:16:36 EDT 2024

% Result   : Unsatisfiable 0.10s 0.36s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   25 (  14 unt;   0 def)
%            Number of atoms       :   46 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   44 (  23   ~;  21   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   31 (  31   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] :
      ( sum(additive_identity,X,X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Z,Y] :
      ( less_or_equal(X,Z)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [U,V,X,Y,Z] :
      ( less_or_equal(U,V)
      | ~ less_or_equal(X,Y)
      | ~ sum(X,Z,U)
      | ~ sum(Y,Z,V) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,hypothesis,
    defined(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    less_or_equal(additive_identity,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    less_or_equal(additive_identity,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,negated_conjecture,
    sum(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,negated_conjecture,
    ~ less_or_equal(additive_identity,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f38,plain,
    ! [X0] :
      ( sum(additive_identity,X0,X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f65,plain,
    ! [Z,Y] :
      ( ! [X] :
          ( less_or_equal(X,Z)
          | ~ less_or_equal(X,Y) )
      | ~ less_or_equal(Y,Z) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X0,X2)
      | ~ less_or_equal(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f69,plain,
    ! [V,Y,Z] :
      ( ! [U,X] :
          ( less_or_equal(U,V)
          | ~ less_or_equal(X,Y)
          | ~ sum(X,Z,U) )
      | ~ sum(Y,Z,V) ),
    inference(miniscoping,[status(esa)],[f24]) ).

fof(f70,plain,
    ! [X0,X1,X2,X3,X4] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X2,X3)
      | ~ sum(X2,X4,X0)
      | ~ sum(X3,X4,X1) ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f74,plain,
    defined(b),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f76,plain,
    less_or_equal(additive_identity,a),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f77,plain,
    less_or_equal(additive_identity,b),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f78,plain,
    sum(a,b,c),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f79,plain,
    ~ less_or_equal(additive_identity,c),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f82,plain,
    sum(additive_identity,b,b),
    inference(resolution,[status(thm)],[f38,f74]) ).

fof(f86,plain,
    ! [X0] :
      ( less_or_equal(additive_identity,X0)
      | ~ less_or_equal(b,X0) ),
    inference(resolution,[status(thm)],[f66,f77]) ).

fof(f252,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ sum(additive_identity,X2,X0)
      | ~ sum(a,X2,X1) ),
    inference(resolution,[status(thm)],[f70,f76]) ).

fof(f340,plain,
    ! [X0] :
      ( less_or_equal(b,X0)
      | ~ sum(a,b,X0) ),
    inference(resolution,[status(thm)],[f82,f252]) ).

fof(f345,plain,
    less_or_equal(b,c),
    inference(resolution,[status(thm)],[f340,f78]) ).

fof(f346,plain,
    less_or_equal(additive_identity,c),
    inference(resolution,[status(thm)],[f345,f86]) ).

fof(f347,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f346,f79]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : FLD070-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.05/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n002.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon Apr 29 23:38:39 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.6.0
% 0.10/0.36  % Refutation found
% 0.10/0.36  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.37  % Elapsed time: 0.045448 seconds
% 0.15/0.37  % CPU time: 0.255189 seconds
% 0.15/0.37  % Total memory used: 11.789 MB
% 0.15/0.37  % Net memory used: 11.515 MB
%------------------------------------------------------------------------------