%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : HEN005-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 12:12:46 EDT 2023

% Result   : Unsatisfiable 0.06s 0.27s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   34 (  21 unt;   0 def)
%            Number of atoms       :   49 (  18 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   32 (  17   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   37 (;  37   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | divide(X,Y) = zero ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( divide(X,Y) != zero
      | less_equal(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] : less_equal(divide(X,Y),X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X] : less_equal(zero,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,X)
      | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,hypothesis,
    less_equal(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,hypothesis,
    less_equal(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ less_equal(a,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | divide(X0,X1) = zero ),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( divide(X0,X1) != zero
      | less_equal(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f13,plain,
    ! [X0,X1] : less_equal(divide(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f14,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f15,plain,
    ! [X0] : less_equal(zero,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f18,plain,
    less_equal(a,b),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f19,plain,
    less_equal(b,c),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f20,plain,
    ~ less_equal(a,c),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,divide(X0,X1))
      | X0 = divide(X0,X1) ),
    inference(resolution,[status(thm)],[f13,f16]) ).

fof(f38,plain,
    ! [X0] : zero = divide(zero,X0),
    inference(resolution,[status(thm)],[f15,f37]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ less_equal(X0,zero)
      | X0 = zero ),
    inference(resolution,[status(thm)],[f15,f16]) ).

fof(f55,plain,
    divide(b,c) = zero,
    inference(resolution,[status(thm)],[f11,f19]) ).

fof(f56,plain,
    divide(a,b) = zero,
    inference(resolution,[status(thm)],[f11,f18]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2)))
      | divide(divide(X0,X1),X2) = divide(divide(X0,X2),divide(X1,X2)) ),
    inference(resolution,[status(thm)],[f14,f16]) ).

fof(f338,plain,
    ! [X0] :
      ( ~ less_equal(divide(zero,X0),divide(divide(a,X0),divide(b,X0)))
      | divide(divide(a,b),X0) = divide(divide(a,X0),divide(b,X0)) ),
    inference(paramodulation,[status(thm)],[f56,f123]) ).

fof(f339,plain,
    ! [X0] :
      ( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
      | divide(divide(a,b),X0) = divide(divide(a,X0),divide(b,X0)) ),
    inference(forward_demodulation,[status(thm)],[f38,f338]) ).

fof(f340,plain,
    ! [X0] :
      ( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
      | divide(zero,X0) = divide(divide(a,X0),divide(b,X0)) ),
    inference(forward_demodulation,[status(thm)],[f56,f339]) ).

fof(f341,plain,
    ! [X0] :
      ( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
      | zero = divide(divide(a,X0),divide(b,X0)) ),
    inference(forward_demodulation,[status(thm)],[f38,f340]) ).

fof(f342,plain,
    ! [X0] : zero = divide(divide(a,X0),divide(b,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f341,f15]) ).

fof(f515,plain,
    ! [X0] : less_equal(divide(a,X0),divide(b,X0)),
    inference(resolution,[status(thm)],[f342,f12]) ).

fof(f580,plain,
    less_equal(divide(a,c),zero),
    inference(paramodulation,[status(thm)],[f55,f515]) ).

fof(f585,plain,
    divide(a,c) = zero,
    inference(resolution,[status(thm)],[f580,f39]) ).

fof(f598,plain,
    less_equal(a,c),
    inference(resolution,[status(thm)],[f585,f12]) ).

fof(f599,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f598,f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem  : HEN005-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25  % Computer : n010.cluster.edu
% 0.06/0.25  % Model    : x86_64 x86_64
% 0.06/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25  % Memory   : 8042.1875MB
% 0.06/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25  % CPULimit : 300
% 0.06/0.25  % WCLimit  : 300
% 0.06/0.25  % DateTime : Tue May 30 09:23:37 EDT 2023
% 0.06/0.25  % CPUTime  : 
% 0.06/0.25  % Drodi V3.5.1
% 0.06/0.27  % Refutation found
% 0.06/0.27  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.06/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.33  % Elapsed time: 0.081382 seconds
% 0.09/0.33  % CPU time: 0.028928 seconds
% 0.09/0.33  % Memory used: 1.300 MB
%------------------------------------------------------------------------------