TSTP Solution File: HEN008-4 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : HEN008-4 : 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 12:12:49 EDT 2023

% Result   : Unsatisfiable 0.06s 0.27s
% Output   : CNFRefutation 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   35 (  19 unt;   0 def)
%            Number of atoms       :   56 (  16 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   46 (  25   ~;  21   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 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   :   49 (;  49   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
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(f9,axiom,
    ! [X] : divide(zero,X) = zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X,Y,Z] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,Z)
      | less_equal(X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X,Y,Z] :
      ( ~ less_equal(divide(X,Y),Z)
      | less_equal(divide(X,Z),Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,hypothesis,
    less_equal(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,negated_conjecture,
    ~ less_equal(divide(a,c),divide(b,c)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,plain,
    ! [X0,X1] :
      ( divide(X0,X1) != zero
      | less_equal(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f19,plain,
    ! [X0,X1] : less_equal(divide(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f20,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(f21,plain,
    ! [X0] : less_equal(zero,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f25,plain,
    ! [X0] : divide(zero,X0) = zero,
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f28,plain,
    ! [X,Z] :
      ( ! [Y] :
          ( ~ less_equal(X,Y)
          | ~ less_equal(Y,Z) )
      | less_equal(X,Z) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X2)
      | less_equal(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(X0,X1),X2)
      | less_equal(divide(X0,X2),X1) ),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f33,plain,
    less_equal(a,b),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f34,plain,
    ~ less_equal(divide(a,c),divide(b,c)),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2)))
      | divide(divide(X0,X2),divide(X1,X2)) = divide(divide(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f22,f20]) ).

fof(f74,plain,
    ! [X0] :
      ( ~ less_equal(X0,a)
      | less_equal(X0,b) ),
    inference(resolution,[status(thm)],[f29,f33]) ).

fof(f96,plain,
    ! [X0] : less_equal(divide(a,X0),b),
    inference(resolution,[status(thm)],[f74,f19]) ).

fof(f177,plain,
    ! [X0] : less_equal(divide(a,b),X0),
    inference(resolution,[status(thm)],[f30,f96]) ).

fof(f232,plain,
    ! [X0] :
      ( ~ less_equal(X0,zero)
      | X0 = zero ),
    inference(resolution,[status(thm)],[f21,f22]) ).

fof(f337,plain,
    divide(a,b) = zero,
    inference(resolution,[status(thm)],[f177,f232]) ).

fof(f555,plain,
    divide(divide(a,c),divide(b,c)) != zero,
    inference(resolution,[status(thm)],[f18,f34]) ).

fof(f716,plain,
    ! [X0] :
      ( ~ less_equal(divide(zero,X0),divide(divide(a,X0),divide(b,X0)))
      | divide(divide(a,X0),divide(b,X0)) = divide(divide(a,b),X0) ),
    inference(paramodulation,[status(thm)],[f337,f40]) ).

fof(f717,plain,
    ! [X0] :
      ( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
      | divide(divide(a,X0),divide(b,X0)) = divide(divide(a,b),X0) ),
    inference(forward_demodulation,[status(thm)],[f25,f716]) ).

fof(f718,plain,
    ! [X0] :
      ( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
      | divide(divide(a,X0),divide(b,X0)) = divide(zero,X0) ),
    inference(forward_demodulation,[status(thm)],[f337,f717]) ).

fof(f719,plain,
    ! [X0] :
      ( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
      | divide(divide(a,X0),divide(b,X0)) = zero ),
    inference(forward_demodulation,[status(thm)],[f25,f718]) ).

fof(f720,plain,
    ! [X0] : divide(divide(a,X0),divide(b,X0)) = zero,
    inference(forward_subsumption_resolution,[status(thm)],[f719,f21]) ).

fof(f849,plain,
    zero != zero,
    inference(backward_demodulation,[status(thm)],[f720,f555]) ).

fof(f850,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f849]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.06  % Problem  : HEN008-4 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.07  % 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 09:23:22 EDT 2023
% 0.06/0.25  % CPUTime  : 
% 0.06/0.26  % 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
% 0.06/0.28  % Elapsed time: 0.020664 seconds
% 0.06/0.28  % CPU time: 0.084374 seconds
% 0.06/0.28  % Memory used: 14.068 MB
%------------------------------------------------------------------------------