TSTP Solution File: HEN006-7 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : HEN006-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 12:12:48 EDT 2023

% Result   : Unsatisfiable 0.20s 0.45s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   57 (  31 unt;   0 def)
%            Number of atoms       :  112 (  13 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  112 (  57   ~;  55   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :  123 (; 123   !;   0   ?)

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

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

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

fof(f4,axiom,
    ! [X,Y,V1,Z,V2,V3,V4,V5] :
      ( ~ quotient(X,Y,V1)
      | ~ quotient(Y,Z,V2)
      | ~ quotient(X,Z,V3)
      | ~ quotient(V3,V2,V4)
      | ~ quotient(V1,Z,V5)
      | less_equal(V4,V5) ),
    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,axiom,
    ! [X,Y] : quotient(X,Y,divide(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y,Z,W] :
      ( ~ quotient(X,Y,Z)
      | ~ quotient(X,Y,W)
      | Z = W ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X] : quotient(X,zero,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,hypothesis,
    quotient(x,y,xQy),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f16,hypothesis,
    quotient(x,z,xQz),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,negated_conjecture,
    ~ less_equal(xQz,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | quotient(X0,X1,zero) ),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ quotient(X0,X1,zero)
      | less_equal(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f20,plain,
    ! [X,Z] :
      ( ! [Y] : ~ quotient(X,Y,Z)
      | less_equal(Z,X) ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ~ quotient(X0,X1,X2)
      | less_equal(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f22,plain,
    ! [V4,V5] :
      ( ! [V1,Z] :
          ( ! [V2,V3] :
              ( ! [X] :
                  ( ! [Y] :
                      ( ~ quotient(X,Y,V1)
                      | ~ quotient(Y,Z,V2) )
                  | ~ quotient(X,Z,V3) )
              | ~ quotient(V3,V2,V4) )
          | ~ quotient(V1,Z,V5) )
      | less_equal(V4,V5) ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(X1,X3,X4)
      | ~ quotient(X0,X3,X5)
      | ~ quotient(X5,X4,X6)
      | ~ quotient(X2,X3,X7)
      | less_equal(X6,X7) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0] : less_equal(zero,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f27,plain,
    ! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f28,plain,
    ! [Z,W] :
      ( ! [X,Y] :
          ( ~ quotient(X,Y,Z)
          | ~ quotient(X,Y,W) )
      | Z = W ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f33,plain,
    ! [X0] : quotient(X0,zero,X0),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f34,plain,
    quotient(x,y,xQy),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f35,plain,
    less_equal(xQy,z),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f36,plain,
    quotient(x,z,xQz),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f37,plain,
    ~ less_equal(xQz,y),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f41,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ quotient(y,X0,X1)
      | ~ quotient(x,X0,X2)
      | ~ quotient(X2,X1,X3)
      | ~ quotient(xQy,X0,X4)
      | less_equal(X3,X4) ),
    inference(resolution,[status(thm)],[f23,f34]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ less_equal(X0,zero)
      | zero = X0 ),
    inference(resolution,[status(thm)],[f24,f25]) ).

fof(f75,plain,
    quotient(xQy,z,zero),
    inference(resolution,[status(thm)],[f35,f18]) ).

fof(f90,plain,
    ! [X0,X1,X2,X3] :
      ( ~ quotient(x,X0,X1)
      | ~ quotient(X1,divide(y,X0),X2)
      | ~ quotient(xQy,X0,X3)
      | less_equal(X2,X3) ),
    inference(resolution,[status(thm)],[f27,f41]) ).

fof(f92,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(X3,X1,X4)
      | ~ quotient(X4,X2,X5)
      | ~ quotient(divide(X3,X0),X1,X6)
      | less_equal(X5,X6) ),
    inference(resolution,[status(thm)],[f27,f23]) ).

fof(f93,plain,
    ! [X0,X1] : less_equal(divide(X0,X1),X0),
    inference(resolution,[status(thm)],[f27,f21]) ).

fof(f94,plain,
    ! [X0] : zero = divide(zero,X0),
    inference(resolution,[status(thm)],[f93,f58]) ).

fof(f95,plain,
    ! [X0,X1] : quotient(divide(X0,X1),X0,zero),
    inference(resolution,[status(thm)],[f93,f18]) ).

fof(f114,plain,
    ! [X0,X1,X2] :
      ( ~ quotient(divide(X0,X1),X0,X2)
      | zero = X2 ),
    inference(resolution,[status(thm)],[f29,f95]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ~ quotient(X0,zero,X1)
      | X0 = X1 ),
    inference(resolution,[status(thm)],[f29,f33]) ).

fof(f159,plain,
    ! [X0,X1] : zero = divide(divide(X0,X1),X0),
    inference(resolution,[status(thm)],[f114,f27]) ).

fof(f233,plain,
    ! [X0] : X0 = divide(X0,zero),
    inference(resolution,[status(thm)],[f122,f27]) ).

fof(f301,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(X2,divide(X3,X1),X4)
      | ~ quotient(divide(X0,X3),X1,X5)
      | less_equal(X4,X5) ),
    inference(resolution,[status(thm)],[f92,f27]) ).

fof(f459,plain,
    ! [X0,X1,X2] :
      ( ~ quotient(x,X0,X1)
      | ~ quotient(xQy,X0,X2)
      | less_equal(divide(X1,divide(y,X0)),X2) ),
    inference(resolution,[status(thm)],[f90,f27]) ).

fof(f1219,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ quotient(divide(X0,X1),divide(X2,X1),X3)
      | ~ quotient(divide(X0,X2),X1,X4)
      | less_equal(X3,X4) ),
    inference(resolution,[status(thm)],[f301,f27]) ).

fof(f1921,plain,
    ! [X0] :
      ( ~ quotient(xQy,z,X0)
      | less_equal(divide(xQz,divide(y,z)),X0) ),
    inference(resolution,[status(thm)],[f459,f36]) ).

fof(f1933,plain,
    less_equal(divide(xQz,divide(y,z)),zero),
    inference(resolution,[status(thm)],[f1921,f75]) ).

fof(f1936,plain,
    zero = divide(xQz,divide(y,z)),
    inference(resolution,[status(thm)],[f1933,f58]) ).

fof(f2893,plain,
    ! [X0,X1,X2,X3] :
      ( ~ quotient(divide(X0,X1),X2,X3)
      | less_equal(divide(divide(X0,X2),divide(X1,X2)),X3) ),
    inference(resolution,[status(thm)],[f1219,f27]) ).

fof(f3870,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
    inference(resolution,[status(thm)],[f2893,f27]) ).

fof(f4004,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)),
    inference(paramodulation,[status(thm)],[f159,f3870]) ).

fof(f4005,plain,
    ! [X0,X1,X2] : less_equal(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
    inference(forward_demodulation,[status(thm)],[f233,f4004]) ).

fof(f4197,plain,
    less_equal(divide(xQz,y),divide(zero,y)),
    inference(paramodulation,[status(thm)],[f1936,f4005]) ).

fof(f4198,plain,
    less_equal(divide(xQz,y),zero),
    inference(forward_demodulation,[status(thm)],[f94,f4197]) ).

fof(f4269,plain,
    zero = divide(xQz,y),
    inference(resolution,[status(thm)],[f4198,f58]) ).

fof(f4357,plain,
    quotient(xQz,y,zero),
    inference(paramodulation,[status(thm)],[f4269,f27]) ).

fof(f4366,plain,
    less_equal(xQz,y),
    inference(resolution,[status(thm)],[f4357,f19]) ).

fof(f4367,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f4366,f37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : HEN006-7 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35  % Computer : n005.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Tue May 30 09:31:21 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.12/0.36  % Drodi V3.5.1
% 0.20/0.45  % Refutation found
% 0.20/0.45  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.45  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.46  % Elapsed time: 0.106759 seconds
% 0.20/0.46  % CPU time: 0.736792 seconds
% 0.20/0.46  % Memory used: 20.859 MB
%------------------------------------------------------------------------------