TSTP Solution File: HEN010-3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : HEN010-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 20:21:48 EDT 2024

% Result   : Unsatisfiable 6.36s 1.14s
% Output   : CNFRefutation 6.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   87 (  64 unt;   0 def)
%            Number of atoms       :  112 (  58 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   53 (  28   ~;  25   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    6 (   2 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   :  202 ( 202   !;   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(f7,axiom,
    ! [X] : less_equal(X,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,negated_conjecture,
    divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | divide(X0,X1) = zero ),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( divide(X0,X1) != zero
      | less_equal(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f11,plain,
    ! [X0,X1] : less_equal(divide(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f12,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(f13,plain,
    ! [X0] : less_equal(zero,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f15,plain,
    ! [X0] : less_equal(X0,identity),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f16,plain,
    divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f17,plain,
    ! [X0,X1] : divide(divide(X0,X1),X0) = zero,
    inference(resolution,[status(thm)],[f9,f11]) ).

fof(f18,plain,
    ! [X0] : divide(zero,X0) = zero,
    inference(resolution,[status(thm)],[f9,f13]) ).

fof(f19,plain,
    ! [X0] : divide(X0,identity) = zero,
    inference(resolution,[status(thm)],[f9,f15]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,divide(X0,X1))
      | divide(X0,X1) = X0 ),
    inference(resolution,[status(thm)],[f14,f11]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ less_equal(X0,zero)
      | zero = X0 ),
    inference(resolution,[status(thm)],[f14,f13]) ).

fof(f68,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)],[f12,f14]) ).

fof(f69,plain,
    ! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
    inference(resolution,[status(thm)],[f12,f9]) ).

fof(f82,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)),
    inference(paramodulation,[status(thm)],[f17,f12]) ).

fof(f88,plain,
    ! [X0,X1] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
    inference(paramodulation,[status(thm)],[f17,f12]) ).

fof(f150,plain,
    ! [X0,X1] : zero = divide(divide(X0,X0),divide(X1,X0)),
    inference(resolution,[status(thm)],[f88,f50]) ).

fof(f170,plain,
    ! [X0,X1] : less_equal(divide(X0,X0),divide(X1,X0)),
    inference(resolution,[status(thm)],[f150,f10]) ).

fof(f201,plain,
    ! [X0] : divide(divide(X0,X0),X0) = divide(X0,X0),
    inference(resolution,[status(thm)],[f170,f49]) ).

fof(f202,plain,
    ! [X0] : zero = divide(X0,X0),
    inference(forward_demodulation,[status(thm)],[f17,f201]) ).

fof(f268,plain,
    ! [X0,X1] :
      ( ~ less_equal(zero,divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))))
      | divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = divide(divide(X0,X1),divide(X0,X1)) ),
    inference(paramodulation,[status(thm)],[f202,f68]) ).

fof(f269,plain,
    ! [X0,X1] :
      ( ~ less_equal(zero,divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))))
      | divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = zero ),
    inference(forward_demodulation,[status(thm)],[f202,f268]) ).

fof(f270,plain,
    ! [X0,X1] : divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = zero,
    inference(forward_subsumption_resolution,[status(thm)],[f269,f13]) ).

fof(f276,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(zero,X0),divide(divide(divide(X1,X2),X0),divide(X1,X0)))
      | divide(divide(divide(X1,X2),X0),divide(X1,X0)) = divide(divide(divide(X1,X2),X1),X0) ),
    inference(paramodulation,[status(thm)],[f17,f68]) ).

fof(f277,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2)))
      | divide(divide(divide(X0,X1),X2),divide(X0,X2)) = divide(divide(divide(X0,X1),X0),X2) ),
    inference(forward_demodulation,[status(thm)],[f18,f276]) ).

fof(f278,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2)))
      | divide(divide(divide(X0,X1),X2),divide(X0,X2)) = divide(zero,X2) ),
    inference(forward_demodulation,[status(thm)],[f17,f277]) ).

fof(f279,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2)))
      | divide(divide(divide(X0,X1),X2),divide(X0,X2)) = zero ),
    inference(forward_demodulation,[status(thm)],[f18,f278]) ).

fof(f280,plain,
    ! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),divide(X0,X2)) = zero,
    inference(forward_subsumption_resolution,[status(thm)],[f279,f13]) ).

fof(f376,plain,
    ! [X0,X1,X2] : divide(divide(divide(divide(X0,X1),divide(divide(X0,X2),X1)),divide(divide(X2,X1),divide(divide(X0,X2),X1))),zero) = zero,
    inference(paramodulation,[status(thm)],[f69,f69]) ).

fof(f471,plain,
    ! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
    inference(paramodulation,[status(thm)],[f19,f82]) ).

fof(f501,plain,
    ! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
    inference(paramodulation,[status(thm)],[f202,f471]) ).

fof(f512,plain,
    ! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
    inference(resolution,[status(thm)],[f501,f50]) ).

fof(f527,plain,
    ! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
    inference(resolution,[status(thm)],[f512,f10]) ).

fof(f593,plain,
    ! [X0] : zero = divide(X0,divide(X0,zero)),
    inference(resolution,[status(thm)],[f527,f50]) ).

fof(f608,plain,
    ! [X0] : less_equal(X0,divide(X0,zero)),
    inference(resolution,[status(thm)],[f593,f10]) ).

fof(f706,plain,
    ! [X0] : divide(X0,zero) = X0,
    inference(resolution,[status(thm)],[f608,f49]) ).

fof(f716,plain,
    ! [X0,X1,X2] : less_equal(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
    inference(backward_demodulation,[status(thm)],[f706,f82]) ).

fof(f793,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(X0,X1))
      | divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1) ),
    inference(resolution,[status(thm)],[f716,f14]) ).

fof(f1194,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),X2),divide(X0,X2)),
    inference(resolution,[status(thm)],[f280,f10]) ).

fof(f1222,plain,
    ! [X0,X1,X2,X3] : divide(divide(divide(divide(divide(X0,X1),divide(X2,X1)),X3),divide(divide(X0,X2),X1)),zero) = zero,
    inference(paramodulation,[status(thm)],[f69,f280]) ).

fof(f1223,plain,
    ! [X0,X1,X2,X3] : divide(divide(divide(divide(X0,X1),divide(X2,X1)),X3),divide(divide(X0,X2),X1)) = zero,
    inference(forward_demodulation,[status(thm)],[f706,f1222]) ).

fof(f1251,plain,
    ! [X0,X1,X2] : divide(divide(divide(divide(X0,X1),divide(X0,X2)),divide(X2,divide(X0,X2))),zero) = zero,
    inference(paramodulation,[status(thm)],[f280,f69]) ).

fof(f1252,plain,
    ! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(X0,X2)),divide(X2,divide(X0,X2))) = zero,
    inference(forward_demodulation,[status(thm)],[f706,f1251]) ).

fof(f1324,plain,
    ! [X0,X1,X2] : divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1),
    inference(backward_subsumption_resolution,[status(thm)],[f793,f1194]) ).

fof(f1388,plain,
    ! [X0,X1,X2,X3] : divide(divide(X0,divide(divide(X1,X2),X3)),X1) = divide(divide(X0,divide(X1,X2)),X1),
    inference(paramodulation,[status(thm)],[f1324,f1324]) ).

fof(f1389,plain,
    ! [X0,X1,X2,X3] : divide(divide(X0,divide(divide(X1,X2),X3)),X1) = divide(X0,X1),
    inference(forward_demodulation,[status(thm)],[f1324,f1388]) ).

fof(f1456,plain,
    ! [X0,X1,X2] : divide(divide(X0,X1),divide(X0,divide(X1,X2))) = zero,
    inference(paramodulation,[status(thm)],[f1324,f17]) ).

fof(f1457,plain,
    ! [X0,X1,X2] : less_equal(divide(X0,X1),divide(X0,divide(X1,X2))),
    inference(paramodulation,[status(thm)],[f1324,f11]) ).

fof(f2598,plain,
    ! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),divide(divide(X0,X2),X1)) = zero,
    inference(paramodulation,[status(thm)],[f1324,f1223]) ).

fof(f6277,plain,
    ! [X0,X1,X2] : divide(divide(divide(divide(X0,X1),divide(X0,X2)),X2),zero) = zero,
    inference(paramodulation,[status(thm)],[f1252,f1456]) ).

fof(f6278,plain,
    ! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(X0,X2)),X2) = zero,
    inference(forward_demodulation,[status(thm)],[f706,f6277]) ).

fof(f6941,plain,
    ! [X0,X1] : divide(divide(X0,divide(X0,X1)),X1) = zero,
    inference(paramodulation,[status(thm)],[f1389,f6278]) ).

fof(f7434,plain,
    ! [X0,X1,X2] : divide(divide(divide(X0,divide(X0,divide(X1,X2))),X1),zero) = zero,
    inference(paramodulation,[status(thm)],[f6941,f1456]) ).

fof(f7435,plain,
    ! [X0,X1,X2] : divide(divide(X0,divide(X0,divide(X1,X2))),X1) = zero,
    inference(forward_demodulation,[status(thm)],[f706,f7434]) ).

fof(f7586,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(divide(X0,divide(X1,divide(X1,X2))),X2),divide(divide(X0,X2),zero))
      | divide(divide(X0,X2),divide(divide(X1,divide(X1,X2)),X2)) = divide(divide(X0,divide(X1,divide(X1,X2))),X2) ),
    inference(paramodulation,[status(thm)],[f6941,f68]) ).

fof(f7587,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(divide(X0,divide(X1,divide(X1,X2))),X2),divide(X0,X2))
      | divide(divide(X0,X2),divide(divide(X1,divide(X1,X2)),X2)) = divide(divide(X0,divide(X1,divide(X1,X2))),X2) ),
    inference(forward_demodulation,[status(thm)],[f706,f7586]) ).

fof(f7588,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(divide(X0,divide(X1,divide(X1,X2))),X2),divide(X0,X2))
      | divide(divide(X0,X2),zero) = divide(divide(X0,divide(X1,divide(X1,X2))),X2) ),
    inference(forward_demodulation,[status(thm)],[f6941,f7587]) ).

fof(f7589,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(divide(X0,divide(X1,divide(X1,X2))),X2),divide(X0,X2))
      | divide(X0,X2) = divide(divide(X0,divide(X1,divide(X1,X2))),X2) ),
    inference(forward_demodulation,[status(thm)],[f706,f7588]) ).

fof(f7590,plain,
    ! [X0,X1,X2] : divide(X0,X1) = divide(divide(X0,divide(X2,divide(X2,X1))),X1),
    inference(forward_subsumption_resolution,[status(thm)],[f7589,f1194]) ).

fof(f7886,plain,
    ! [X0,X1,X2] : less_equal(divide(X0,divide(X0,divide(X1,X2))),X1),
    inference(resolution,[status(thm)],[f7435,f10]) ).

fof(f8311,plain,
    ! [X0,X1,X2,X3] : less_equal(divide(divide(X0,divide(X0,divide(divide(X1,X2),X3))),zero),X1),
    inference(paramodulation,[status(thm)],[f7435,f7886]) ).

fof(f8312,plain,
    ! [X0,X1,X2,X3] : less_equal(divide(X0,divide(X0,divide(divide(X1,X2),X3))),X1),
    inference(forward_demodulation,[status(thm)],[f706,f8311]) ).

fof(f8405,plain,
    ! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(divide(X0,X2),X1)),divide(divide(X2,X1),divide(divide(X0,X2),X1))) = zero,
    inference(forward_demodulation,[status(thm)],[f706,f376]) ).

fof(f12980,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(divide(X0,X1),divide(divide(X0,X2),X1)),zero),X2),
    inference(paramodulation,[status(thm)],[f8405,f8312]) ).

fof(f12981,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(divide(X0,X2),X1)),X2),
    inference(forward_demodulation,[status(thm)],[f706,f12980]) ).

fof(f28241,plain,
    ! [X0,X1] : less_equal(divide(divide(X0,divide(X1,divide(X0,X1))),zero),divide(X0,X1)),
    inference(paramodulation,[status(thm)],[f270,f12981]) ).

fof(f28242,plain,
    ! [X0,X1] : less_equal(divide(X0,divide(X1,divide(X0,X1))),divide(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f706,f28241]) ).

fof(f28726,plain,
    ! [X0,X1] :
      ( ~ less_equal(divide(X0,X1),divide(X0,divide(X1,divide(X0,X1))))
      | divide(X0,divide(X1,divide(X0,X1))) = divide(X0,X1) ),
    inference(resolution,[status(thm)],[f28242,f14]) ).

fof(f28727,plain,
    ! [X0,X1] : divide(X0,divide(X1,divide(X0,X1))) = divide(X0,X1),
    inference(forward_subsumption_resolution,[status(thm)],[f28726,f1457]) ).

fof(f29516,plain,
    ! [X0,X1] :
      ( divide(X0,X1) != zero
      | less_equal(X0,divide(X1,divide(X0,X1))) ),
    inference(paramodulation,[status(thm)],[f28727,f10]) ).

fof(f29867,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),X2),divide(divide(divide(X0,X2),X1),divide(divide(divide(X0,X1),X2),divide(divide(X0,X2),X1)))),
    inference(resolution,[status(thm)],[f2598,f29516]) ).

fof(f29868,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),X2),divide(divide(divide(X0,X2),X1),zero)),
    inference(forward_demodulation,[status(thm)],[f2598,f29867]) ).

fof(f29869,plain,
    ! [X0,X1,X2] : less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),X1)),
    inference(forward_demodulation,[status(thm)],[f706,f29868]) ).

fof(f30732,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),X1))
      | divide(divide(X0,X2),X1) = divide(divide(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f29869,f14]) ).

fof(f30733,plain,
    ! [X0,X1,X2] : divide(divide(X0,X1),X2) = divide(divide(X0,X2),X1),
    inference(forward_subsumption_resolution,[status(thm)],[f30732,f29869]) ).

fof(f31105,plain,
    ! [X0,X1,X2] : divide(X0,X1) = divide(divide(X0,X1),divide(X2,divide(X2,X1))),
    inference(paramodulation,[status(thm)],[f7590,f30733]) ).

fof(f32553,plain,
    divide(identity,a) != divide(identity,a),
    inference(backward_demodulation,[status(thm)],[f31105,f16]) ).

fof(f32554,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f32553]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : HEN010-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26  % Computer : n018.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit : 300
% 0.06/0.26  % WCLimit  : 300
% 0.06/0.26  % DateTime : Mon Apr 29 20:21:42 EDT 2024
% 0.06/0.26  % CPUTime  : 
% 0.06/0.27  % Drodi V3.6.0
% 6.36/1.14  % Refutation found
% 6.36/1.14  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.36/1.14  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.13/1.21  % Elapsed time: 0.927438 seconds
% 7.13/1.21  % CPU time: 7.185003 seconds
% 7.13/1.21  % Total memory used: 236.585 MB
% 7.13/1.21  % Net memory used: 226.426 MB
%------------------------------------------------------------------------------