TSTP Solution File: GRP172-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP172-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 20:19:37 EDT 2024

% Result   : Unsatisfiable 0.16s 0.58s
% Output   : CNFRefutation 1.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   44 (  44 unt;   0 def)
%            Number of atoms       :   44 (  43 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   61 (  61   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X] : multiply(identity,X) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X] : multiply(inverse(X),X) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

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

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

fof(f10,axiom,
    ! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [Y,Z,X] : multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,hypothesis,
    greatest_lower_bound(identity,a) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,hypothesis,
    greatest_lower_bound(identity,b) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,plain,
    ! [X0] : multiply(identity,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f20,plain,
    ! [X0] : multiply(inverse(X0),X0) = identity,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f21,plain,
    ! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f22,plain,
    ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f23,plain,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f24,plain,
    ! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f28,plain,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f29,plain,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f32,plain,
    ! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f34,plain,
    greatest_lower_bound(identity,a) = identity,
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f35,plain,
    greatest_lower_bound(identity,b) = identity,
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f36,plain,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f138,plain,
    ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f19,f32]) ).

fof(f155,plain,
    ! [X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(multiply(X0,X1),identity),
    inference(paramodulation,[status(thm)],[f20,f32]) ).

fof(f156,plain,
    ! [X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(identity,multiply(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f23,f155]) ).

fof(f161,plain,
    ! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
    inference(paramodulation,[status(thm)],[f20,f21]) ).

fof(f162,plain,
    ! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f19,f161]) ).

fof(f168,plain,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
    inference(paramodulation,[status(thm)],[f22,f28]) ).

fof(f175,plain,
    least_upper_bound(b,identity) = b,
    inference(paramodulation,[status(thm)],[f35,f168]) ).

fof(f176,plain,
    least_upper_bound(identity,b) = b,
    inference(forward_demodulation,[status(thm)],[f23,f175]) ).

fof(f199,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
    inference(paramodulation,[status(thm)],[f162,f162]) ).

fof(f334,plain,
    ! [X0,X1,X2] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) = X0,
    inference(paramodulation,[status(thm)],[f24,f168]) ).

fof(f718,plain,
    ! [X0] : least_upper_bound(a,greatest_lower_bound(X0,identity)) = a,
    inference(paramodulation,[status(thm)],[f34,f334]) ).

fof(f841,plain,
    ! [X0] : least_upper_bound(a,greatest_lower_bound(identity,X0)) = a,
    inference(paramodulation,[status(thm)],[f22,f718]) ).

fof(f1232,plain,
    ! [X0] : multiply(X0,inverse(X0)) = identity,
    inference(paramodulation,[status(thm)],[f20,f199]) ).

fof(f2345,plain,
    ! [X0,X1] : greatest_lower_bound(X0,multiply(least_upper_bound(identity,X1),X0)) = X0,
    inference(paramodulation,[status(thm)],[f138,f29]) ).

fof(f2360,plain,
    ! [X0] : greatest_lower_bound(X0,multiply(b,X0)) = X0,
    inference(paramodulation,[status(thm)],[f176,f2345]) ).

fof(f2440,plain,
    greatest_lower_bound(inverse(b),identity) = inverse(b),
    inference(paramodulation,[status(thm)],[f1232,f2360]) ).

fof(f2441,plain,
    greatest_lower_bound(identity,inverse(b)) = inverse(b),
    inference(forward_demodulation,[status(thm)],[f22,f2440]) ).

fof(f2788,plain,
    least_upper_bound(a,inverse(b)) = a,
    inference(paramodulation,[status(thm)],[f2441,f841]) ).

fof(f3129,plain,
    multiply(a,b) = least_upper_bound(identity,multiply(a,b)),
    inference(paramodulation,[status(thm)],[f2788,f156]) ).

fof(f3130,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f3129,f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.13  % Problem  : GRP172-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.02/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.34  % Computer : n016.cluster.edu
% 0.09/0.34  % Model    : x86_64 x86_64
% 0.09/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34  % Memory   : 8042.1875MB
% 0.09/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.34  % CPULimit : 300
% 0.09/0.34  % WCLimit  : 300
% 0.09/0.34  % DateTime : Tue Apr 30 01:00:55 EDT 2024
% 0.09/0.34  % CPUTime  : 
% 0.09/0.34  % Drodi V3.6.0
% 0.16/0.58  % Refutation found
% 0.16/0.58  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.58  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.67/0.60  % Elapsed time: 0.257174 seconds
% 1.67/0.60  % CPU time: 1.934045 seconds
% 1.67/0.60  % Total memory used: 45.397 MB
% 1.67/0.60  % Net memory used: 44.854 MB
%------------------------------------------------------------------------------