%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GRP186-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 12:10:55 EDT 2023

% Result   : Unsatisfiable 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   22 (  22 unt;   0 def)
%            Number of atoms       :   22 (  21 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   31 (;  31   !;   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(f5,axiom,
    ! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X,Y,Z] : multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,negated_conjecture,
    least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,plain,
    ! [X0] : multiply(identity,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f18,plain,
    ! [X0] : multiply(inverse(X0),X0) = identity,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f19,plain,
    ! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f21,plain,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f28,plain,
    ! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f32,plain,
    least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f33,plain,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,least_upper_bound(inverse(a),b)),
    inference(forward_demodulation,[status(thm)],[f21,f32]) ).

fof(f34,plain,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,least_upper_bound(b,inverse(a))),
    inference(forward_demodulation,[status(thm)],[f21,f33]) ).

fof(f38,plain,
    ! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
    inference(paramodulation,[status(thm)],[f18,f19]) ).

fof(f39,plain,
    ! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f17,f38]) ).

fof(f42,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
    inference(paramodulation,[status(thm)],[f39,f39]) ).

fof(f59,plain,
    ! [X0] : multiply(X0,inverse(X0)) = identity,
    inference(paramodulation,[status(thm)],[f18,f42]) ).

fof(f180,plain,
    ! [X0,X1] : multiply(X0,least_upper_bound(X1,inverse(X0))) = least_upper_bound(multiply(X0,X1),identity),
    inference(paramodulation,[status(thm)],[f59,f28]) ).

fof(f181,plain,
    ! [X0,X1] : multiply(X0,least_upper_bound(X1,inverse(X0))) = least_upper_bound(identity,multiply(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f21,f180]) ).

fof(f197,plain,
    least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b)),
    inference(backward_demodulation,[status(thm)],[f181,f34]) ).

fof(f198,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f197]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP186-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 11:25:57 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.13/0.36  % Refutation found
% 0.13/0.36  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37  % Elapsed time: 0.018985 seconds
% 0.13/0.37  % CPU time: 0.049738 seconds
% 0.13/0.37  % Memory used: 1.163 MB
%------------------------------------------------------------------------------