%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP165-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n020.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 20:19:34 EDT 2024

% Result   : Unsatisfiable 0.20s 0.46s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   25 (  25 unt;   0 def)
%            Number of atoms       :   25 (  24 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   30 (  30   !;   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(f13,axiom,
    ! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f17,negated_conjecture,
    greatest_lower_bound(a,multiply(a,a)) != a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,plain,
    ! [X0] : multiply(identity,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f19,plain,
    ! [X0] : multiply(inverse(X0),X0) = identity,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f20,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] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f30,plain,
    ! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f33,plain,
    greatest_lower_bound(a,identity) = identity,
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f34,plain,
    greatest_lower_bound(a,multiply(a,a)) != a,
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f35,plain,
    greatest_lower_bound(identity,a) = identity,
    inference(forward_demodulation,[status(thm)],[f21,f33]) ).

fof(f40,plain,
    ! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
    inference(paramodulation,[status(thm)],[f19,f20]) ).

fof(f41,plain,
    ! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f18,f40]) ).

fof(f92,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
    inference(paramodulation,[status(thm)],[f41,f41]) ).

fof(f93,plain,
    ! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
    inference(paramodulation,[status(thm)],[f19,f41]) ).

fof(f94,plain,
    ! [X0] : X0 = multiply(X0,identity),
    inference(forward_demodulation,[status(thm)],[f92,f93]) ).

fof(f547,plain,
    ! [X0,X1] : multiply(X0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(X0,multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f94,f30]) ).

fof(f585,plain,
    multiply(a,greatest_lower_bound(identity,a)) != a,
    inference(backward_demodulation,[status(thm)],[f547,f34]) ).

fof(f586,plain,
    multiply(a,identity) != a,
    inference(forward_demodulation,[status(thm)],[f35,f585]) ).

fof(f587,plain,
    a != a,
    inference(forward_demodulation,[status(thm)],[f94,f586]) ).

fof(f588,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f587]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRP165-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Apr 30 00:26:47 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.37  % Drodi V3.6.0
% 0.20/0.46  % Refutation found
% 0.20/0.46  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.46  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.47  % Elapsed time: 0.093699 seconds
% 0.20/0.47  % CPU time: 0.640271 seconds
% 0.20/0.47  % Total memory used: 19.110 MB
% 0.20/0.47  % Net memory used: 18.865 MB
%------------------------------------------------------------------------------