%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP175-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 20:19:38 EDT 2024

% Result   : Unsatisfiable 0.19s 0.52s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (  23 unt;   0 def)
%            Number of atoms       :   23 (  22 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    7 (   7   ~;   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   :   24 (  24   !;   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(f11,axiom,
    ! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,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(f15,axiom,
    ! [Y,Z,X] : multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f17,negated_conjecture,
    greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
    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(f28,plain,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f11]) ).

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(f32,plain,
    ! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f15]) ).

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

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

fof(f47,plain,
    identity = greatest_lower_bound(identity,b),
    inference(paramodulation,[status(thm)],[f33,f28]) ).

fof(f76,plain,
    ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
    inference(paramodulation,[status(thm)],[f19,f30]) ).

fof(f250,plain,
    ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f18,f32]) ).

fof(f1054,plain,
    identity != multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),
    inference(paramodulation,[status(thm)],[f76,f34]) ).

fof(f3260,plain,
    identity != multiply(inverse(a),multiply(greatest_lower_bound(identity,b),a)),
    inference(backward_demodulation,[status(thm)],[f250,f1054]) ).

fof(f3302,plain,
    identity != multiply(inverse(a),multiply(identity,a)),
    inference(forward_demodulation,[status(thm)],[f47,f3260]) ).

fof(f3303,plain,
    identity != multiply(inverse(a),a),
    inference(forward_demodulation,[status(thm)],[f18,f3302]) ).

fof(f3304,plain,
    identity != identity,
    inference(forward_demodulation,[status(thm)],[f19,f3303]) ).

fof(f3305,plain,
    $false,
    inference(equality_resolution,[status(esa)],[f3304]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP175-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n006.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 Apr 30 00:24:35 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.19/0.52  % Refutation found
% 0.19/0.52  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.52  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.53  % Elapsed time: 0.179270 seconds
% 0.19/0.53  % CPU time: 1.344734 seconds
% 0.19/0.53  % Total memory used: 32.759 MB
% 0.19/0.53  % Net memory used: 32.408 MB
%------------------------------------------------------------------------------