%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LAT034-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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  : 600s
% DateTime : Sun Jul 17 05:59:02 EDT 2022

% Result   : Unsatisfiable 0.14s 0.36s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (  10 unt;   0 nHn;   9 RR)
%            Number of literals    :   20 (  19 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   13 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(absorption1,axiom,
    meet(X,join(X,Y)) = X ).

cnf(absorption2,axiom,
    join(X,meet(X,Y)) = X ).

cnf(idempotence_of_meet,negated_conjecture,
    meet(xx,xx) != xx ).

cnf(refute_0_0,plain,
    meet(X,join(X,meet(X,X_3))) = X,
    inference(subst,[],[absorption1:[bind(Y,$fot(meet(X,X_3)))]]) ).

cnf(refute_0_1,plain,
    join(X,meet(X,X_3)) = X,
    inference(subst,[],[absorption2:[bind(Y,$fot(X_3))]]) ).

cnf(refute_0_2,plain,
    ( join(X,meet(X,X_3)) != X
    | meet(X,join(X,meet(X,X_3))) != X
    | meet(X,X) = X ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(X,meet(X,X_3))),X) ),[0,1],$fot(X)]]) ).

cnf(refute_0_3,plain,
    ( meet(X,join(X,meet(X,X_3))) != X
    | meet(X,X) = X ),
    inference(resolve,[$cnf( $equal(join(X,meet(X,X_3)),X) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    meet(X,X) = X,
    inference(resolve,[$cnf( $equal(meet(X,join(X,meet(X,X_3))),X) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    meet(xx,xx) = xx,
    inference(subst,[],[refute_0_4:[bind(X,$fot(xx))]]) ).

cnf(refute_0_6,plain,
    ( meet(xx,xx) != xx
    | xx != xx
    | meet(xx,xx) = xx ),
    introduced(tautology,[equality,[$cnf( ~ $equal(meet(xx,xx),xx) ),[0],$fot(xx)]]) ).

cnf(refute_0_7,plain,
    ( xx != xx
    | meet(xx,xx) = xx ),
    inference(resolve,[$cnf( $equal(meet(xx,xx),xx) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    xx != xx,
    inference(resolve,[$cnf( $equal(meet(xx,xx),xx) )],[refute_0_7,idempotence_of_meet]) ).

cnf(refute_0_9,plain,
    xx = xx,
    introduced(tautology,[refl,[$fot(xx)]]) ).

cnf(refute_0_10,plain,
    $false,
    inference(resolve,[$cnf( $equal(xx,xx) )],[refute_0_9,refute_0_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : LAT034-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Thu Jun 30 07:26:03 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  
% 0.14/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37  
%------------------------------------------------------------------------------