%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LAT039-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 05:59:04 EDT 2022

% Result   : Unsatisfiable 0.11s 0.34s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   8 unt;   0 nHn;  10 RR)
%            Number of literals    :   20 (  19 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(dist_join,hypothesis,
    join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ).

cnf(rhs,negated_conjecture,
    join(xx,meet(yy,zz)) != meet(join(xx,yy),join(xx,zz)) ).

cnf(refute_0_0,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_1,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( join(X,meet(Y,Z)) != meet(join(X,Y),join(X,Z))
    | meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X,meet(Y,Z)))),bind(Y0,$fot(meet(join(X,Y),join(X,Z))))]]) ).

cnf(refute_0_4,plain,
    meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)),
    inference(resolve,[$cnf( $equal(join(X,meet(Y,Z)),meet(join(X,Y),join(X,Z))) )],[dist_join,refute_0_3]) ).

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

cnf(refute_0_6,plain,
    ( join(xx,meet(yy,zz)) != join(xx,meet(yy,zz))
    | meet(join(xx,yy),join(xx,zz)) != join(xx,meet(yy,zz))
    | join(xx,meet(yy,zz)) = meet(join(xx,yy),join(xx,zz)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(xx,meet(yy,zz)),meet(join(xx,yy),join(xx,zz))) ),[1],$fot(join(xx,meet(yy,zz)))]]) ).

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

cnf(refute_0_8,plain,
    join(xx,meet(yy,zz)) != join(xx,meet(yy,zz)),
    inference(resolve,[$cnf( $equal(join(xx,meet(yy,zz)),meet(join(xx,yy),join(xx,zz))) )],[refute_0_7,rhs]) ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : LAT039-2 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.11/0.33  % Computer : n029.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Thu Jun 30 14:50:53 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34  
% 0.11/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.11/0.34  
%------------------------------------------------------------------------------