%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LAT014-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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 05:58:54 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% 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    :    6 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (  11 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(mckenzie2,axiom,
    meet(X,join(Y,join(X,Z))) = X ).

cnf(mckenzie3,axiom,
    join(join(meet(X,Y),meet(Y,Z)),Y) = Y ).

cnf(prove_absorbtion,negated_conjecture,
    meet(a,join(a,b)) != a ).

cnf(refute_0_0,plain,
    meet(X,join(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15)),join(X,Z))) = X,
    inference(subst,[],[mckenzie2:[bind(Y,$fot(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15))))]]) ).

cnf(refute_0_1,plain,
    join(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15)),join(X,Z)) = join(X,Z),
    inference(subst,[],[mckenzie3:[bind(X,$fot(X_13)),bind(Y,$fot(join(X,Z))),bind(Z,$fot(X_15))]]) ).

cnf(refute_0_2,plain,
    ( join(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15)),join(X,Z)) != join(X,Z)
    | meet(X,join(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15)),join(X,Z))) != X
    | meet(X,join(X,Z)) = X ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15)),join(X,Z))),X) ),[0,1],$fot(join(X,Z))]]) ).

cnf(refute_0_3,plain,
    ( meet(X,join(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15)),join(X,Z))) != X
    | meet(X,join(X,Z)) = X ),
    inference(resolve,[$cnf( $equal(join(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15)),join(X,Z)),join(X,Z)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    meet(X,join(X,Z)) = X,
    inference(resolve,[$cnf( $equal(meet(X,join(join(meet(X_13,join(X,Z)),meet(join(X,Z),X_15)),join(X,Z))),X) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    meet(a,join(a,b)) = a,
    inference(subst,[],[refute_0_4:[bind(X,$fot(a)),bind(Z,$fot(b))]]) ).

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

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

cnf(refute_0_8,plain,
    a != a,
    inference(resolve,[$cnf( $equal(meet(a,join(a,b)),a) )],[refute_0_7,prove_absorbtion]) ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : LAT014-1 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n003.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  : 600
% 0.13/0.34  % DateTime : Wed Jun 29 15:36:36 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------