%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP182-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n022.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 : Sat Jul 16 10:37:41 EDT 2022

% Result   : Unsatisfiable 0.15s 0.38s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   8 unt;   0 nHn;   9 RR)
%            Number of literals    :   18 (  17 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 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   :   10 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(symmetry_of_lub,axiom,
    least_upper_bound(X,Y) = least_upper_bound(Y,X) ).

cnf(glb_absorbtion,axiom,
    greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).

cnf(prove_p17b,negated_conjecture,
    greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity ).

cnf(refute_0_0,plain,
    ( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
    | least_upper_bound(X,Y) != least_upper_bound(Y,X)
    | greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) ),[0,1],$fot(least_upper_bound(Y,X))]]) ).

cnf(refute_0_1,plain,
    ( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
    | greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_0]) ).

cnf(refute_0_2,plain,
    greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) )],[glb_absorbtion,refute_0_1]) ).

cnf(refute_0_3,plain,
    greatest_lower_bound(identity,least_upper_bound(a,identity)) = identity,
    inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(a))]]) ).

cnf(refute_0_4,plain,
    ( greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity
    | identity != identity
    | greatest_lower_bound(identity,least_upper_bound(a,identity)) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,least_upper_bound(a,identity)),identity) ),[0],$fot(identity)]]) ).

cnf(refute_0_5,plain,
    ( identity != identity
    | greatest_lower_bound(identity,least_upper_bound(a,identity)) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(a,identity)),identity) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    identity != identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(a,identity)),identity) )],[refute_0_5,prove_p17b]) ).

cnf(refute_0_7,plain,
    identity = identity,
    introduced(tautology,[refl,[$fot(identity)]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_7,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP182-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14  % Command  : metis --show proof --show saturation %s
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Mon Jun 13 16:20:48 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.38  
% 0.15/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.38  
%------------------------------------------------------------------------------