%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP151-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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 10:37:04 EDT 2022

% Result   : Unsatisfiable 0.14s 0.36s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :   11 (  10 equ;   5 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   :    2 (   1 sgn)

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

cnf(prove_ax_lub2b,negated_conjecture,
    greatest_lower_bound(a,least_upper_bound(a,b)) != a ).

cnf(refute_0_0,plain,
    greatest_lower_bound(a,least_upper_bound(a,b)) = a,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_1,plain,
    ( a != a
    | greatest_lower_bound(a,least_upper_bound(a,b)) != a
    | greatest_lower_bound(a,least_upper_bound(a,b)) = a ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,b)),a) ),[0,0],$fot(a)]]) ).

cnf(refute_0_2,plain,
    ( a != a
    | greatest_lower_bound(a,least_upper_bound(a,b)) = a ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,b)),a) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    a != a,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,b)),a) )],[refute_0_2,prove_ax_lub2b]) ).

cnf(refute_0_4,plain,
    a = a,
    introduced(tautology,[refl,[$fot(a)]]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_4,refute_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP151-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue Jun 14 08:58:22 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36  
% 0.14/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36  
%------------------------------------------------------------------------------