%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP137-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n019.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 10:36:59 EDT 2022

% Result   : Unsatisfiable 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   16 (   9 unt;   0 nHn;  15 RR)
%            Number of literals    :   26 (  25 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    5 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(ax_antisymb_1,hypothesis,
    greatest_lower_bound(a,b) = a ).

cnf(ax_antisymb_2,hypothesis,
    greatest_lower_bound(a,b) = b ).

cnf(prove_ax_antisymb,negated_conjecture,
    a != b ).

cnf(refute_0_0,plain,
    ( greatest_lower_bound(a,b) != a
    | greatest_lower_bound(a,b) != b
    | a = b ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,b),b) ),[0],$fot(a)]]) ).

cnf(refute_0_1,plain,
    ( greatest_lower_bound(a,b) != b
    | a = b ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[ax_antisymb_1,refute_0_0]) ).

cnf(refute_0_2,plain,
    a = b,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),b) )],[ax_antisymb_2,refute_0_1]) ).

cnf(refute_0_3,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_4,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_5,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( a != b
    | b = a ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_7,plain,
    b = a,
    inference(resolve,[$cnf( $equal(a,b) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( a != a
    | b != a
    | a = b ),
    introduced(tautology,[equality,[$cnf( ~ $equal(a,b) ),[1],$fot(a)]]) ).

cnf(refute_0_9,plain,
    ( a != a
    | a = b ),
    inference(resolve,[$cnf( $equal(b,a) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    a != a,
    inference(resolve,[$cnf( $equal(a,b) )],[refute_0_9,prove_ax_antisymb]) ).

cnf(refute_0_11,plain,
    a = a,
    introduced(tautology,[refl,[$fot(a)]]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_11,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRP137-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n019.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
% 0.14/0.36  % DateTime : Mon Jun 13 19:59:24 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37  
% 0.14/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37  
%------------------------------------------------------------------------------