%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP142-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n010.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 10:37:01 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   20 (  11 unt;   0 nHn;  16 RR)
%            Number of literals    :   34 (  33 equ;  16 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   :   19 (   1 sgn)

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

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

cnf(prove_ax_glb2a,negated_conjecture,
    least_upper_bound(greatest_lower_bound(a,b),a) != a ).

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

cnf(refute_0_1,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_3,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( least_upper_bound(X,Y) != least_upper_bound(Y,X)
    | least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
    inference(subst,[],[refute_0_3:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).

cnf(refute_0_5,plain,
    least_upper_bound(Y,X) = least_upper_bound(X,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_4]) ).

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

cnf(refute_0_7,plain,
    ( Y0 != X0
    | Y0 != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_8,plain,
    ( X0 != Y0
    | Y0 != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_3,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( least_upper_bound(a,greatest_lower_bound(a,b)) != a
    | least_upper_bound(greatest_lower_bound(a,b),a) != least_upper_bound(a,greatest_lower_bound(a,b))
    | least_upper_bound(greatest_lower_bound(a,b),a) = a ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,b),a))),bind(Y0,$fot(least_upper_bound(a,greatest_lower_bound(a,b)))),bind(Z,$fot(a))]]) ).

cnf(refute_0_10,plain,
    ( least_upper_bound(a,greatest_lower_bound(a,b)) != a
    | least_upper_bound(greatest_lower_bound(a,b),a) = a ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),a),least_upper_bound(a,greatest_lower_bound(a,b))) )],[refute_0_6,refute_0_9]) ).

cnf(refute_0_11,plain,
    least_upper_bound(greatest_lower_bound(a,b),a) = a,
    inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,b)),a) )],[refute_0_0,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( a != a
    | least_upper_bound(greatest_lower_bound(a,b),a) != a
    | least_upper_bound(greatest_lower_bound(a,b),a) = a ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),a),a) ),[0,0,0],$fot(a)]]) ).

cnf(refute_0_13,plain,
    ( a != a
    | least_upper_bound(greatest_lower_bound(a,b),a) = a ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),a),a) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    a != a,
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),a),a) )],[refute_0_13,prove_ax_glb2a]) ).

cnf(refute_0_15,plain,
    a = a,
    introduced(tautology,[refl,[$fot(a)]]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_15,refute_0_14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP142-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 16:32:09 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------