%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP182-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n012.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 10:37:40 EDT 2022

% Result   : Unsatisfiable 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   19 (  12 unt;   0 nHn;  12 RR)
%            Number of literals    :   29 (  28 equ;  12 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   :   23 (   3 sgn)

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

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

cnf(prove_p17a,negated_conjecture,
    least_upper_bound(identity,greatest_lower_bound(a,identity)) != identity ).

cnf(refute_0_0,plain,
    least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)) = X_14,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_1,plain,
    greatest_lower_bound(X_15,X_14) = greatest_lower_bound(X_14,X_15),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_15)),bind(Y,$fot(X_14))]]) ).

cnf(refute_0_2,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_3,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_4,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( greatest_lower_bound(X_15,X_14) != greatest_lower_bound(X_14,X_15)
    | greatest_lower_bound(X_14,X_15) = greatest_lower_bound(X_15,X_14) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_15,X_14))),bind(Y0,$fot(greatest_lower_bound(X_14,X_15)))]]) ).

cnf(refute_0_6,plain,
    greatest_lower_bound(X_14,X_15) = greatest_lower_bound(X_15,X_14),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,X_14),greatest_lower_bound(X_14,X_15)) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( greatest_lower_bound(X_14,X_15) != greatest_lower_bound(X_15,X_14)
    | least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)) != X_14
    | least_upper_bound(X_14,greatest_lower_bound(X_15,X_14)) = X_14 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)),X_14) ),[0,1],$fot(greatest_lower_bound(X_15,X_14))]]) ).

cnf(refute_0_8,plain,
    ( least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)) != X_14
    | least_upper_bound(X_14,greatest_lower_bound(X_15,X_14)) = X_14 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_14,X_15),greatest_lower_bound(X_15,X_14)) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    least_upper_bound(X_14,greatest_lower_bound(X_15,X_14)) = X_14,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)),X_14) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    least_upper_bound(identity,greatest_lower_bound(a,identity)) = identity,
    inference(subst,[],[refute_0_9:[bind(X_14,$fot(identity)),bind(X_15,$fot(a))]]) ).

cnf(refute_0_11,plain,
    ( identity != identity
    | least_upper_bound(identity,greatest_lower_bound(a,identity)) != identity
    | least_upper_bound(identity,greatest_lower_bound(a,identity)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,identity)),identity) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_12,plain,
    ( identity != identity
    | least_upper_bound(identity,greatest_lower_bound(a,identity)) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,identity)),identity) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    identity != identity,
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,identity)),identity) )],[refute_0_12,prove_p17a]) ).

cnf(refute_0_14,plain,
    identity = identity,
    introduced(tautology,[refl,[$fot(identity)]]) ).

cnf(refute_0_15,plain,
    $false,
    inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_14,refute_0_13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP182-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n012.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
% 0.14/0.35  % DateTime : Tue Jun 14 08:08:10 EDT 2022
% 0.14/0.35  % 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  
%------------------------------------------------------------------------------