%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP182-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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 0.19s 0.36s
% Output   : CNFRefutation 0.19s
% 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_8,greatest_lower_bound(X_8,X_9)) = X_8,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).

cnf(refute_0_1,plain,
    greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).

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_9,X_8) != greatest_lower_bound(X_8,X_9)
    | greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).

cnf(refute_0_6,plain,
    greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
    | least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).

cnf(refute_0_8,plain,
    ( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[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_8,$fot(identity)),bind(X_9,$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
% 0.04/0.12  % Problem  : GRP182-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 03:24:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36  
% 0.19/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36  
%------------------------------------------------------------------------------