%------------------------------------------------------------------------------
% File     : MaedMax---1.4
% Problem  : GRP172-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_maedmax %d %s

% Computer : n018.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  : 300s
% DateTime : Tue Jul 26 07:02:17 EDT 2022

% Result   : Unsatisfiable 0.85s 1.08s
% Output   : CNFRefutation 0.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   28 (  28 unt;   0 nHn;  12 RR)
%            Number of literals    :   28 (  27 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   31 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
    X = multiply(identity,X),
    file('/tmp/MaedMax_22226') ).

cnf(eq_1,axiom,
    greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
    file('/tmp/MaedMax_22226') ).

cnf(eq_2,axiom,
    least_upper_bound(X,Y) = least_upper_bound(Y,X),
    file('/tmp/MaedMax_22226') ).

cnf(eq_3,axiom,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
    file('/tmp/MaedMax_22226') ).

cnf(eq_4,axiom,
    X = least_upper_bound(X,greatest_lower_bound(X,Y)),
    file('/tmp/MaedMax_22226') ).

cnf(eq_5,axiom,
    X = greatest_lower_bound(X,least_upper_bound(X,Y)),
    file('/tmp/MaedMax_22226') ).

cnf(eq_6,axiom,
    multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
    file('/tmp/MaedMax_22226') ).

cnf(eq_7,axiom,
    identity = greatest_lower_bound(identity,a),
    file('/tmp/MaedMax_22226') ).

cnf(eq_8,axiom,
    identity = greatest_lower_bound(identity,b),
    file('/tmp/MaedMax_22226') ).

cnf(eq_9,negated_conjecture,
    identity != greatest_lower_bound(identity,multiply(a,b)),
    file('/tmp/MaedMax_22226') ).

cnf(eq_10,negated_conjecture,
    identity != greatest_lower_bound(multiply(a,b),identity),
    inference(rw,[status(thm)],[eq_9,eq_1]) ).

cnf(eq_11,plain,
    greatest_lower_bound(a,identity) = identity,
    inference(cp,[status(thm)],[eq_1,eq_7]) ).

cnf(eq_12,plain,
    greatest_lower_bound(b,identity) = identity,
    inference(cp,[status(thm)],[eq_1,eq_8]) ).

cnf(eq_13,plain,
    greatest_lower_bound(greatest_lower_bound(X,Y),x102) = greatest_lower_bound(Y,greatest_lower_bound(X,x102)),
    inference(cp,[status(thm)],[eq_1,eq_3]) ).

cnf(eq_14,plain,
    greatest_lower_bound(X,x102) = greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),x102)),
    inference(cp,[status(thm)],[eq_5,eq_3]) ).

cnf(eq_15,plain,
    greatest_lower_bound(identity,x102) = greatest_lower_bound(identity,greatest_lower_bound(b,x102)),
    inference(cp,[status(thm)],[eq_8,eq_3]) ).

cnf(eq_16,plain,
    least_upper_bound(multiply(x100,X),X) = multiply(least_upper_bound(x100,identity),X),
    inference(cp,[status(thm)],[eq_0,eq_6]) ).

cnf(eq_17,plain,
    greatest_lower_bound(identity,X) = greatest_lower_bound(b,greatest_lower_bound(identity,X)),
    inference(rw,[status(thm)],[eq_15,eq_19]) ).

cnf(eq_18,plain,
    greatest_lower_bound(X,Y) = greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Z),Y)),
    eq_14 ).

cnf(eq_19,plain,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
    inference(rw,[status(thm)],[eq_13,eq_3]) ).

cnf(eq_20,plain,
    multiply(least_upper_bound(X,identity),Y) = least_upper_bound(Y,multiply(X,Y)),
    inference(rw,[status(thm)],[eq_16,eq_2]) ).

cnf(eq_21,plain,
    least_upper_bound(a,identity) = a,
    inference(cp,[status(thm)],[eq_11,eq_4]) ).

cnf(eq_22,plain,
    identity = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,x102),identity)),
    inference(cp,[status(thm)],[eq_12,eq_18]) ).

cnf(eq_23,plain,
    identity = greatest_lower_bound(identity,least_upper_bound(b,X)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_22,eq_1]),eq_17]) ).

cnf(eq_24,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X,identity),b)) = identity,
    inference(cp,[status(thm)],[eq_20,eq_23]) ).

cnf(eq_25,plain,
    greatest_lower_bound(identity,multiply(a,b)) = identity,
    inference(cp,[status(thm)],[eq_21,eq_24]) ).

cnf(eq_26,negated_conjecture,
    identity != identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_10,eq_1]),eq_25]) ).

cnf(bot,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[eq_26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP172-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12  % Command  : run_maedmax %d %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Jul 26 04:29:30 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.85/1.08  % SZS status Unsatisfiable
% 0.85/1.08  % SZS output start CNFRefutation for /tmp/MaedMax_22226
% See solution above
% 0.85/1.08  
%------------------------------------------------------------------------------