%------------------------------------------------------------------------------
% File     : MaedMax---1.4
% Problem  : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_maedmax %d %s

% Computer : n026.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 07:02:22 EDT 2022

% Result   : Unsatisfiable 1.04s 1.22s
% Output   : CNFRefutation 1.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   49 (  49 unt;   0 nHn;  14 RR)
%            Number of literals    :   49 (  48 equ;  10 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   60 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
    X = multiply(identity,X),
    file('/tmp/MaedMax_6575') ).

cnf(eq_1,axiom,
    identity = multiply(inverse(X),X),
    file('/tmp/MaedMax_6575') ).

cnf(eq_2,axiom,
    greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
    file('/tmp/MaedMax_6575') ).

cnf(eq_3,axiom,
    least_upper_bound(X,Y) = least_upper_bound(Y,X),
    file('/tmp/MaedMax_6575') ).

cnf(eq_4,axiom,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
    file('/tmp/MaedMax_6575') ).

cnf(eq_5,axiom,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
    file('/tmp/MaedMax_6575') ).

cnf(eq_6,axiom,
    X = greatest_lower_bound(X,X),
    file('/tmp/MaedMax_6575') ).

cnf(eq_7,axiom,
    multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
    file('/tmp/MaedMax_6575') ).

cnf(eq_8,axiom,
    multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
    file('/tmp/MaedMax_6575') ).

cnf(eq_9,axiom,
    multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
    file('/tmp/MaedMax_6575') ).

cnf(eq_10,axiom,
    identity = inverse(identity),
    file('/tmp/MaedMax_6575') ).

cnf(eq_11,axiom,
    X = inverse(inverse(X)),
    file('/tmp/MaedMax_6575') ).

cnf(eq_12,axiom,
    multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
    file('/tmp/MaedMax_6575') ).

cnf(eq_13,axiom,
    inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)),
    file('/tmp/MaedMax_6575') ).

cnf(eq_14,axiom,
    inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)),
    file('/tmp/MaedMax_6575') ).

cnf(eq_15,negated_conjecture,
    multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
    file('/tmp/MaedMax_6575') ).

cnf(eq_16,plain,
    multiply(X,inverse(X)) = identity,
    inference(cp,[status(thm)],[eq_11,eq_1]) ).

cnf(eq_17,plain,
    multiply(identity,inverse(x101)) = inverse(multiply(x101,identity)),
    inference(cp,[status(thm)],[eq_10,eq_12]) ).

cnf(eq_18,plain,
    multiply(inverse(x100),X) = inverse(multiply(inverse(X),x100)),
    inference(cp,[status(thm)],[eq_11,eq_12]) ).

cnf(eq_19,plain,
    greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Z),Z)) = greatest_lower_bound(X,Z),
    inference(cp,[status(thm)],[eq_30,eq_6]) ).

cnf(eq_20,plain,
    greatest_lower_bound(X,multiply(x102,X)) = multiply(greatest_lower_bound(identity,x102),X),
    inference(cp,[status(thm)],[eq_0,eq_9]) ).

cnf(eq_21,plain,
    greatest_lower_bound(identity,inverse(x101)) = inverse(least_upper_bound(identity,x101)),
    inference(cp,[status(thm)],[eq_10,eq_14]) ).

cnf(eq_22,plain,
    greatest_lower_bound(greatest_lower_bound(X,Y),x102) = greatest_lower_bound(Y,greatest_lower_bound(X,x102)),
    inference(cp,[status(thm)],[eq_2,eq_4]) ).

cnf(eq_23,plain,
    least_upper_bound(X,multiply(x102,X)) = multiply(least_upper_bound(identity,x102),X),
    inference(cp,[status(thm)],[eq_0,eq_8]) ).

cnf(eq_24,plain,
    multiply(least_upper_bound(identity,X),Y) = least_upper_bound(Y,multiply(X,Y)),
    eq_23 ).

cnf(eq_25,plain,
    multiply(greatest_lower_bound(identity,X),Y) = greatest_lower_bound(Y,multiply(X,Y)),
    eq_20 ).

cnf(eq_26,plain,
    greatest_lower_bound(X,Y) = greatest_lower_bound(X,greatest_lower_bound(X,Y)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_19,eq_4]),eq_6]) ).

cnf(eq_27,plain,
    inverse(X) = inverse(multiply(X,identity)),
    inference(rw,[status(thm)],[eq_17,eq_0]) ).

cnf(eq_28,plain,
    inverse(least_upper_bound(identity,X)) = greatest_lower_bound(identity,inverse(X)),
    eq_21 ).

cnf(eq_29,plain,
    multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
    eq_18 ).

cnf(eq_30,plain,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
    inference(rw,[status(thm)],[eq_22,eq_4]) ).

cnf(eq_31,plain,
    inverse(inverse(X)) = multiply(X,identity),
    inference(cp,[status(thm)],[eq_27,eq_11]) ).

cnf(eq_32,plain,
    inverse(greatest_lower_bound(inverse(X),inverse(Y))) = least_upper_bound(X,Y),
    inference(cp,[status(thm)],[eq_14,eq_11]) ).

cnf(eq_33,plain,
    greatest_lower_bound(multiply(X,x101),identity) = multiply(X,greatest_lower_bound(x101,inverse(X))),
    inference(cp,[status(thm)],[eq_16,eq_7]) ).

cnf(eq_34,plain,
    X = multiply(X,identity),
    inference(rw,[status(thm)],[eq_31,eq_11]) ).

cnf(eq_35,plain,
    multiply(X,greatest_lower_bound(Y,inverse(X))) = greatest_lower_bound(multiply(X,Y),identity),
    eq_33 ).

cnf(eq_36,negated_conjecture,
    multiply(inverse(multiply(greatest_lower_bound(a,identity),identity)),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
    inference(cp,[status(thm)],[eq_27,eq_15]) ).

cnf(eq_37,negated_conjecture,
    multiply(least_upper_bound(identity,inverse(a)),least_upper_bound(identity,a)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,inverse(a))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_36,eq_2]),eq_3]),eq_34]),eq_13]),eq_10]),eq_3]),eq_2]),eq_13]),eq_10]) ).

cnf(eq_38,plain,
    inverse(greatest_lower_bound(identity,inverse(X))) = least_upper_bound(identity,X),
    inference(cp,[status(thm)],[eq_28,eq_11]) ).

cnf(eq_39,plain,
    greatest_lower_bound(X,identity) = multiply(greatest_lower_bound(identity,inverse(X)),X),
    inference(cp,[status(thm)],[eq_1,eq_25]) ).

cnf(eq_40,plain,
    multiply(greatest_lower_bound(identity,inverse(X)),X) = greatest_lower_bound(X,identity),
    eq_39 ).

cnf(eq_41,negated_conjecture,
    least_upper_bound(least_upper_bound(identity,a),multiply(inverse(a),least_upper_bound(identity,a))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,inverse(a))),
    inference(cp,[status(thm)],[eq_24,eq_37]) ).

cnf(eq_42,negated_conjecture,
    multiply(least_upper_bound(identity,a),least_upper_bound(identity,inverse(a))) != least_upper_bound(identity,least_upper_bound(a,multiply(inverse(a),least_upper_bound(identity,a)))),
    inference(rw,[status(thm)],[eq_41,eq_5]) ).

cnf(eq_43,negated_conjecture,
    inverse(greatest_lower_bound(identity,inverse(least_upper_bound(a,multiply(inverse(a),least_upper_bound(identity,a)))))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,inverse(a))),
    inference(cp,[status(thm)],[eq_38,eq_42]) ).

cnf(eq_44,negated_conjecture,
    multiply(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(a)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_43,eq_3]),eq_14]),eq_29]),eq_14]),eq_10]),eq_2]),eq_40]),eq_30]),eq_2]),eq_30]),eq_26]),eq_3]) ).

cnf(eq_45,negated_conjecture,
    inverse(multiply(greatest_lower_bound(identity,a),greatest_lower_bound(identity,inverse(a)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_44,eq_32]),eq_32]),eq_10]),eq_10]),eq_11]),eq_2]),eq_12]),eq_30]) ).

cnf(eq_46,negated_conjecture,
    inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(a)),multiply(a,greatest_lower_bound(identity,inverse(a))))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a)))),
    inference(cp,[status(thm)],[eq_25,eq_45]) ).

cnf(eq_47,negated_conjecture,
    inverse(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(a)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(a)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_46,eq_35]),eq_34]),eq_4]),eq_30]),eq_2]),eq_30]),eq_26]),eq_30]) ).

cnf(bot,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[eq_47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13  % Command  : run_maedmax %d %s
% 0.12/0.34  % Computer : n026.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 04:23:23 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.04/1.22  % SZS status Unsatisfiable
% 1.04/1.22  % SZS output start CNFRefutation for /tmp/MaedMax_6575
% See solution above
% 1.04/1.22  
%------------------------------------------------------------------------------