%------------------------------------------------------------------------------
% File     : MaedMax---1.4
% Problem  : GRP183-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_maedmax %d %s

% Computer : n011.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 07:02:21 EDT 2022

% Result   : Unsatisfiable 147.97s 148.20s
% Output   : CNFRefutation 147.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   82 (  82 unt;   0 nHn;  20 RR)
%            Number of literals    :   82 (  81 equ;  14 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   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   :  112 (  15 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
    X = multiply(identity,X),
    file('/tmp/MaedMax_25826') ).

cnf(eq_1,axiom,
    identity = multiply(inverse(X),X),
    file('/tmp/MaedMax_25826') ).

cnf(eq_2,axiom,
    multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
    file('/tmp/MaedMax_25826') ).

cnf(eq_3,axiom,
    greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
    file('/tmp/MaedMax_25826') ).

cnf(eq_4,axiom,
    least_upper_bound(X,Y) = least_upper_bound(Y,X),
    file('/tmp/MaedMax_25826') ).

cnf(eq_5,axiom,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
    file('/tmp/MaedMax_25826') ).

cnf(eq_6,axiom,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
    file('/tmp/MaedMax_25826') ).

cnf(eq_7,axiom,
    X = greatest_lower_bound(X,X),
    file('/tmp/MaedMax_25826') ).

cnf(eq_8,axiom,
    X = least_upper_bound(X,greatest_lower_bound(X,Y)),
    file('/tmp/MaedMax_25826') ).

cnf(eq_9,axiom,
    X = greatest_lower_bound(X,least_upper_bound(X,Y)),
    file('/tmp/MaedMax_25826') ).

cnf(eq_10,axiom,
    multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
    file('/tmp/MaedMax_25826') ).

cnf(eq_11,axiom,
    multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
    file('/tmp/MaedMax_25826') ).

cnf(eq_12,axiom,
    multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
    file('/tmp/MaedMax_25826') ).

cnf(eq_13,axiom,
    identity = inverse(identity),
    file('/tmp/MaedMax_25826') ).

cnf(eq_14,axiom,
    X = inverse(inverse(X)),
    file('/tmp/MaedMax_25826') ).

cnf(eq_15,axiom,
    multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
    file('/tmp/MaedMax_25826') ).

cnf(eq_16,negated_conjecture,
    identity != greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
    file('/tmp/MaedMax_25826') ).

cnf(eq_17,plain,
    multiply(X,inverse(X)) = identity,
    inference(cp,[status(thm)],[eq_14,eq_1]) ).

cnf(eq_18,plain,
    multiply(X,inverse(x101)) = inverse(multiply(x101,inverse(X))),
    inference(cp,[status(thm)],[eq_14,eq_15]) ).

cnf(eq_19,plain,
    multiply(inverse(x100),identity) = inverse(multiply(identity,x100)),
    inference(cp,[status(thm)],[eq_13,eq_15]) ).

cnf(eq_20,plain,
    multiply(inverse(x100),X) = inverse(multiply(inverse(X),x100)),
    inference(cp,[status(thm)],[eq_14,eq_15]) ).

cnf(eq_21,plain,
    greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Z),Z)) = greatest_lower_bound(X,Z),
    inference(cp,[status(thm)],[eq_34,eq_7]) ).

cnf(eq_22,plain,
    greatest_lower_bound(multiply(x100,X),X) = multiply(greatest_lower_bound(x100,identity),X),
    inference(cp,[status(thm)],[eq_0,eq_12]) ).

cnf(eq_23,plain,
    greatest_lower_bound(greatest_lower_bound(X,Y),x102) = greatest_lower_bound(Y,greatest_lower_bound(X,x102)),
    inference(cp,[status(thm)],[eq_3,eq_5]) ).

cnf(eq_24,plain,
    greatest_lower_bound(X,x102) = greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),x102)),
    inference(cp,[status(thm)],[eq_9,eq_5]) ).

cnf(eq_25,plain,
    least_upper_bound(Y,greatest_lower_bound(X,Y)) = Y,
    inference(cp,[status(thm)],[eq_3,eq_8]) ).

cnf(eq_26,plain,
    least_upper_bound(X,multiply(x102,X)) = multiply(least_upper_bound(identity,x102),X),
    inference(cp,[status(thm)],[eq_0,eq_11]) ).

cnf(eq_27,plain,
    multiply(least_upper_bound(identity,X),Y) = least_upper_bound(Y,multiply(X,Y)),
    eq_26 ).

cnf(eq_28,plain,
    greatest_lower_bound(X,Y) = greatest_lower_bound(X,greatest_lower_bound(X,Y)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_21,eq_5]),eq_7]) ).

cnf(eq_29,plain,
    multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
    eq_20 ).

cnf(eq_30,plain,
    multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
    eq_18 ).

cnf(eq_31,plain,
    X = least_upper_bound(X,greatest_lower_bound(Y,X)),
    eq_25 ).

cnf(eq_32,plain,
    greatest_lower_bound(X,Y) = greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Z),Y)),
    eq_24 ).

cnf(eq_33,plain,
    multiply(greatest_lower_bound(X,identity),Y) = greatest_lower_bound(Y,multiply(X,Y)),
    inference(rw,[status(thm)],[eq_22,eq_3]) ).

cnf(eq_34,plain,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
    inference(rw,[status(thm)],[eq_23,eq_5]) ).

cnf(eq_35,plain,
    multiply(inverse(X),identity) = inverse(X),
    inference(rw,[status(thm)],[eq_19,eq_0]) ).

cnf(eq_36,plain,
    multiply(identity,x102) = multiply(X,multiply(inverse(X),x102)),
    inference(cp,[status(thm)],[eq_17,eq_2]) ).

cnf(eq_37,plain,
    least_upper_bound(multiply(x100,inverse(X)),identity) = multiply(least_upper_bound(x100,X),inverse(X)),
    inference(cp,[status(thm)],[eq_17,eq_11]) ).

cnf(eq_38,plain,
    multiply(X,identity) = inverse(inverse(X)),
    inference(cp,[status(thm)],[eq_14,eq_35]) ).

cnf(eq_39,plain,
    X = multiply(X,identity),
    inference(rw,[status(thm)],[eq_38,eq_14]) ).

cnf(eq_40,plain,
    X = multiply(Y,multiply(inverse(Y),X)),
    inference(rw,[status(thm)],[eq_36,eq_0]) ).

cnf(eq_41,plain,
    multiply(least_upper_bound(X,Y),inverse(Y)) = least_upper_bound(identity,multiply(X,inverse(Y))),
    inference(rw,[status(thm)],[eq_37,eq_4]) ).

cnf(eq_42,plain,
    multiply(X,inverse(multiply(Y,X))) = inverse(Y),
    inference(cp,[status(thm)],[eq_15,eq_40]) ).

cnf(eq_43,plain,
    greatest_lower_bound(X,multiply(X,x102)) = multiply(X,greatest_lower_bound(identity,x102)),
    inference(cp,[status(thm)],[eq_39,eq_10]) ).

cnf(eq_44,plain,
    multiply(X,greatest_lower_bound(identity,Y)) = greatest_lower_bound(X,multiply(X,Y)),
    eq_43 ).

cnf(eq_45,plain,
    multiply(inverse(multiply(Y,X)),inverse(inverse(Y))) = inverse(X),
    inference(cp,[status(thm)],[eq_42,eq_42]) ).

cnf(eq_46,plain,
    multiply(inverse(multiply(X,Y)),X) = inverse(Y),
    inference(rw,[status(thm)],[eq_45,eq_14]) ).

cnf(eq_47,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,identity),multiply(X,inverse(multiply(greatest_lower_bound(a,identity),X)))) != identity,
    inference(cp,[status(thm)],[eq_42,eq_16]) ).

cnf(eq_48,plain,
    greatest_lower_bound(X,identity) = multiply(greatest_lower_bound(inverse(X),identity),X),
    inference(cp,[status(thm)],[eq_1,eq_33]) ).

cnf(eq_49,plain,
    multiply(greatest_lower_bound(identity,inverse(X)),X) = greatest_lower_bound(X,identity),
    inference(rw,[status(thm)],[eq_48,eq_3]) ).

cnf(eq_50,plain,
    inverse(greatest_lower_bound(inverse(x101),identity)) = multiply(x101,inverse(greatest_lower_bound(identity,inverse(inverse(x101))))),
    inference(cp,[status(thm)],[eq_49,eq_30]) ).

cnf(eq_51,plain,
    multiply(greatest_lower_bound(identity,X),inverse(X)) = greatest_lower_bound(inverse(X),identity),
    inference(cp,[status(thm)],[eq_14,eq_49]) ).

cnf(eq_52,plain,
    multiply(X,inverse(greatest_lower_bound(identity,X))) = inverse(greatest_lower_bound(identity,inverse(X))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_50,eq_3]),eq_14]) ).

cnf(eq_53,plain,
    multiply(greatest_lower_bound(identity,X),inverse(X)) = greatest_lower_bound(identity,inverse(X)),
    inference(rw,[status(thm)],[eq_51,eq_3]) ).

cnf(eq_54,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(Y,x101),x102),Y) = greatest_lower_bound(Y,x102),
    inference(cp,[status(thm)],[eq_3,eq_32]) ).

cnf(eq_55,plain,
    greatest_lower_bound(X,Y) = greatest_lower_bound(least_upper_bound(X,Z),greatest_lower_bound(Y,X)),
    inference(rw,[status(thm)],[eq_54,eq_5]) ).

cnf(eq_56,plain,
    greatest_lower_bound(X,identity) = multiply(X,greatest_lower_bound(identity,inverse(X))),
    inference(cp,[status(thm)],[eq_17,eq_44]) ).

cnf(eq_57,plain,
    multiply(X,greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(X,identity),
    eq_56 ).

cnf(eq_58,plain,
    multiply(inverse(greatest_lower_bound(X,identity)),X) = inverse(greatest_lower_bound(identity,inverse(X))),
    inference(cp,[status(thm)],[eq_57,eq_46]) ).

cnf(eq_59,plain,
    inverse(greatest_lower_bound(inverse(x100),identity)) = multiply(inverse(greatest_lower_bound(identity,inverse(inverse(x100)))),x100),
    inference(cp,[status(thm)],[eq_57,eq_29]) ).

cnf(eq_60,plain,
    multiply(inverse(greatest_lower_bound(identity,X)),X) = inverse(greatest_lower_bound(identity,inverse(X))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_59,eq_3]),eq_14]) ).

cnf(eq_61,plain,
    multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,Y))),
    inference(cp,[status(thm)],[eq_28,eq_53]) ).

cnf(eq_62,plain,
    identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X))),
    inference(rw,[status(thm)],[eq_61,eq_17]) ).

cnf(eq_63,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X)),identity) = inverse(greatest_lower_bound(identity,X)),
    inference(cp,[status(thm)],[eq_62,eq_31]) ).

cnf(eq_64,plain,
    inverse(greatest_lower_bound(identity,X)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X))),
    inference(rw,[status(thm)],[eq_63,eq_4]) ).

cnf(eq_65,plain,
    greatest_lower_bound(multiply(X,inverse(greatest_lower_bound(X,Y))),multiply(Y,inverse(greatest_lower_bound(X,Y)))) = identity,
    inference(cp,[status(thm)],[eq_12,eq_17]) ).

cnf(eq_66,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(identity,x101)),multiply(x101,inverse(greatest_lower_bound(identity,x101)))) = identity,
    inference(cp,[status(thm)],[eq_0,eq_65]) ).

cnf(eq_67,plain,
    identity = greatest_lower_bound(inverse(greatest_lower_bound(identity,X)),multiply(X,inverse(greatest_lower_bound(identity,X)))),
    eq_66 ).

cnf(eq_68,negated_conjecture,
    greatest_lower_bound(least_upper_bound(least_upper_bound(a,identity),Z),greatest_lower_bound(multiply(x100,inverse(multiply(greatest_lower_bound(a,identity),x100))),least_upper_bound(a,identity))) != identity,
    inference(cp,[status(thm)],[eq_55,eq_47]) ).

cnf(eq_69,negated_conjecture,
    identity != greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(least_upper_bound(a,least_upper_bound(identity,X)),inverse(greatest_lower_bound(a,identity)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_68,eq_6]),eq_42]),eq_3]),eq_34]) ).

cnf(eq_70,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,least_upper_bound(identity,x100)))) != identity,
    inference(cp,[status(thm)],[eq_3,eq_69]) ).

cnf(eq_71,negated_conjecture,
    identity != greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,least_upper_bound(identity,X)))),
    eq_70 ).

cnf(eq_72,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,multiply(least_upper_bound(X,Y),inverse(Y))))) != identity,
    inference(cp,[status(thm)],[eq_41,eq_71]) ).

cnf(eq_73,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,least_upper_bound(identity,multiply(X,inverse(Y)))))) != identity,
    inference(cp,[status(thm)],[eq_41,eq_72]) ).

cnf(eq_74,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(x101)))))))) != identity,
    inference(cp,[status(thm)],[eq_60,eq_73]) ).

cnf(eq_75,negated_conjecture,
    identity != greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,inverse(greatest_lower_bound(identity,X))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_74,eq_14]),eq_64]) ).

cnf(eq_76,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,multiply(inverse(greatest_lower_bound(X,identity)),X)))) != identity,
    inference(cp,[status(thm)],[eq_58,eq_75]) ).

cnf(eq_77,plain,
    identity = greatest_lower_bound(inverse(greatest_lower_bound(identity,X)),inverse(greatest_lower_bound(identity,inverse(X)))),
    inference(rw,[status(thm)],[eq_67,eq_52]) ).

cnf(eq_78,negated_conjecture,
    greatest_lower_bound(least_upper_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))),a))) != identity,
    inference(cp,[status(thm)],[eq_27,eq_76]) ).

cnf(eq_79,negated_conjecture,
    identity != greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),inverse(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)],[eq_78,eq_4]),eq_3]),eq_3]),eq_64]),eq_60]) ).

cnf(eq_80,negated_conjecture,
    identity != identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_79,eq_77]),eq_3]),eq_9]) ).

cnf(bot,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[eq_80]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP183-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : run_maedmax %d %s
% 0.13/0.34  % Computer : n011.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  : 300
% 0.13/0.34  % DateTime : Tue Jul 26 04:06:54 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 147.97/148.20  % SZS status Unsatisfiable
% 147.97/148.20  % SZS output start CNFRefutation for /tmp/MaedMax_25826
% See solution above
% 147.97/148.20  
%------------------------------------------------------------------------------