%------------------------------------------------------------------------------
% File     : MaedMax---1.4
% Problem  : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_maedmax %d %s

% Computer : n009.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 07:02:25 EDT 2022

% Result   : Unsatisfiable 20.84s 21.09s
% Output   : CNFRefutation 20.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   97 (  97 unt;   0 nHn;  30 RR)
%            Number of literals    :   97 (  96 equ;   8 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :  126 (  32 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
    X = multiply(identity,X),
    file('/tmp/MaedMax_20410') ).

cnf(eq_1,axiom,
    identity = multiply(inverse(X),X),
    file('/tmp/MaedMax_20410') ).

cnf(eq_2,axiom,
    multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
    file('/tmp/MaedMax_20410') ).

cnf(eq_3,axiom,
    greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
    file('/tmp/MaedMax_20410') ).

cnf(eq_4,axiom,
    least_upper_bound(X,Y) = least_upper_bound(Y,X),
    file('/tmp/MaedMax_20410') ).

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_20410') ).

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_20410') ).

cnf(eq_7,axiom,
    X = least_upper_bound(X,X),
    file('/tmp/MaedMax_20410') ).

cnf(eq_8,axiom,
    X = least_upper_bound(X,greatest_lower_bound(X,Y)),
    file('/tmp/MaedMax_20410') ).

cnf(eq_9,axiom,
    X = greatest_lower_bound(X,least_upper_bound(X,Y)),
    file('/tmp/MaedMax_20410') ).

cnf(eq_10,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
    file('/tmp/MaedMax_20410') ).

cnf(eq_11,axiom,
    multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
    file('/tmp/MaedMax_20410') ).

cnf(eq_12,axiom,
    least_upper_bound(identity,b) = b,
    file('/tmp/MaedMax_20410') ).

cnf(eq_13,axiom,
    least_upper_bound(identity,c) = c,
    file('/tmp/MaedMax_20410') ).

cnf(eq_14,axiom,
    identity = greatest_lower_bound(a,b),
    file('/tmp/MaedMax_20410') ).

cnf(eq_15,axiom,
    multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
    file('/tmp/MaedMax_20410') ).

cnf(eq_16,negated_conjecture,
    greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
    file('/tmp/MaedMax_20410') ).

cnf(eq_17,plain,
    multiply(inverse(X),X) = greatest_lower_bound(a,b),
    inference(rw,[status(thm)],[eq_1,eq_14]) ).

cnf(eq_18,plain,
    greatest_lower_bound(Y,least_upper_bound(X,least_upper_bound(Y,Z))) = Y,
    inference(cp,[status(thm)],[eq_35,eq_9]) ).

cnf(eq_19,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_20,plain,
    least_upper_bound(Y,greatest_lower_bound(X,Y)) = Y,
    inference(cp,[status(thm)],[eq_3,eq_8]) ).

cnf(eq_21,plain,
    least_upper_bound(b,identity) = b,
    inference(cp,[status(thm)],[eq_4,eq_12]) ).

cnf(eq_22,plain,
    least_upper_bound(c,identity) = c,
    inference(cp,[status(thm)],[eq_4,eq_13]) ).

cnf(eq_23,plain,
    least_upper_bound(x100,x101) = least_upper_bound(x100,least_upper_bound(x101,greatest_lower_bound(least_upper_bound(x100,x101),Y))),
    inference(cp,[status(thm)],[eq_8,eq_6]) ).

cnf(eq_24,plain,
    least_upper_bound(X,x102) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Y),x102)),
    inference(cp,[status(thm)],[eq_8,eq_6]) ).

cnf(eq_25,plain,
    least_upper_bound(least_upper_bound(Y,X),x102) = least_upper_bound(X,least_upper_bound(Y,x102)),
    inference(cp,[status(thm)],[eq_4,eq_6]) ).

cnf(eq_26,plain,
    least_upper_bound(c,x102) = least_upper_bound(identity,least_upper_bound(c,x102)),
    inference(cp,[status(thm)],[eq_13,eq_6]) ).

cnf(eq_27,plain,
    greatest_lower_bound(x100,greatest_lower_bound(X,Y)) = greatest_lower_bound(Y,greatest_lower_bound(x100,X)),
    inference(cp,[status(thm)],[eq_3,eq_37]) ).

cnf(eq_28,plain,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Z,least_upper_bound(X,Y)),
    inference(cp,[status(thm)],[eq_6,eq_4]) ).

cnf(eq_29,plain,
    least_upper_bound(x100,X) = least_upper_bound(X,least_upper_bound(x100,X)),
    inference(cp,[status(thm)],[eq_7,eq_35]) ).

cnf(eq_30,plain,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(Z,X)),
    eq_28 ).

cnf(eq_31,plain,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(Z,X)),
    eq_27 ).

cnf(eq_32,plain,
    X = greatest_lower_bound(X,least_upper_bound(Y,least_upper_bound(X,Z))),
    eq_18 ).

cnf(eq_33,plain,
    X = least_upper_bound(X,greatest_lower_bound(Y,X)),
    eq_20 ).

cnf(eq_34,plain,
    least_upper_bound(X,Y) = least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(least_upper_bound(X,Y),Z))),
    eq_23 ).

cnf(eq_35,plain,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
    inference(rw,[status(thm)],[eq_25,eq_6]) ).

cnf(eq_36,plain,
    least_upper_bound(X,Y) = least_upper_bound(Y,least_upper_bound(X,Y)),
    eq_29 ).

cnf(eq_37,plain,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
    inference(rw,[status(thm)],[eq_19,eq_5]) ).

cnf(eq_38,plain,
    least_upper_bound(X,Y) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Z),Y)),
    eq_24 ).

cnf(eq_39,plain,
    greatest_lower_bound(c,a) = least_upper_bound(greatest_lower_bound(c,a),greatest_lower_bound(a,multiply(b,c))),
    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_15,eq_14]),eq_3]),eq_0]),eq_14]),eq_3]),eq_0]),eq_4]) ).

cnf(eq_40,negated_conjecture,
    greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(c,a),
    inference(rw,[status(thm)],[eq_16,eq_3]) ).

cnf(eq_41,plain,
    multiply(identity,x102) = multiply(inverse(X),multiply(X,x102)),
    inference(cp,[status(thm)],[eq_1,eq_2]) ).

cnf(eq_42,plain,
    greatest_lower_bound(b,a) = identity,
    inference(cp,[status(thm)],[eq_3,eq_14]) ).

cnf(eq_43,plain,
    greatest_lower_bound(Y,least_upper_bound(x101,least_upper_bound(X,Y))) = Y,
    inference(cp,[status(thm)],[eq_36,eq_32]) ).

cnf(eq_44,plain,
    identity = greatest_lower_bound(b,a),
    inference(cp,[status(thm)],[eq_14,eq_3]) ).

cnf(eq_45,plain,
    X = multiply(inverse(Y),multiply(Y,X)),
    inference(rw,[status(thm)],[eq_41,eq_0]) ).

cnf(eq_46,plain,
    X = greatest_lower_bound(X,least_upper_bound(Y,least_upper_bound(Z,X))),
    eq_43 ).

cnf(eq_47,plain,
    least_upper_bound(c,X) = least_upper_bound(c,least_upper_bound(identity,X)),
    inference(rw,[status(thm)],[eq_26,eq_35]) ).

cnf(eq_48,plain,
    least_upper_bound(c,greatest_lower_bound(b,a)) = c,
    inference(rw,[status(thm)],[eq_22,eq_44]) ).

cnf(eq_49,plain,
    X = multiply(greatest_lower_bound(b,a),X),
    inference(rw,[status(thm)],[eq_0,eq_44]) ).

cnf(eq_50,plain,
    greatest_lower_bound(multiply(Y,Z),least_upper_bound(x101,multiply(least_upper_bound(X,Y),Z))) = multiply(Y,Z),
    inference(cp,[status(thm)],[eq_11,eq_46]) ).

cnf(eq_51,plain,
    multiply(X,Y) = greatest_lower_bound(multiply(X,Y),least_upper_bound(Z,multiply(least_upper_bound(x3,X),Y))),
    eq_50 ).

cnf(eq_52,plain,
    least_upper_bound(x100,X) = least_upper_bound(greatest_lower_bound(Y,X),least_upper_bound(x100,X)),
    inference(cp,[status(thm)],[eq_33,eq_30]) ).

cnf(eq_53,plain,
    least_upper_bound(X,Y) = least_upper_bound(greatest_lower_bound(Z,Y),least_upper_bound(X,Y)),
    eq_52 ).

cnf(eq_54,plain,
    multiply(inverse(inverse(Y)),X) = multiply(Y,X),
    inference(cp,[status(thm)],[eq_45,eq_45]) ).

cnf(eq_55,plain,
    multiply(inverse(inverse(X)),greatest_lower_bound(a,b)) = X,
    inference(cp,[status(thm)],[eq_17,eq_45]) ).

cnf(eq_56,plain,
    multiply(X,Y) = multiply(inverse(inverse(X)),Y),
    eq_54 ).

cnf(eq_57,plain,
    X = multiply(inverse(inverse(X)),greatest_lower_bound(a,b)),
    eq_55 ).

cnf(eq_58,plain,
    X = multiply(X,greatest_lower_bound(b,a)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_57,eq_3]),eq_56]) ).

cnf(eq_59,plain,
    multiply(X,inverse(X)) = greatest_lower_bound(a,b),
    inference(cp,[status(thm)],[eq_56,eq_17]) ).

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

cnf(eq_61,plain,
    least_upper_bound(c,multiply(X,inverse(X))) = c,
    inference(cp,[status(thm)],[eq_60,eq_48]) ).

cnf(eq_62,plain,
    multiply(X,greatest_lower_bound(b,a)) = inverse(inverse(X)),
    inference(cp,[status(thm)],[eq_56,eq_58]) ).

cnf(eq_63,plain,
    least_upper_bound(greatest_lower_bound(X,Y),least_upper_bound(x102,X)) = least_upper_bound(x102,X),
    inference(cp,[status(thm)],[eq_3,eq_53]) ).

cnf(eq_64,plain,
    least_upper_bound(X,Y) = least_upper_bound(greatest_lower_bound(Y,Z),least_upper_bound(X,Y)),
    eq_63 ).

cnf(eq_65,plain,
    X = inverse(inverse(X)),
    inference(rw,[status(thm)],[eq_58,eq_62]) ).

cnf(eq_66,plain,
    least_upper_bound(inverse(inverse(X)),multiply(X,x102)) = multiply(X,least_upper_bound(greatest_lower_bound(b,a),x102)),
    inference(cp,[status(thm)],[eq_62,eq_10]) ).

cnf(eq_67,plain,
    multiply(X,least_upper_bound(identity,Y)) = least_upper_bound(X,multiply(X,Y)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_66,eq_65]),eq_42]) ).

cnf(eq_68,plain,
    multiply(c,least_upper_bound(identity,inverse(c))) = c,
    inference(cp,[status(thm)],[eq_67,eq_61]) ).

cnf(eq_69,plain,
    multiply(inverse(c),c) = least_upper_bound(identity,inverse(c)),
    inference(cp,[status(thm)],[eq_68,eq_45]) ).

cnf(eq_70,plain,
    identity = least_upper_bound(identity,inverse(c)),
    inference(rw,[status(thm)],[eq_69,eq_1]) ).

cnf(eq_71,plain,
    least_upper_bound(c,identity) = least_upper_bound(c,inverse(c)),
    inference(cp,[status(thm)],[eq_70,eq_47]) ).

cnf(eq_72,plain,
    least_upper_bound(c,inverse(c)) = c,
    inference(rw,[status(thm)],[eq_71,eq_22]) ).

cnf(eq_73,plain,
    greatest_lower_bound(inverse(c),least_upper_bound(x101,c)) = inverse(c),
    inference(cp,[status(thm)],[eq_72,eq_46]) ).

cnf(eq_74,plain,
    inverse(c) = greatest_lower_bound(inverse(c),least_upper_bound(X,c)),
    eq_73 ).

cnf(eq_75,plain,
    inverse(c) = greatest_lower_bound(least_upper_bound(X,c),inverse(c)),
    inference(cp,[status(thm)],[eq_74,eq_3]) ).

cnf(eq_76,plain,
    greatest_lower_bound(least_upper_bound(c,X),inverse(c)) = inverse(c),
    inference(cp,[status(thm)],[eq_4,eq_75]) ).

cnf(eq_77,plain,
    least_upper_bound(c,least_upper_bound(X,inverse(c))) = least_upper_bound(c,X),
    inference(cp,[status(thm)],[eq_76,eq_34]) ).

cnf(eq_78,plain,
    least_upper_bound(c,X) = least_upper_bound(c,least_upper_bound(X,inverse(c))),
    eq_77 ).

cnf(eq_79,plain,
    greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(x101,greatest_lower_bound(c,a))) = greatest_lower_bound(a,multiply(b,c)),
    inference(cp,[status(thm)],[eq_39,eq_46]) ).

cnf(eq_80,plain,
    greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),least_upper_bound(X,greatest_lower_bound(c,a)))),
    inference(rw,[status(thm)],[eq_79,eq_5]) ).

cnf(eq_81,plain,
    greatest_lower_bound(least_upper_bound(x100,greatest_lower_bound(c,a)),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
    inference(cp,[status(thm)],[eq_31,eq_80]) ).

cnf(eq_82,plain,
    greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X,greatest_lower_bound(c,a)),multiply(b,c))),
    inference(rw,[status(thm)],[eq_81,eq_37]) ).

cnf(eq_83,negated_conjecture,
    greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),least_upper_bound(X,greatest_lower_bound(c,a)))) != greatest_lower_bound(c,a),
    inference(cp,[status(thm)],[eq_80,eq_40]) ).

cnf(eq_84,plain,
    greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(greatest_lower_bound(c,a),X),multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
    inference(cp,[status(thm)],[eq_4,eq_82]) ).

cnf(eq_85,negated_conjecture,
    greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),least_upper_bound(c,least_upper_bound(greatest_lower_bound(c,a),inverse(c))))) != greatest_lower_bound(c,a),
    inference(cp,[status(thm)],[eq_78,eq_83]) ).

cnf(eq_86,negated_conjecture,
    greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))) != greatest_lower_bound(c,a),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_85,eq_38]),eq_72]),eq_3]),eq_37]) ).

cnf(eq_87,plain,
    greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X,c),multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
    inference(cp,[status(thm)],[eq_64,eq_84]) ).

cnf(eq_88,plain,
    greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X,c),multiply(b,c))),
    eq_87 ).

cnf(eq_89,plain,
    greatest_lower_bound(multiply(identity,x101),least_upper_bound(x102,multiply(b,x101))) = multiply(identity,x101),
    inference(cp,[status(thm)],[eq_21,eq_51]) ).

cnf(eq_90,plain,
    X = greatest_lower_bound(X,least_upper_bound(Y,multiply(b,X))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_89,eq_44]),eq_49]),eq_44]),eq_49]) ).

cnf(eq_91,negated_conjecture,
    greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X,c),multiply(b,c)))) != greatest_lower_bound(c,a),
    inference(cp,[status(thm)],[eq_88,eq_86]) ).

cnf(eq_92,plain,
    greatest_lower_bound(x100,multiply(b,x100)) = x100,
    inference(cp,[status(thm)],[eq_7,eq_90]) ).

cnf(eq_93,plain,
    X = greatest_lower_bound(X,multiply(b,X)),
    eq_92 ).

cnf(eq_94,negated_conjecture,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(x100,c),multiply(b,c))),c) != greatest_lower_bound(c,a),
    inference(cp,[status(thm)],[eq_3,eq_91]) ).

cnf(eq_95,negated_conjecture,
    greatest_lower_bound(c,a) != greatest_lower_bound(c,a),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_94,eq_87]),eq_5]),eq_3]),eq_93]),eq_3]) ).

cnf(bot,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[eq_95]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : run_maedmax %d %s
% 0.13/0.34  % Computer : n009.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Jul 26 04:06:51 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 20.84/21.09  % SZS status Unsatisfiable
% 20.84/21.09  % SZS output start CNFRefutation for /tmp/MaedMax_20410
% See solution above
% 20.84/21.09  
%------------------------------------------------------------------------------