%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : GRP170-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n005.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 22.60s 22.84s
% Output : CNFRefutation 22.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 21 RR)
% Number of literals : 70 ( 69 equ; 7 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 : 95 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
X = multiply(identity,X),
file('/tmp/MaedMax_10450') ).
cnf(eq_1,axiom,
identity = multiply(inverse(X),X),
file('/tmp/MaedMax_10450') ).
cnf(eq_2,axiom,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('/tmp/MaedMax_10450') ).
cnf(eq_3,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/tmp/MaedMax_10450') ).
cnf(eq_4,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/tmp/MaedMax_10450') ).
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_10450') ).
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_10450') ).
cnf(eq_7,axiom,
X = least_upper_bound(X,X),
file('/tmp/MaedMax_10450') ).
cnf(eq_8,axiom,
X = greatest_lower_bound(X,least_upper_bound(X,Y)),
file('/tmp/MaedMax_10450') ).
cnf(eq_9,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/tmp/MaedMax_10450') ).
cnf(eq_10,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('/tmp/MaedMax_10450') ).
cnf(eq_11,axiom,
least_upper_bound(a,b) = b,
file('/tmp/MaedMax_10450') ).
cnf(eq_12,axiom,
least_upper_bound(c,d) = d,
file('/tmp/MaedMax_10450') ).
cnf(eq_13,negated_conjecture,
multiply(a,c) != greatest_lower_bound(multiply(a,c),multiply(b,d)),
file('/tmp/MaedMax_10450') ).
cnf(eq_14,negated_conjecture,
multiply(a,c) != greatest_lower_bound(multiply(b,d),multiply(a,c)),
inference(rw,[status(thm)],[eq_13,eq_3]) ).
cnf(eq_15,plain,
multiply(identity,x102) = multiply(inverse(X),multiply(X,x102)),
inference(cp,[status(thm)],[eq_1,eq_2]) ).
cnf(eq_16,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(cp,[status(thm)],[eq_4,eq_8]) ).
cnf(eq_17,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_18,plain,
greatest_lower_bound(X,x102) = greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),x102)),
inference(cp,[status(thm)],[eq_8,eq_5]) ).
cnf(eq_19,plain,
least_upper_bound(multiply(inverse(X),x101),identity) = multiply(inverse(X),least_upper_bound(x101,X)),
inference(cp,[status(thm)],[eq_1,eq_9]) ).
cnf(eq_20,plain,
least_upper_bound(X,multiply(x102,X)) = multiply(least_upper_bound(identity,x102),X),
inference(cp,[status(thm)],[eq_0,eq_10]) ).
cnf(eq_21,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_22,plain,
least_upper_bound(d,x102) = least_upper_bound(c,least_upper_bound(d,x102)),
inference(cp,[status(thm)],[eq_12,eq_6]) ).
cnf(eq_23,plain,
least_upper_bound(b,a) = b,
inference(cp,[status(thm)],[eq_4,eq_11]) ).
cnf(eq_24,plain,
least_upper_bound(d,c) = d,
inference(cp,[status(thm)],[eq_4,eq_12]) ).
cnf(eq_25,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_26,plain,
least_upper_bound(x101,x102) = least_upper_bound(x101,least_upper_bound(least_upper_bound(x101,x102),x102)),
inference(cp,[status(thm)],[eq_7,eq_34]) ).
cnf(eq_27,plain,
least_upper_bound(x100,X) = least_upper_bound(X,least_upper_bound(x100,X)),
inference(cp,[status(thm)],[eq_7,eq_34]) ).
cnf(eq_28,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(Z,X)),
eq_25 ).
cnf(eq_29,plain,
least_upper_bound(d,X) = least_upper_bound(d,least_upper_bound(c,X)),
inference(rw,[status(thm)],[eq_22,eq_34]) ).
cnf(eq_30,plain,
multiply(inverse(X),least_upper_bound(Y,X)) = least_upper_bound(identity,multiply(inverse(X),Y)),
inference(rw,[status(thm)],[eq_19,eq_4]) ).
cnf(eq_31,plain,
multiply(least_upper_bound(identity,X),Y) = least_upper_bound(Y,multiply(X,Y)),
eq_20 ).
cnf(eq_32,plain,
least_upper_bound(X,Y) = least_upper_bound(X,least_upper_bound(X,Y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_26,eq_6]),eq_7]) ).
cnf(eq_33,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference(rw,[status(thm)],[eq_15,eq_0]) ).
cnf(eq_34,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(rw,[status(thm)],[eq_21,eq_6]) ).
cnf(eq_35,plain,
greatest_lower_bound(X,Y) = greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Z),Y)),
eq_18 ).
cnf(eq_36,plain,
least_upper_bound(X,Y) = least_upper_bound(Y,least_upper_bound(X,Y)),
eq_27 ).
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_17,eq_5]) ).
cnf(eq_38,plain,
least_upper_bound(multiply(inverse(Y),x101),X) = multiply(inverse(Y),least_upper_bound(x101,multiply(Y,X))),
inference(cp,[status(thm)],[eq_33,eq_9]) ).
cnf(eq_39,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(cp,[status(thm)],[eq_1,eq_33]) ).
cnf(eq_40,plain,
greatest_lower_bound(Z,least_upper_bound(X,least_upper_bound(Y,Z))) = Z,
inference(cp,[status(thm)],[eq_6,eq_16]) ).
cnf(eq_41,plain,
least_upper_bound(d,X) = least_upper_bound(least_upper_bound(c,X),d),
inference(cp,[status(thm)],[eq_29,eq_4]) ).
cnf(eq_42,plain,
least_upper_bound(d,least_upper_bound(d,X)) = least_upper_bound(d,least_upper_bound(c,X)),
inference(cp,[status(thm)],[eq_29,eq_32]) ).
cnf(eq_43,plain,
least_upper_bound(d,least_upper_bound(Y,c)) = least_upper_bound(d,Y),
inference(cp,[status(thm)],[eq_4,eq_29]) ).
cnf(eq_44,plain,
least_upper_bound(c,least_upper_bound(X,d)) = least_upper_bound(d,X),
inference(rw,[status(thm)],[eq_41,eq_6]) ).
cnf(eq_45,plain,
X = greatest_lower_bound(X,least_upper_bound(Y,least_upper_bound(Z,X))),
eq_40 ).
cnf(eq_46,plain,
multiply(inverse(X),least_upper_bound(Y,multiply(X,Z))) = least_upper_bound(multiply(inverse(X),Y),Z),
eq_38 ).
cnf(eq_47,plain,
least_upper_bound(d,least_upper_bound(c,X)) = least_upper_bound(d,least_upper_bound(d,X)),
eq_42 ).
cnf(eq_48,plain,
least_upper_bound(d,X) = least_upper_bound(d,least_upper_bound(X,c)),
eq_43 ).
cnf(eq_49,plain,
multiply(inverse(inverse(inverse(X))),X) = identity,
inference(cp,[status(thm)],[eq_39,eq_33]) ).
cnf(eq_50,plain,
multiply(inverse(inverse(inverse(inverse(X)))),identity) = X,
inference(cp,[status(thm)],[eq_49,eq_33]) ).
cnf(eq_51,plain,
X = inverse(inverse(X)),
inference(rw,[status(thm)],[eq_50,eq_39]) ).
cnf(eq_52,negated_conjecture,
greatest_lower_bound(multiply(b,d),greatest_lower_bound(least_upper_bound(multiply(b,d),Z),multiply(a,c))) != multiply(a,c),
inference(cp,[status(thm)],[eq_35,eq_14]) ).
cnf(eq_53,negated_conjecture,
multiply(a,c) != greatest_lower_bound(multiply(b,d),greatest_lower_bound(least_upper_bound(multiply(b,d),X),multiply(a,c))),
eq_52 ).
cnf(eq_54,plain,
multiply(inverse(least_upper_bound(X,Y)),least_upper_bound(X,Y)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X,Y)),Y)),
inference(cp,[status(thm)],[eq_36,eq_30]) ).
cnf(eq_55,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X,Y)),Y)),
inference(rw,[status(thm)],[eq_54,eq_1]) ).
cnf(eq_56,plain,
least_upper_bound(identity,multiply(inverse(b),a)) = identity,
inference(cp,[status(thm)],[eq_23,eq_55]) ).
cnf(eq_57,plain,
multiply(identity,x101) = least_upper_bound(x101,multiply(multiply(inverse(b),a),x101)),
inference(cp,[status(thm)],[eq_56,eq_31]) ).
cnf(eq_58,plain,
X = least_upper_bound(X,multiply(inverse(b),multiply(a,X))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_57,eq_0]),eq_2]) ).
cnf(eq_59,plain,
least_upper_bound(x100,least_upper_bound(d,X)) = least_upper_bound(least_upper_bound(X,c),least_upper_bound(x100,d)),
inference(cp,[status(thm)],[eq_48,eq_28]) ).
cnf(eq_60,plain,
least_upper_bound(X,least_upper_bound(d,Y)) = least_upper_bound(Y,least_upper_bound(d,X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_59,eq_6]),eq_44]) ).
cnf(eq_61,plain,
least_upper_bound(d,c) = least_upper_bound(d,least_upper_bound(d,multiply(inverse(b),multiply(a,c)))),
inference(cp,[status(thm)],[eq_58,eq_47]) ).
cnf(eq_62,plain,
least_upper_bound(d,multiply(inverse(b),multiply(a,c))) = d,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_61,eq_24]),eq_32]) ).
cnf(eq_63,plain,
multiply(inverse(inverse(b)),d) = least_upper_bound(multiply(inverse(inverse(b)),d),multiply(a,c)),
inference(cp,[status(thm)],[eq_62,eq_46]) ).
cnf(eq_64,plain,
multiply(b,d) = least_upper_bound(multiply(b,d),multiply(a,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_63,eq_51]),eq_51]) ).
cnf(eq_65,negated_conjecture,
greatest_lower_bound(multiply(b,d),greatest_lower_bound(least_upper_bound(Y,least_upper_bound(d,multiply(b,d))),multiply(a,c))) != multiply(a,c),
inference(cp,[status(thm)],[eq_60,eq_53]) ).
cnf(eq_66,negated_conjecture,
multiply(a,c) != greatest_lower_bound(multiply(b,d),greatest_lower_bound(multiply(a,c),least_upper_bound(X,least_upper_bound(d,multiply(b,d))))),
inference(rw,[status(thm)],[eq_65,eq_3]) ).
cnf(eq_67,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = multiply(a,c),
inference(cp,[status(thm)],[eq_64,eq_16]) ).
cnf(eq_68,negated_conjecture,
multiply(a,c) != multiply(a,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_66,eq_37]),eq_45]),eq_67]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP170-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_maedmax %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jul 26 04:09:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 22.60/22.84 % SZS status Unsatisfiable
% 22.60/22.84 % SZS output start CNFRefutation for /tmp/MaedMax_10450
% See solution above
% 22.60/22.84
%------------------------------------------------------------------------------