TSTP Solution File: GRP184-1 by MaedMax---1.4
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- Process Solution
%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : GRP184-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n020.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 80.27s 80.45s
% Output : CNFRefutation 80.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 11 RR)
% Number of literals : 75 ( 74 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 : 131 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
X = multiply(identity,X),
file('/tmp/MaedMax_1496') ).
cnf(eq_1,axiom,
identity = multiply(inverse(X),X),
file('/tmp/MaedMax_1496') ).
cnf(eq_2,axiom,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('/tmp/MaedMax_1496') ).
cnf(eq_3,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/tmp/MaedMax_1496') ).
cnf(eq_4,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/tmp/MaedMax_1496') ).
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_1496') ).
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_1496') ).
cnf(eq_7,axiom,
X = greatest_lower_bound(X,X),
file('/tmp/MaedMax_1496') ).
cnf(eq_8,axiom,
X = least_upper_bound(X,greatest_lower_bound(X,Y)),
file('/tmp/MaedMax_1496') ).
cnf(eq_9,axiom,
X = greatest_lower_bound(X,least_upper_bound(X,Y)),
file('/tmp/MaedMax_1496') ).
cnf(eq_10,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/tmp/MaedMax_1496') ).
cnf(eq_11,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/tmp/MaedMax_1496') ).
cnf(eq_12,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('/tmp/MaedMax_1496') ).
cnf(eq_13,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('/tmp/MaedMax_1496') ).
cnf(eq_14,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_1496') ).
cnf(eq_15,negated_conjecture,
least_upper_bound(multiply(inverse(greatest_lower_bound(identity,a)),identity),multiply(inverse(greatest_lower_bound(identity,a)),a)) != least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,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)],[eq_14,eq_3]),eq_4]),eq_10]),eq_4]),eq_3]),eq_12]),eq_0]) ).
cnf(eq_16,plain,
multiply(identity,x102) = multiply(inverse(X),multiply(X,x102)),
inference(cp,[status(thm)],[eq_1,eq_2]) ).
cnf(eq_17,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Z),Z)) = greatest_lower_bound(X,Z),
inference(cp,[status(thm)],[eq_25,eq_7]) ).
cnf(eq_18,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(cp,[status(thm)],[eq_4,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(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_22,plain,
X = least_upper_bound(X,greatest_lower_bound(Y,X)),
eq_20 ).
cnf(eq_23,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference(rw,[status(thm)],[eq_16,eq_0]) ).
cnf(eq_24,plain,
greatest_lower_bound(X,Y) = greatest_lower_bound(X,greatest_lower_bound(X,Y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_17,eq_5]),eq_7]) ).
cnf(eq_25,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_26,plain,
least_upper_bound(X,Y) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Z),Y)),
eq_21 ).
cnf(eq_27,plain,
greatest_lower_bound(X,multiply(x102,X)) = multiply(greatest_lower_bound(identity,x102),X),
inference(cp,[status(thm)],[eq_0,eq_13]) ).
cnf(eq_28,plain,
multiply(inverse(inverse(Y)),X) = multiply(Y,X),
inference(cp,[status(thm)],[eq_23,eq_23]) ).
cnf(eq_29,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(cp,[status(thm)],[eq_1,eq_23]) ).
cnf(eq_30,plain,
greatest_lower_bound(X,Y) = greatest_lower_bound(greatest_lower_bound(X,Y),X),
inference(cp,[status(thm)],[eq_24,eq_3]) ).
cnf(eq_31,plain,
greatest_lower_bound(x100,X) = greatest_lower_bound(X,greatest_lower_bound(x100,least_upper_bound(Y,X))),
inference(cp,[status(thm)],[eq_18,eq_25]) ).
cnf(eq_32,plain,
least_upper_bound(greatest_lower_bound(X,Z),greatest_lower_bound(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(X,Z),
inference(cp,[status(thm)],[eq_25,eq_22]) ).
cnf(eq_33,plain,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,greatest_lower_bound(X,least_upper_bound(Z,Y))),
eq_31 ).
cnf(eq_34,plain,
multiply(greatest_lower_bound(identity,X),Y) = greatest_lower_bound(Y,multiply(X,Y)),
eq_27 ).
cnf(eq_35,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
eq_28 ).
cnf(eq_36,plain,
X = multiply(inverse(inverse(X)),identity),
eq_29 ).
cnf(eq_37,plain,
greatest_lower_bound(X,Y) = greatest_lower_bound(X,greatest_lower_bound(Y,X)),
inference(rw,[status(thm)],[eq_30,eq_5]) ).
cnf(eq_38,plain,
greatest_lower_bound(X,Y) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,greatest_lower_bound(Z,Y))),
eq_32 ).
cnf(eq_39,plain,
X = multiply(X,identity),
inference(rw,[status(thm)],[eq_36,eq_35]) ).
cnf(eq_40,plain,
multiply(X,inverse(X)) = identity,
inference(cp,[status(thm)],[eq_35,eq_1]) ).
cnf(eq_41,plain,
X = multiply(x100,multiply(inverse(x100),X)),
inference(cp,[status(thm)],[eq_23,eq_35]) ).
cnf(eq_42,plain,
least_upper_bound(greatest_lower_bound(Y,X),greatest_lower_bound(X,Y)) = greatest_lower_bound(Y,X),
inference(cp,[status(thm)],[eq_37,eq_22]) ).
cnf(eq_43,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X,x101),x102),X) = least_upper_bound(X,x102),
inference(cp,[status(thm)],[eq_4,eq_26]) ).
cnf(eq_44,plain,
X = multiply(Y,multiply(inverse(Y),X)),
eq_41 ).
cnf(eq_45,plain,
least_upper_bound(X,Y) = least_upper_bound(greatest_lower_bound(X,Z),least_upper_bound(Y,X)),
inference(rw,[status(thm)],[eq_43,eq_6]) ).
cnf(eq_46,plain,
greatest_lower_bound(X,Y) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)),
eq_42 ).
cnf(eq_47,plain,
multiply(X,multiply(Y,identity)) = multiply(X,Y),
inference(cp,[status(thm)],[eq_2,eq_39]) ).
cnf(eq_48,plain,
multiply(X,identity) = inverse(inverse(X)),
inference(cp,[status(thm)],[eq_35,eq_39]) ).
cnf(eq_49,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(cp,[status(thm)],[eq_2,eq_40]) ).
cnf(eq_50,plain,
least_upper_bound(greatest_lower_bound(X,Y),least_upper_bound(x102,Y)) = least_upper_bound(Y,x102),
inference(cp,[status(thm)],[eq_33,eq_45]) ).
cnf(eq_51,plain,
multiply(X,Y) = multiply(X,multiply(Y,identity)),
eq_47 ).
cnf(eq_52,plain,
least_upper_bound(X,Y) = least_upper_bound(greatest_lower_bound(Z,X),least_upper_bound(Y,X)),
eq_50 ).
cnf(eq_53,negated_conjecture,
least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(cp,[status(thm)],[eq_39,eq_15]) ).
cnf(eq_54,plain,
X = inverse(inverse(X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_36,eq_35]),eq_48]) ).
cnf(eq_55,plain,
multiply(X,Y) = multiply(X,inverse(inverse(Y))),
inference(rw,[status(thm)],[eq_51,eq_48]) ).
cnf(eq_56,plain,
multiply(inverse(X),identity) = multiply(Y,inverse(multiply(X,Y))),
inference(cp,[status(thm)],[eq_49,eq_23]) ).
cnf(eq_57,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(inverse(inverse(Y))),
inference(rw,[status(thm)],[eq_56,eq_48]) ).
cnf(eq_58,negated_conjecture,
least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),inverse(inverse(a)))) != least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(cp,[status(thm)],[eq_55,eq_53]) ).
cnf(eq_59,plain,
multiply(inverse(X),inverse(inverse(inverse(Y)))) = inverse(multiply(Y,X)),
inference(cp,[status(thm)],[eq_57,eq_23]) ).
cnf(eq_60,plain,
least_upper_bound(greatest_lower_bound(x100,greatest_lower_bound(Y,X)),greatest_lower_bound(X,Y)) = least_upper_bound(greatest_lower_bound(Y,X),greatest_lower_bound(X,Y)),
inference(cp,[status(thm)],[eq_46,eq_52]) ).
cnf(eq_61,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(rw,[status(thm)],[eq_59,eq_54]) ).
cnf(eq_62,plain,
greatest_lower_bound(X,Y) = least_upper_bound(greatest_lower_bound(Z,greatest_lower_bound(X,Y)),greatest_lower_bound(Y,X)),
inference(rw,[status(thm)],[eq_60,eq_46]) ).
cnf(eq_63,negated_conjecture,
least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(multiply(inverse(a),greatest_lower_bound(identity,a)))) != least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(cp,[status(thm)],[eq_61,eq_58]) ).
cnf(eq_64,negated_conjecture,
least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))) != least_upper_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)],[eq_63,eq_11]),eq_39]),eq_1]),eq_3]) ).
cnf(eq_65,plain,
least_upper_bound(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(Z,X)) = greatest_lower_bound(X,Z),
inference(cp,[status(thm)],[eq_25,eq_62]) ).
cnf(eq_66,plain,
greatest_lower_bound(X,Y) = least_upper_bound(greatest_lower_bound(X,greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,X)),
eq_65 ).
cnf(eq_67,negated_conjecture,
least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(Z,a)),greatest_lower_bound(a,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) != least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a)))),
inference(cp,[status(thm)],[eq_66,eq_64]) ).
cnf(eq_68,negated_conjecture,
least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),inverse(least_upper_bound(greatest_lower_bound(a,identity),greatest_lower_bound(identity,greatest_lower_bound(X,a))))) != least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_67,eq_4]),eq_3]),eq_4]),eq_3]) ).
cnf(eq_69,plain,
greatest_lower_bound(X,identity) = multiply(greatest_lower_bound(identity,inverse(X)),X),
inference(cp,[status(thm)],[eq_1,eq_34]) ).
cnf(eq_70,plain,
multiply(greatest_lower_bound(identity,inverse(X)),X) = greatest_lower_bound(X,identity),
eq_69 ).
cnf(eq_71,plain,
inverse(greatest_lower_bound(X,identity)) = multiply(inverse(X),inverse(greatest_lower_bound(identity,inverse(X)))),
inference(cp,[status(thm)],[eq_70,eq_61]) ).
cnf(eq_72,negated_conjecture,
least_upper_bound(multiply(a,multiply(inverse(a),inverse(greatest_lower_bound(identity,inverse(a))))),inverse(least_upper_bound(greatest_lower_bound(a,identity),greatest_lower_bound(identity,greatest_lower_bound(x100,a))))) != least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))),
inference(cp,[status(thm)],[eq_71,eq_68]) ).
cnf(eq_73,negated_conjecture,
least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a)))) != least_upper_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_72,eq_44]),eq_3]),eq_38]),eq_4]),eq_3]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP184-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_maedmax %d %s
% 0.12/0.33 % Computer : n020.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 04:14:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 80.27/80.45 % SZS status Unsatisfiable
% 80.27/80.45 % SZS output start CNFRefutation for /tmp/MaedMax_1496
% See solution above
% 80.27/80.45
%------------------------------------------------------------------------------