TSTP Solution File: GRP184-2 by MaedMax---1.4
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%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : GRP184-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n029.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 141.40s 141.67s
% Output : CNFRefutation 141.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 14 RR)
% Number of literals : 56 ( 55 equ; 10 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
X = multiply(identity,X),
file('/tmp/MaedMax_16120') ).
cnf(eq_1,axiom,
identity = multiply(inverse(X),X),
file('/tmp/MaedMax_16120') ).
cnf(eq_2,axiom,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('/tmp/MaedMax_16120') ).
cnf(eq_3,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/tmp/MaedMax_16120') ).
cnf(eq_4,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/tmp/MaedMax_16120') ).
cnf(eq_5,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/tmp/MaedMax_16120') ).
cnf(eq_6,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/tmp/MaedMax_16120') ).
cnf(eq_7,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('/tmp/MaedMax_16120') ).
cnf(eq_8,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('/tmp/MaedMax_16120') ).
cnf(eq_9,axiom,
identity = inverse(identity),
file('/tmp/MaedMax_16120') ).
cnf(eq_10,axiom,
X = inverse(inverse(X)),
file('/tmp/MaedMax_16120') ).
cnf(eq_11,axiom,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
file('/tmp/MaedMax_16120') ).
cnf(eq_12,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_16120') ).
cnf(eq_13,plain,
multiply(identity,x102) = multiply(inverse(X),multiply(X,x102)),
inference(cp,[status(thm)],[eq_1,eq_2]) ).
cnf(eq_14,plain,
multiply(X,inverse(X)) = identity,
inference(cp,[status(thm)],[eq_10,eq_1]) ).
cnf(eq_15,plain,
multiply(X,inverse(x101)) = inverse(multiply(x101,inverse(X))),
inference(cp,[status(thm)],[eq_10,eq_11]) ).
cnf(eq_16,plain,
multiply(inverse(x100),identity) = inverse(multiply(identity,x100)),
inference(cp,[status(thm)],[eq_9,eq_11]) ).
cnf(eq_17,plain,
greatest_lower_bound(X,multiply(x102,X)) = multiply(greatest_lower_bound(identity,x102),X),
inference(cp,[status(thm)],[eq_0,eq_8]) ).
cnf(eq_18,plain,
least_upper_bound(X,multiply(x102,X)) = multiply(least_upper_bound(identity,x102),X),
inference(cp,[status(thm)],[eq_0,eq_7]) ).
cnf(eq_19,plain,
multiply(least_upper_bound(identity,X),Y) = least_upper_bound(Y,multiply(X,Y)),
eq_18 ).
cnf(eq_20,plain,
multiply(greatest_lower_bound(identity,X),Y) = greatest_lower_bound(Y,multiply(X,Y)),
eq_17 ).
cnf(eq_21,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference(rw,[status(thm)],[eq_13,eq_0]) ).
cnf(eq_22,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
eq_15 ).
cnf(eq_23,plain,
multiply(inverse(X),identity) = inverse(X),
inference(rw,[status(thm)],[eq_16,eq_0]) ).
cnf(eq_24,plain,
multiply(identity,x102) = multiply(X,multiply(inverse(X),x102)),
inference(cp,[status(thm)],[eq_14,eq_2]) ).
cnf(eq_25,plain,
greatest_lower_bound(multiply(X,x101),identity) = multiply(X,greatest_lower_bound(x101,inverse(X))),
inference(cp,[status(thm)],[eq_14,eq_6]) ).
cnf(eq_26,plain,
multiply(X,identity) = inverse(inverse(X)),
inference(cp,[status(thm)],[eq_10,eq_23]) ).
cnf(eq_27,plain,
X = multiply(X,identity),
inference(rw,[status(thm)],[eq_26,eq_10]) ).
cnf(eq_28,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference(rw,[status(thm)],[eq_24,eq_0]) ).
cnf(eq_29,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(cp,[status(thm)],[eq_11,eq_28]) ).
cnf(eq_30,plain,
greatest_lower_bound(X,multiply(X,x102)) = multiply(X,greatest_lower_bound(identity,x102)),
inference(cp,[status(thm)],[eq_27,eq_6]) ).
cnf(eq_31,plain,
least_upper_bound(X,multiply(X,x102)) = multiply(X,least_upper_bound(identity,x102)),
inference(cp,[status(thm)],[eq_27,eq_5]) ).
cnf(eq_32,plain,
multiply(X,greatest_lower_bound(identity,Y)) = greatest_lower_bound(X,multiply(X,Y)),
eq_30 ).
cnf(eq_33,plain,
multiply(X,least_upper_bound(identity,Y)) = least_upper_bound(X,multiply(X,Y)),
eq_31 ).
cnf(eq_34,plain,
multiply(inverse(multiply(Y,X)),inverse(inverse(Y))) = inverse(X),
inference(cp,[status(thm)],[eq_29,eq_29]) ).
cnf(eq_35,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference(rw,[status(thm)],[eq_34,eq_10]) ).
cnf(eq_36,plain,
greatest_lower_bound(X,identity) = multiply(greatest_lower_bound(identity,inverse(X)),X),
inference(cp,[status(thm)],[eq_1,eq_20]) ).
cnf(eq_37,plain,
multiply(greatest_lower_bound(identity,inverse(X)),X) = greatest_lower_bound(X,identity),
eq_36 ).
cnf(eq_38,plain,
inverse(greatest_lower_bound(inverse(x101),identity)) = multiply(x101,inverse(greatest_lower_bound(identity,inverse(inverse(x101))))),
inference(cp,[status(thm)],[eq_37,eq_22]) ).
cnf(eq_39,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_38,eq_3]),eq_10]) ).
cnf(eq_40,plain,
greatest_lower_bound(X,identity) = multiply(X,greatest_lower_bound(identity,inverse(X))),
inference(cp,[status(thm)],[eq_14,eq_32]) ).
cnf(eq_41,plain,
least_upper_bound(inverse(X),identity) = multiply(inverse(X),least_upper_bound(identity,X)),
inference(cp,[status(thm)],[eq_1,eq_33]) ).
cnf(eq_42,plain,
multiply(X,greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(X,identity),
eq_40 ).
cnf(eq_43,plain,
multiply(inverse(X),least_upper_bound(identity,X)) = least_upper_bound(identity,inverse(X)),
inference(rw,[status(thm)],[eq_41,eq_4]) ).
cnf(eq_44,plain,
multiply(inverse(X),greatest_lower_bound(X,identity)) = greatest_lower_bound(identity,inverse(X)),
inference(cp,[status(thm)],[eq_42,eq_21]) ).
cnf(eq_45,plain,
multiply(X,greatest_lower_bound(Y,inverse(X))) = greatest_lower_bound(multiply(X,Y),identity),
eq_25 ).
cnf(eq_46,negated_conjecture,
multiply(multiply(inverse(multiply(X,greatest_lower_bound(a,identity))),X),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(cp,[status(thm)],[eq_35,eq_12]) ).
cnf(eq_47,negated_conjecture,
multiply(inverse(multiply(X,greatest_lower_bound(a,identity))),multiply(X,least_upper_bound(a,identity))) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(rw,[status(thm)],[eq_46,eq_2]) ).
cnf(eq_48,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,inverse(a))),multiply(inverse(a),least_upper_bound(a,identity))) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(cp,[status(thm)],[eq_44,eq_47]) ).
cnf(eq_49,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,inverse(a))),multiply(inverse(a),least_upper_bound(identity,a))) != multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_48,eq_4]),eq_4]),eq_3]) ).
cnf(eq_50,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,inverse(a))),least_upper_bound(identity,inverse(a))) != multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),
inference(rw,[status(thm)],[eq_49,eq_43]) ).
cnf(eq_51,negated_conjecture,
least_upper_bound(inverse(greatest_lower_bound(identity,inverse(a))),multiply(inverse(greatest_lower_bound(identity,inverse(a))),inverse(a))) != multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),
inference(cp,[status(thm)],[eq_33,eq_50]) ).
cnf(eq_52,negated_conjecture,
multiply(least_upper_bound(identity,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)],[inference(rw,[status(thm)],[eq_51,eq_11]),eq_45]),eq_27]),eq_3]),eq_4]) ).
cnf(eq_53,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(cp,[status(thm)],[eq_19,eq_52]) ).
cnf(eq_54,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)],[eq_53,eq_39]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP184-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : run_maedmax %d %s
% 0.12/0.34 % Computer : n029.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 04:19:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 141.40/141.67 % SZS status Unsatisfiable
% 141.40/141.67 % SZS output start CNFRefutation for /tmp/MaedMax_16120
% See solution above
% 141.40/141.67
%------------------------------------------------------------------------------