TSTP Solution File: GRP166-1 by MaedMax---1.4
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- Process Solution
%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : GRP166-1 : 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 07:02:15 EDT 2022
% Result : Unsatisfiable 15.45s 15.67s
% Output : CNFRefutation 15.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of clauses : 86 ( 86 unt; 0 nHn; 25 RR)
% Number of literals : 86 ( 85 equ; 2 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 104 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
X = multiply(identity,X),
file('/tmp/MaedMax_31293') ).
cnf(eq_1,axiom,
identity = multiply(inverse(X),X),
file('/tmp/MaedMax_31293') ).
cnf(eq_2,axiom,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('/tmp/MaedMax_31293') ).
cnf(eq_3,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/tmp/MaedMax_31293') ).
cnf(eq_4,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/tmp/MaedMax_31293') ).
cnf(eq_5,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('/tmp/MaedMax_31293') ).
cnf(eq_6,axiom,
X = least_upper_bound(X,greatest_lower_bound(X,Y)),
file('/tmp/MaedMax_31293') ).
cnf(eq_7,axiom,
X = greatest_lower_bound(X,least_upper_bound(X,Y)),
file('/tmp/MaedMax_31293') ).
cnf(eq_8,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/tmp/MaedMax_31293') ).
cnf(eq_9,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/tmp/MaedMax_31293') ).
cnf(eq_10,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('/tmp/MaedMax_31293') ).
cnf(eq_11,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('/tmp/MaedMax_31293') ).
cnf(eq_12,axiom,
least_upper_bound(a,identity) = a,
file('/tmp/MaedMax_31293') ).
cnf(eq_13,axiom,
least_upper_bound(b,identity) = b,
file('/tmp/MaedMax_31293') ).
cnf(eq_14,negated_conjecture,
multiply(a,b) != least_upper_bound(a,multiply(a,b)),
file('/tmp/MaedMax_31293') ).
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_7]) ).
cnf(eq_17,plain,
greatest_lower_bound(Y,least_upper_bound(X,least_upper_bound(Y,Z))) = Y,
inference(cp,[status(thm)],[eq_29,eq_7]) ).
cnf(eq_18,plain,
greatest_lower_bound(multiply(x100,x102),multiply(x100,x101)) = multiply(x100,greatest_lower_bound(x101,x102)),
inference(cp,[status(thm)],[eq_3,eq_9]) ).
cnf(eq_19,plain,
greatest_lower_bound(X,multiply(x102,X)) = multiply(greatest_lower_bound(identity,x102),X),
inference(cp,[status(thm)],[eq_0,eq_11]) ).
cnf(eq_20,plain,
least_upper_bound(Y,greatest_lower_bound(X,Y)) = Y,
inference(cp,[status(thm)],[eq_3,eq_6]) ).
cnf(eq_21,plain,
least_upper_bound(multiply(x100,X),X) = multiply(least_upper_bound(x100,identity),X),
inference(cp,[status(thm)],[eq_0,eq_10]) ).
cnf(eq_22,plain,
least_upper_bound(a,x102) = least_upper_bound(a,least_upper_bound(identity,x102)),
inference(cp,[status(thm)],[eq_12,eq_5]) ).
cnf(eq_23,plain,
least_upper_bound(b,x102) = least_upper_bound(b,least_upper_bound(identity,x102)),
inference(cp,[status(thm)],[eq_13,eq_5]) ).
cnf(eq_24,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_5]) ).
cnf(eq_25,plain,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(Y,Z),multiply(X,Z)),
inference(cp,[status(thm)],[eq_11,eq_3]) ).
cnf(eq_26,plain,
multiply(greatest_lower_bound(X,Y),Z) = multiply(greatest_lower_bound(Y,X),Z),
inference(rw,[status(thm)],[eq_25,eq_11]) ).
cnf(eq_27,plain,
multiply(greatest_lower_bound(identity,X),Y) = greatest_lower_bound(Y,multiply(X,Y)),
eq_19 ).
cnf(eq_28,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference(rw,[status(thm)],[eq_15,eq_0]) ).
cnf(eq_29,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(rw,[status(thm)],[eq_24,eq_5]) ).
cnf(eq_30,plain,
multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(rw,[status(thm)],[eq_18,eq_9]) ).
cnf(eq_31,plain,
least_upper_bound(b,X) = least_upper_bound(b,least_upper_bound(identity,X)),
eq_23 ).
cnf(eq_32,plain,
X = greatest_lower_bound(X,least_upper_bound(Y,least_upper_bound(X,Z))),
eq_17 ).
cnf(eq_33,plain,
X = least_upper_bound(X,greatest_lower_bound(Y,X)),
eq_20 ).
cnf(eq_34,plain,
least_upper_bound(a,X) = least_upper_bound(a,least_upper_bound(identity,X)),
eq_22 ).
cnf(eq_35,plain,
multiply(least_upper_bound(X,identity),Y) = least_upper_bound(Y,multiply(X,Y)),
inference(rw,[status(thm)],[eq_21,eq_4]) ).
cnf(eq_36,plain,
multiply(inverse(inverse(Y)),X) = multiply(Y,X),
inference(cp,[status(thm)],[eq_28,eq_28]) ).
cnf(eq_37,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(cp,[status(thm)],[eq_1,eq_28]) ).
cnf(eq_38,plain,
greatest_lower_bound(identity,least_upper_bound(a,X)) = identity,
inference(cp,[status(thm)],[eq_34,eq_32]) ).
cnf(eq_39,plain,
greatest_lower_bound(a,least_upper_bound(x101,a)) = a,
inference(cp,[status(thm)],[eq_12,eq_32]) ).
cnf(eq_40,plain,
least_upper_bound(b,identity) = least_upper_bound(b,greatest_lower_bound(identity,Y)),
inference(cp,[status(thm)],[eq_6,eq_31]) ).
cnf(eq_41,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
eq_36 ).
cnf(eq_42,plain,
least_upper_bound(b,greatest_lower_bound(identity,X)) = b,
inference(rw,[status(thm)],[eq_40,eq_13]) ).
cnf(eq_43,plain,
X = multiply(inverse(inverse(X)),identity),
eq_37 ).
cnf(eq_44,plain,
greatest_lower_bound(a,least_upper_bound(X,a)) = a,
eq_39 ).
cnf(eq_45,plain,
multiply(inverse(greatest_lower_bound(Y,Z)),greatest_lower_bound(Z,Y)) = identity,
inference(cp,[status(thm)],[eq_30,eq_1]) ).
cnf(eq_46,plain,
identity = multiply(inverse(greatest_lower_bound(X,Y)),greatest_lower_bound(Y,X)),
eq_45 ).
cnf(eq_47,plain,
X = multiply(X,identity),
inference(rw,[status(thm)],[eq_43,eq_41]) ).
cnf(eq_48,plain,
multiply(X,inverse(X)) = identity,
inference(cp,[status(thm)],[eq_41,eq_1]) ).
cnf(eq_49,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X,identity),a)) = identity,
inference(cp,[status(thm)],[eq_35,eq_38]) ).
cnf(eq_50,plain,
identity = multiply(X,inverse(X)),
eq_48 ).
cnf(eq_51,plain,
multiply(greatest_lower_bound(X,Y),identity) = greatest_lower_bound(Y,X),
inference(cp,[status(thm)],[eq_26,eq_47]) ).
cnf(eq_52,plain,
multiply(X,identity) = inverse(inverse(X)),
inference(cp,[status(thm)],[eq_41,eq_47]) ).
cnf(eq_53,plain,
multiply(x100,multiply(X,inverse(X))) = x100,
inference(cp,[status(thm)],[eq_50,eq_47]) ).
cnf(eq_54,plain,
X = multiply(X,multiply(Y,inverse(Y))),
eq_53 ).
cnf(eq_55,plain,
X = inverse(inverse(X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_43,eq_41]),eq_52]) ).
cnf(eq_56,plain,
multiply(identity,x101) = greatest_lower_bound(x101,multiply(least_upper_bound(Y,identity),x101)),
inference(cp,[status(thm)],[eq_16,eq_27]) ).
cnf(eq_57,plain,
X = greatest_lower_bound(X,multiply(least_upper_bound(Y,identity),X)),
inference(rw,[status(thm)],[eq_56,eq_0]) ).
cnf(eq_58,plain,
greatest_lower_bound(identity,multiply(b,a)) = identity,
inference(cp,[status(thm)],[eq_13,eq_49]) ).
cnf(eq_59,plain,
multiply(identity,x101) = greatest_lower_bound(x101,multiply(multiply(b,a),x101)),
inference(cp,[status(thm)],[eq_58,eq_27]) ).
cnf(eq_60,plain,
X = greatest_lower_bound(X,multiply(b,multiply(a,X))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_59,eq_0]),eq_2]) ).
cnf(eq_61,plain,
greatest_lower_bound(x100,multiply(a,x100)) = x100,
inference(cp,[status(thm)],[eq_12,eq_57]) ).
cnf(eq_62,plain,
greatest_lower_bound(x100,multiply(b,x100)) = x100,
inference(cp,[status(thm)],[eq_13,eq_57]) ).
cnf(eq_63,plain,
X = greatest_lower_bound(X,multiply(b,X)),
eq_62 ).
cnf(eq_64,plain,
X = greatest_lower_bound(X,multiply(a,X)),
eq_61 ).
cnf(eq_65,plain,
greatest_lower_bound(inverse(a),identity) = inverse(a),
inference(cp,[status(thm)],[eq_48,eq_64]) ).
cnf(eq_66,plain,
least_upper_bound(multiply(b,X),X) = multiply(b,X),
inference(cp,[status(thm)],[eq_63,eq_33]) ).
cnf(eq_67,plain,
multiply(b,X) = least_upper_bound(X,multiply(b,X)),
inference(rw,[status(thm)],[eq_66,eq_4]) ).
cnf(eq_68,plain,
inverse(a) = greatest_lower_bound(identity,inverse(a)),
inference(rw,[status(thm)],[eq_65,eq_3]) ).
cnf(eq_69,plain,
least_upper_bound(b,inverse(a)) = b,
inference(cp,[status(thm)],[eq_68,eq_42]) ).
cnf(eq_70,plain,
greatest_lower_bound(inverse(a),multiply(b,identity)) = inverse(a),
inference(cp,[status(thm)],[eq_48,eq_60]) ).
cnf(eq_71,plain,
inverse(a) = greatest_lower_bound(b,inverse(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_70,eq_47]),eq_3]) ).
cnf(eq_72,plain,
greatest_lower_bound(inverse(a),b) = inverse(a),
inference(cp,[status(thm)],[eq_69,eq_16]) ).
cnf(eq_73,plain,
multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),b)) = identity,
inference(cp,[status(thm)],[eq_71,eq_46]) ).
cnf(eq_74,plain,
identity = multiply(a,greatest_lower_bound(inverse(a),b)),
inference(rw,[status(thm)],[eq_73,eq_55]) ).
cnf(eq_75,plain,
identity = multiply(a,inverse(a)),
inference(rw,[status(thm)],[eq_74,eq_72]) ).
cnf(eq_76,plain,
multiply(X,inverse(X)) = multiply(a,inverse(a)),
inference(rw,[status(thm)],[eq_50,eq_75]) ).
cnf(eq_77,plain,
multiply(a,identity) = greatest_lower_bound(least_upper_bound(X,a),a),
inference(cp,[status(thm)],[eq_44,eq_51]) ).
cnf(eq_78,plain,
multiply(a,multiply(a,inverse(a))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_77,eq_75]),eq_3]),eq_16]) ).
cnf(eq_79,plain,
multiply(a,multiply(X,inverse(X))) = a,
inference(cp,[status(thm)],[eq_76,eq_78]) ).
cnf(eq_80,plain,
least_upper_bound(a,multiply(a,x102)) = multiply(a,least_upper_bound(multiply(X,inverse(X)),x102)),
inference(cp,[status(thm)],[eq_79,eq_8]) ).
cnf(eq_81,plain,
multiply(a,least_upper_bound(multiply(X,inverse(X)),Y)) = least_upper_bound(a,multiply(a,Y)),
eq_80 ).
cnf(eq_82,plain,
multiply(a,multiply(b,multiply(x100,inverse(x100)))) = least_upper_bound(a,multiply(a,multiply(b,multiply(x100,inverse(x100))))),
inference(cp,[status(thm)],[eq_67,eq_81]) ).
cnf(eq_83,plain,
multiply(a,b) = least_upper_bound(a,multiply(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_82,eq_54]),eq_54]) ).
cnf(eq_84,negated_conjecture,
multiply(a,b) != multiply(a,b),
inference(cp,[status(thm)],[eq_83,eq_14]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP166-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : run_maedmax %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Jul 26 04:30:43 EDT 2022
% 0.14/0.34 % CPUTime :
% 15.45/15.67 % SZS status Unsatisfiable
% 15.45/15.67 % SZS output start CNFRefutation for /tmp/MaedMax_31293
% See solution above
% 15.45/15.67
%------------------------------------------------------------------------------