TSTP Solution File: GRP181-4 by MaedMax---1.4
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- Process Solution
%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : GRP181-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n026.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 07:02:20 EDT 2022
% Result : Unsatisfiable 9.72s 9.90s
% Output : CNFRefutation 9.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 68 ( 68 unt; 0 nHn; 22 RR)
% Number of literals : 68 ( 67 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 79 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
X = multiply(identity,X),
file('/tmp/MaedMax_381') ).
cnf(eq_1,axiom,
identity = multiply(inverse(X),X),
file('/tmp/MaedMax_381') ).
cnf(eq_2,axiom,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('/tmp/MaedMax_381') ).
cnf(eq_3,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/tmp/MaedMax_381') ).
cnf(eq_4,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/tmp/MaedMax_381') ).
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_381') ).
cnf(eq_6,axiom,
X = least_upper_bound(X,greatest_lower_bound(X,Y)),
file('/tmp/MaedMax_381') ).
cnf(eq_7,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/tmp/MaedMax_381') ).
cnf(eq_8,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('/tmp/MaedMax_381') ).
cnf(eq_9,axiom,
identity = inverse(identity),
file('/tmp/MaedMax_381') ).
cnf(eq_10,axiom,
X = inverse(inverse(X)),
file('/tmp/MaedMax_381') ).
cnf(eq_11,axiom,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
file('/tmp/MaedMax_381') ).
cnf(eq_12,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/tmp/MaedMax_381') ).
cnf(eq_13,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/tmp/MaedMax_381') ).
cnf(eq_14,axiom,
inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)),
file('/tmp/MaedMax_381') ).
cnf(eq_15,negated_conjecture,
a != b,
file('/tmp/MaedMax_381') ).
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,
multiply(X,inverse(X)) = identity,
inference(cp,[status(thm)],[eq_10,eq_1]) ).
cnf(eq_18,plain,
identity = inverse(multiply(x101,inverse(x101))),
inference(cp,[status(thm)],[eq_1,eq_11]) ).
cnf(eq_19,plain,
multiply(identity,inverse(x101)) = inverse(multiply(x101,identity)),
inference(cp,[status(thm)],[eq_9,eq_11]) ).
cnf(eq_20,plain,
inverse(greatest_lower_bound(inverse(X),inverse(Y))) = least_upper_bound(X,Y),
inference(cp,[status(thm)],[eq_14,eq_10]) ).
cnf(eq_21,plain,
inverse(least_upper_bound(b,c)) = greatest_lower_bound(inverse(a),inverse(c)),
inference(cp,[status(thm)],[eq_13,eq_14]) ).
cnf(eq_22,plain,
greatest_lower_bound(multiply(inverse(X),x101),identity) = multiply(inverse(X),greatest_lower_bound(x101,X)),
inference(cp,[status(thm)],[eq_1,eq_7]) ).
cnf(eq_23,plain,
greatest_lower_bound(identity,multiply(x102,X)) = multiply(greatest_lower_bound(inverse(X),x102),X),
inference(cp,[status(thm)],[eq_1,eq_8]) ).
cnf(eq_24,plain,
greatest_lower_bound(multiply(x100,X),identity) = multiply(greatest_lower_bound(x100,inverse(X)),X),
inference(cp,[status(thm)],[eq_1,eq_8]) ).
cnf(eq_25,plain,
greatest_lower_bound(greatest_lower_bound(b,c),x102) = greatest_lower_bound(a,greatest_lower_bound(c,x102)),
inference(cp,[status(thm)],[eq_12,eq_5]) ).
cnf(eq_26,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_27,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(b,c),
inference(cp,[status(thm)],[eq_3,eq_12]) ).
cnf(eq_28,plain,
least_upper_bound(Y,greatest_lower_bound(X,Y)) = Y,
inference(cp,[status(thm)],[eq_3,eq_6]) ).
cnf(eq_29,plain,
multiply(greatest_lower_bound(X,inverse(Y)),Y) = greatest_lower_bound(multiply(X,Y),identity),
eq_24 ).
cnf(eq_30,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference(rw,[status(thm)],[eq_16,eq_0]) ).
cnf(eq_31,plain,
identity = inverse(multiply(X,inverse(X))),
eq_18 ).
cnf(eq_32,plain,
multiply(greatest_lower_bound(inverse(X),Y),X) = greatest_lower_bound(identity,multiply(Y,X)),
eq_23 ).
cnf(eq_33,plain,
inverse(X) = inverse(multiply(X,identity)),
inference(rw,[status(thm)],[eq_19,eq_0]) ).
cnf(eq_34,plain,
greatest_lower_bound(inverse(c),inverse(a)) = greatest_lower_bound(inverse(c),inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_21,eq_4]),eq_14]),eq_3]) ).
cnf(eq_35,plain,
X = least_upper_bound(X,greatest_lower_bound(Y,X)),
eq_28 ).
cnf(eq_36,plain,
multiply(inverse(X),greatest_lower_bound(Y,X)) = greatest_lower_bound(identity,multiply(inverse(X),Y)),
inference(rw,[status(thm)],[eq_22,eq_3]) ).
cnf(eq_37,plain,
greatest_lower_bound(c,greatest_lower_bound(a,X)) = greatest_lower_bound(c,greatest_lower_bound(b,X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_25,eq_3]),eq_5]),eq_38]) ).
cnf(eq_38,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
inference(rw,[status(thm)],[eq_26,eq_5]) ).
cnf(eq_39,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(cp,[status(thm)],[eq_33,eq_10]) ).
cnf(eq_40,plain,
multiply(identity,multiply(multiply(X,inverse(X)),x101)) = x101,
inference(cp,[status(thm)],[eq_31,eq_30]) ).
cnf(eq_41,plain,
multiply(inverse(inverse(X)),inverse(multiply(Y,X))) = inverse(Y),
inference(cp,[status(thm)],[eq_11,eq_30]) ).
cnf(eq_42,plain,
least_upper_bound(Z,greatest_lower_bound(X,greatest_lower_bound(Y,Z))) = Z,
inference(cp,[status(thm)],[eq_5,eq_35]) ).
cnf(eq_43,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(rw,[status(thm)],[eq_41,eq_10]) ).
cnf(eq_44,plain,
X = multiply(X,identity),
inference(rw,[status(thm)],[eq_39,eq_10]) ).
cnf(eq_45,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_40,eq_2]),eq_0]) ).
cnf(eq_46,plain,
X = least_upper_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Z,X))),
eq_42 ).
cnf(eq_47,plain,
inverse(X) = greatest_lower_bound(inverse(X),inverse(greatest_lower_bound(Y,greatest_lower_bound(Z,X)))),
inference(cp,[status(thm)],[eq_46,eq_14]) ).
cnf(eq_48,plain,
least_upper_bound(a,greatest_lower_bound(x101,greatest_lower_bound(b,c))) = a,
inference(cp,[status(thm)],[eq_27,eq_46]) ).
cnf(eq_49,plain,
least_upper_bound(a,greatest_lower_bound(X,greatest_lower_bound(b,c))) = a,
eq_48 ).
cnf(eq_50,plain,
least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(Y,c))) = a,
inference(cp,[status(thm)],[eq_38,eq_49]) ).
cnf(eq_51,plain,
least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(X,c))) = a,
eq_50 ).
cnf(eq_52,plain,
multiply(greatest_lower_bound(inverse(c),inverse(b)),c) = greatest_lower_bound(identity,multiply(inverse(a),c)),
inference(cp,[status(thm)],[eq_34,eq_32]) ).
cnf(eq_53,plain,
greatest_lower_bound(identity,multiply(inverse(a),c)) = greatest_lower_bound(identity,multiply(inverse(b),c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_52,eq_3]),eq_29]),eq_3]) ).
cnf(eq_54,plain,
multiply(X,greatest_lower_bound(identity,multiply(inverse(X),Y))) = greatest_lower_bound(Y,X),
inference(cp,[status(thm)],[eq_36,eq_45]) ).
cnf(eq_55,plain,
greatest_lower_bound(greatest_lower_bound(b,x100),c) = greatest_lower_bound(c,greatest_lower_bound(a,x100)),
inference(cp,[status(thm)],[eq_3,eq_37]) ).
cnf(eq_56,plain,
greatest_lower_bound(c,greatest_lower_bound(X,b)) = greatest_lower_bound(c,greatest_lower_bound(a,X)),
inference(cp,[status(thm)],[eq_3,eq_37]) ).
cnf(eq_57,plain,
greatest_lower_bound(a,greatest_lower_bound(c,X)) = greatest_lower_bound(c,greatest_lower_bound(X,b)),
inference(rw,[status(thm)],[eq_56,eq_38]) ).
cnf(eq_58,plain,
greatest_lower_bound(a,greatest_lower_bound(c,X)) = greatest_lower_bound(b,greatest_lower_bound(X,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_55,eq_5]),eq_38]) ).
cnf(eq_59,plain,
greatest_lower_bound(c,greatest_lower_bound(X,b)) = greatest_lower_bound(b,greatest_lower_bound(X,c)),
inference(rw,[status(thm)],[eq_58,eq_57]) ).
cnf(eq_60,plain,
multiply(b,greatest_lower_bound(identity,multiply(inverse(a),c))) = greatest_lower_bound(c,b),
inference(cp,[status(thm)],[eq_53,eq_54]) ).
cnf(eq_61,plain,
multiply(b,multiply(inverse(a),greatest_lower_bound(c,a))) = greatest_lower_bound(c,b),
inference(cp,[status(thm)],[eq_36,eq_60]) ).
cnf(eq_62,plain,
multiply(b,multiply(inverse(a),greatest_lower_bound(c,b))) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_61,eq_27]),eq_3]) ).
cnf(eq_63,plain,
multiply(multiply(inverse(a),greatest_lower_bound(c,b)),inverse(greatest_lower_bound(c,b))) = inverse(b),
inference(cp,[status(thm)],[eq_62,eq_43]) ).
cnf(eq_64,plain,
inverse(a) = inverse(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_63,eq_2]),eq_17]),eq_44]) ).
cnf(eq_65,plain,
a = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_51,eq_59]),eq_20]),eq_64]),eq_47]),eq_10]) ).
cnf(eq_66,negated_conjecture,
b != b,
inference(cp,[status(thm)],[eq_65,eq_15]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP181-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : run_maedmax %d %s
% 0.13/0.34 % Computer : n026.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Jul 26 04:22:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.72/9.90 % SZS status Unsatisfiable
% 9.72/9.90 % SZS output start CNFRefutation for /tmp/MaedMax_381
% See solution above
% 9.72/9.90
%------------------------------------------------------------------------------