%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : GRP002-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n011.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 07:01:48 EDT 2022
% Result : Unsatisfiable 1.36s 1.54s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of clauses : 103 ( 103 unt; 0 nHn; 14 RR)
% Number of literals : 103 ( 102 equ; 11 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; 6 con; 0-2 aty)
% Number of variables : 182 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
X = multiply(identity,X),
file('/tmp/MaedMax_12143') ).
cnf(eq_1,axiom,
identity = multiply(inverse(X),X),
file('/tmp/MaedMax_12143') ).
cnf(eq_2,axiom,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('/tmp/MaedMax_12143') ).
cnf(eq_3,axiom,
X = multiply(X,identity),
file('/tmp/MaedMax_12143') ).
cnf(eq_4,axiom,
identity = multiply(X,inverse(X)),
file('/tmp/MaedMax_12143') ).
cnf(eq_5,axiom,
multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) = commutator(X,Y),
file('/tmp/MaedMax_12143') ).
cnf(eq_6,axiom,
identity = multiply(X,multiply(X,X)),
file('/tmp/MaedMax_12143') ).
cnf(eq_7,negated_conjecture,
identity != commutator(commutator(a,b),b),
file('/tmp/MaedMax_12143') ).
cnf(eq_8,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(cp,[status(thm)],[eq_2,eq_4]) ).
cnf(eq_9,plain,
multiply(identity,x102) = multiply(X,multiply(multiply(X,X),x102)),
inference(cp,[status(thm)],[eq_6,eq_2]) ).
cnf(eq_10,plain,
multiply(identity,x102) = multiply(X,multiply(inverse(X),x102)),
inference(cp,[status(thm)],[eq_4,eq_2]) ).
cnf(eq_11,plain,
multiply(identity,x102) = multiply(inverse(X),multiply(X,x102)),
inference(cp,[status(thm)],[eq_1,eq_2]) ).
cnf(eq_12,plain,
X = multiply(Y,multiply(Y,multiply(Y,X))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_9,eq_0]),eq_2]) ).
cnf(eq_13,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference(rw,[status(thm)],[eq_10,eq_0]) ).
cnf(eq_14,plain,
identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
eq_8 ).
cnf(eq_15,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference(rw,[status(thm)],[eq_11,eq_0]) ).
cnf(eq_16,plain,
X = multiply(x100,multiply(x101,multiply(multiply(x100,x101),multiply(multiply(x100,x101),X)))),
inference(cp,[status(thm)],[eq_12,eq_2]) ).
cnf(eq_17,plain,
multiply(Y,multiply(Y,X)) = multiply(inverse(Y),X),
inference(cp,[status(thm)],[eq_13,eq_12]) ).
cnf(eq_18,plain,
multiply(X,multiply(X,identity)) = inverse(X),
inference(cp,[status(thm)],[eq_4,eq_12]) ).
cnf(eq_19,plain,
multiply(X,multiply(Y,multiply(inverse(multiply(X,Y)),x101))) = x101,
inference(cp,[status(thm)],[eq_2,eq_13]) ).
cnf(eq_20,plain,
multiply(x100,identity) = inverse(inverse(x100)),
inference(cp,[status(thm)],[eq_4,eq_13]) ).
cnf(eq_21,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,Z))) = Z,
inference(cp,[status(thm)],[eq_2,eq_15]) ).
cnf(eq_22,plain,
multiply(inverse(X),commutator(X,Y)) = multiply(Y,multiply(inverse(X),inverse(Y))),
inference(cp,[status(thm)],[eq_5,eq_15]) ).
cnf(eq_23,plain,
X = inverse(inverse(X)),
inference(rw,[status(thm)],[eq_20,eq_3]) ).
cnf(eq_24,plain,
X = multiply(Y,multiply(Z,multiply(Y,multiply(Z,multiply(Y,multiply(Z,X)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_16,eq_2]),eq_2]) ).
cnf(eq_25,plain,
multiply(X,multiply(X,Y)) = multiply(inverse(X),Y),
eq_17 ).
cnf(eq_26,plain,
X = multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X))),
eq_21 ).
cnf(eq_27,plain,
X = multiply(Y,multiply(Z,multiply(inverse(multiply(Y,Z)),X))),
eq_19 ).
cnf(eq_28,plain,
multiply(X,multiply(inverse(Y),inverse(X))) = multiply(inverse(Y),commutator(Y,X)),
eq_22 ).
cnf(eq_29,plain,
multiply(X,X) = inverse(X),
inference(rw,[status(thm)],[eq_18,eq_3]) ).
cnf(eq_30,plain,
multiply(X,multiply(Y,multiply(X,Y))) = inverse(multiply(X,Y)),
inference(cp,[status(thm)],[eq_2,eq_29]) ).
cnf(eq_31,plain,
multiply(inverse(X),multiply(x101,multiply(X,inverse(x101)))) = commutator(inverse(X),x101),
inference(cp,[status(thm)],[eq_23,eq_5]) ).
cnf(eq_32,plain,
multiply(x100,multiply(inverse(X),multiply(inverse(x100),X))) = commutator(x100,inverse(X)),
inference(cp,[status(thm)],[eq_23,eq_5]) ).
cnf(eq_33,plain,
multiply(inverse(X),multiply(Y,multiply(X,inverse(Y)))) = commutator(inverse(X),Y),
eq_31 ).
cnf(eq_34,plain,
multiply(X,multiply(inverse(Y),multiply(inverse(X),Y))) = commutator(X,inverse(Y)),
eq_32 ).
cnf(eq_35,plain,
multiply(inverse(X),identity) = multiply(Y,inverse(multiply(X,Y))),
inference(cp,[status(thm)],[eq_8,eq_15]) ).
cnf(eq_36,plain,
multiply(inverse(multiply(x100,X)),multiply(x100,identity)) = inverse(X),
inference(cp,[status(thm)],[eq_4,eq_26]) ).
cnf(eq_37,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(rw,[status(thm)],[eq_35,eq_3]) ).
cnf(eq_38,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference(rw,[status(thm)],[eq_36,eq_3]) ).
cnf(eq_39,negated_conjecture,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) != commutator(commutator(a,b),b),
inference(cp,[status(thm)],[eq_14,eq_7]) ).
cnf(eq_40,plain,
multiply(x100,multiply(multiply(Y,inverse(x100)),inverse(Y))) = commutator(x100,multiply(Y,inverse(x100))),
inference(cp,[status(thm)],[eq_37,eq_5]) ).
cnf(eq_41,plain,
multiply(X,multiply(inverse(multiply(Y,X)),multiply(inverse(inverse(Y)),x102))) = x102,
inference(cp,[status(thm)],[eq_37,eq_27]) ).
cnf(eq_42,plain,
multiply(x100,inverse(Y)) = inverse(multiply(Y,inverse(x100))),
inference(cp,[status(thm)],[eq_37,eq_13]) ).
cnf(eq_43,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(cp,[status(thm)],[eq_37,eq_15]) ).
cnf(eq_44,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference(cp,[status(thm)],[eq_13,eq_38]) ).
cnf(eq_45,plain,
multiply(inverse(inverse(multiply(X,Y))),X) = inverse(multiply(Y,multiply(X,Y))),
inference(cp,[status(thm)],[eq_30,eq_38]) ).
cnf(eq_46,plain,
X = multiply(Y,multiply(inverse(multiply(Z,Y)),multiply(Z,X))),
inference(rw,[status(thm)],[eq_41,eq_23]) ).
cnf(eq_47,plain,
multiply(X,multiply(Y,X)) = inverse(multiply(Y,multiply(X,Y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_45,eq_23]),eq_2]) ).
cnf(eq_48,plain,
commutator(X,Y) = commutator(X,multiply(Y,inverse(X))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_40,eq_2]),eq_5]) ).
cnf(eq_49,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
eq_42 ).
cnf(eq_50,plain,
multiply(X,multiply(Y,inverse(multiply(Y,X)))) = commutator(X,Y),
inference(cp,[status(thm)],[eq_43,eq_5]) ).
cnf(eq_51,plain,
inverse(commutator(X,Y)) = multiply(inverse(multiply(Y,multiply(inverse(X),inverse(Y)))),inverse(X)),
inference(cp,[status(thm)],[eq_5,eq_43]) ).
cnf(eq_52,plain,
commutator(X,Y) = commutator(X,multiply(multiply(Y,inverse(X)),inverse(X))),
inference(cp,[status(thm)],[eq_48,eq_48]) ).
cnf(eq_53,plain,
commutator(multiply(Y,X),inverse(Y)) = commutator(multiply(Y,X),X),
inference(cp,[status(thm)],[eq_37,eq_48]) ).
cnf(eq_54,plain,
commutator(x100,inverse(multiply(inverse(inverse(x100)),X))) = commutator(x100,inverse(X)),
inference(cp,[status(thm)],[eq_44,eq_48]) ).
cnf(eq_55,plain,
commutator(inverse(X),multiply(x101,X)) = commutator(inverse(X),x101),
inference(cp,[status(thm)],[eq_23,eq_48]) ).
cnf(eq_56,plain,
commutator(X,inverse(Y)) = commutator(X,inverse(multiply(X,Y))),
inference(rw,[status(thm)],[eq_54,eq_23]) ).
cnf(eq_57,plain,
commutator(multiply(X,Y),Y) = commutator(multiply(X,Y),inverse(X)),
eq_53 ).
cnf(eq_58,plain,
commutator(X,Y) = commutator(X,multiply(Y,X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_52,eq_2]),eq_29]),eq_23]) ).
cnf(eq_59,plain,
commutator(inverse(X),Y) = commutator(inverse(X),multiply(Y,X)),
eq_55 ).
cnf(eq_60,plain,
inverse(multiply(inverse(Y),commutator(Y,X))) = multiply(inverse(multiply(inverse(Y),inverse(X))),inverse(X)),
inference(cp,[status(thm)],[eq_28,eq_43]) ).
cnf(eq_61,plain,
multiply(multiply(x101,x102),multiply(x101,multiply(multiply(x101,x102),multiply(x101,inverse(multiply(x101,x102)))))) = x102,
inference(cp,[status(thm)],[eq_29,eq_24]) ).
cnf(eq_62,plain,
inverse(commutator(X,Y)) = commutator(Y,X),
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)],[inference(rw,[status(thm)],[eq_51,eq_43]),eq_43]),eq_23]),eq_23]),eq_2]),eq_2]),eq_2]),eq_5]) ).
cnf(eq_63,plain,
X = multiply(Y,multiply(X,multiply(inverse(Y),commutator(X,Y)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_61,eq_43]),eq_2]),eq_5]),eq_25]),eq_2]) ).
cnf(eq_64,negated_conjecture,
multiply(inverse(Y),multiply(commutator(Y,X),inverse(multiply(X,multiply(inverse(Y),inverse(X)))))) != commutator(commutator(a,b),b),
inference(cp,[status(thm)],[eq_28,eq_39]) ).
cnf(eq_65,negated_conjecture,
multiply(inverse(X),multiply(commutator(X,Y),multiply(Y,multiply(X,inverse(Y))))) != commutator(commutator(a,b),b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_64,eq_43]),eq_43]),eq_23]),eq_23]),eq_2]) ).
cnf(eq_66,plain,
multiply(commutator(Y,X),multiply(commutator(X,Y),x101)) = x101,
inference(cp,[status(thm)],[eq_62,eq_15]) ).
cnf(eq_67,plain,
inverse(commutator(multiply(X,Y),inverse(X))) = commutator(Y,multiply(X,Y)),
inference(cp,[status(thm)],[eq_57,eq_62]) ).
cnf(eq_68,plain,
inverse(commutator(X,Y)) = commutator(multiply(Y,X),X),
inference(cp,[status(thm)],[eq_58,eq_62]) ).
cnf(eq_69,plain,
multiply(X,multiply(Y,inverse(X))) = multiply(commutator(X,Y),Y),
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_60,eq_43]),eq_62]),eq_23]),eq_43]),eq_23]),eq_23]),eq_2]) ).
cnf(eq_70,plain,
commutator(X,Y) = commutator(inverse(Y),multiply(Y,X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_67,eq_62]),eq_58]) ).
cnf(eq_71,plain,
commutator(X,Y) = commutator(multiply(X,Y),Y),
inference(rw,[status(thm)],[eq_68,eq_62]) ).
cnf(eq_72,plain,
X = multiply(commutator(Y,Z),multiply(commutator(Z,Y),X)),
eq_66 ).
cnf(eq_73,plain,
commutator(multiply(X,Y),inverse(X)) = commutator(X,Y),
inference(cp,[status(thm)],[eq_57,eq_71]) ).
cnf(eq_74,plain,
commutator(multiply(X,multiply(Y,Z)),Z) = commutator(multiply(X,Y),Z),
inference(cp,[status(thm)],[eq_2,eq_71]) ).
cnf(eq_75,plain,
commutator(inverse(X),multiply(inverse(X),Y)) = commutator(multiply(X,Y),X),
inference(cp,[status(thm)],[eq_25,eq_70]) ).
cnf(eq_76,negated_conjecture,
multiply(inverse(inverse(Y)),multiply(commutator(inverse(Y),X),multiply(inverse(Y),commutator(Y,X)))) != commutator(commutator(a,b),b),
inference(cp,[status(thm)],[eq_28,eq_65]) ).
cnf(eq_77,negated_conjecture,
multiply(X,multiply(commutator(inverse(X),Y),multiply(inverse(X),commutator(X,Y)))) != commutator(commutator(a,b),b),
inference(rw,[status(thm)],[eq_76,eq_23]) ).
cnf(eq_78,plain,
multiply(x100,multiply(inverse(multiply(Y,inverse(x100))),inverse(multiply(Y,multiply(inverse(x100),Y))))) = commutator(x100,inverse(multiply(Y,inverse(x100)))),
inference(cp,[status(thm)],[eq_47,eq_34]) ).
cnf(eq_79,plain,
multiply(inverse(X),multiply(multiply(X,Y),multiply(inverse(inverse(X)),commutator(X,Y)))) = multiply(X,Y),
inference(cp,[status(thm)],[eq_73,eq_63]) ).
cnf(eq_80,plain,
multiply(X,Y) = multiply(Y,multiply(X,commutator(X,Y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_79,eq_23]),eq_2]),eq_15]) ).
cnf(eq_81,plain,
commutator(X,multiply(X,inverse(Y))) = commutator(inverse(X),Y),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_78,eq_49]),eq_2]),eq_43]),eq_2]),eq_2]),eq_29]),eq_43]),eq_49]),eq_2]),eq_25]),eq_33]),eq_49]) ).
cnf(eq_82,plain,
multiply(x100,multiply(X,inverse(multiply(X,x100)))) = commutator(X,inverse(multiply(X,x100))),
inference(cp,[status(thm)],[eq_80,eq_46]) ).
cnf(eq_83,plain,
inverse(commutator(inverse(X),Y)) = commutator(multiply(X,inverse(Y)),X),
inference(cp,[status(thm)],[eq_81,eq_62]) ).
cnf(eq_84,plain,
commutator(X,inverse(Y)) = commutator(inverse(X),multiply(Y,X)),
inference(cp,[status(thm)],[eq_37,eq_81]) ).
cnf(eq_85,plain,
commutator(inverse(inverse(x100)),Y) = commutator(multiply(x100,inverse(Y)),x100),
inference(cp,[status(thm)],[eq_81,eq_75]) ).
cnf(eq_86,plain,
commutator(X,Y) = commutator(Y,inverse(X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_82,eq_50]),eq_56]) ).
cnf(eq_87,plain,
commutator(X,inverse(Y)) = commutator(inverse(X),Y),
inference(rw,[status(thm)],[eq_84,eq_59]) ).
cnf(eq_88,plain,
commutator(X,Y) = commutator(multiply(X,inverse(Y)),X),
inference(rw,[status(thm)],[eq_85,eq_23]) ).
cnf(eq_89,plain,
commutator(X,inverse(Y)) = commutator(multiply(Y,inverse(X)),Y),
inference(rw,[status(thm)],[eq_83,eq_62]) ).
cnf(eq_90,plain,
commutator(inverse(x101),Y) = commutator(multiply(x101,inverse(multiply(inverse(x101),inverse(Y)))),x101),
inference(cp,[status(thm)],[eq_88,eq_89]) ).
cnf(eq_91,plain,
commutator(X,Y) = commutator(inverse(Y),X),
inference(cp,[status(thm)],[eq_86,eq_87]) ).
cnf(eq_92,plain,
commutator(multiply(X,Y),X) = commutator(inverse(X),Y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_90,eq_43]),eq_23]),eq_74]) ).
cnf(eq_93,negated_conjecture,
multiply(x100,multiply(commutator(Y,inverse(inverse(x100))),multiply(inverse(x100),commutator(x100,Y)))) != commutator(commutator(a,b),b),
inference(cp,[status(thm)],[eq_86,eq_77]) ).
cnf(eq_94,negated_conjecture,
multiply(X,multiply(commutator(Y,X),multiply(inverse(X),commutator(X,Y)))) != commutator(commutator(a,b),b),
inference(rw,[status(thm)],[eq_93,eq_23]) ).
cnf(eq_95,plain,
multiply(commutator(inverse(X),Y),X) = multiply(multiply(X,Y),multiply(X,inverse(multiply(X,Y)))),
inference(cp,[status(thm)],[eq_92,eq_69]) ).
cnf(eq_96,plain,
multiply(X,commutator(Y,X)) = multiply(commutator(Y,X),X),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_95,eq_91]),eq_2]),eq_50]) ).
cnf(eq_97,plain,
multiply(X,multiply(commutator(Y,X),inverse(multiply(X,commutator(Y,X))))) = commutator(X,commutator(Y,X)),
inference(cp,[status(thm)],[eq_96,eq_50]) ).
cnf(eq_98,plain,
identity = commutator(X,commutator(Y,X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_97,eq_37]),eq_4]) ).
cnf(eq_99,negated_conjecture,
multiply(commutator(Y,X),multiply(identity,multiply(inverse(commutator(Y,X)),commutator(commutator(Y,X),X)))) != commutator(commutator(a,b),b),
inference(cp,[status(thm)],[eq_98,eq_94]) ).
cnf(eq_100,negated_conjecture,
commutator(commutator(X,Y),Y) != commutator(commutator(a,b),b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_99,eq_62]),eq_0]),eq_72]) ).
cnf(eq_101,negated_conjecture,
commutator(commutator(X,Y),Y) != commutator(commutator(X,Y),Y),
eq_100 ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP002-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_maedmax %d %s
% 0.13/0.34 % Computer : n011.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 04:12:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.36/1.54 % SZS status Unsatisfiable
% 1.36/1.54 % SZS output start CNFRefutation for /tmp/MaedMax_12143
% See solution above
% 1.36/1.54
%------------------------------------------------------------------------------