Metis---2.4.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP002-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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  : 600s
% DateTime : Sat Jul 16 10:32:11 EDT 2022

% Result   : Unsatisfiable 0.41s 0.62s
% Output   : CNFRefutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   85
%            Number of leaves      :  186
% Syntax   : Number of clauses     :  787 ( 406 unt;   0 nHn; 384 RR)
%            Number of literals    : 1341 (1340 equ; 557 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   : 1605 (   4 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X ).

cnf(left_inverse,axiom,
    multiply(inverse(X),X) = identity ).

cnf(associativity,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).

cnf(right_identity,axiom,
    multiply(X,identity) = X ).

cnf(right_inverse,axiom,
    multiply(X,inverse(X)) = identity ).

cnf(commutator,axiom,
    commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) ).

cnf(x_cubed_is_identity,hypothesis,
    multiply(X,multiply(X,X)) = identity ).

cnf(prove_commutator,negated_conjecture,
    commutator(commutator(a,b),b) != identity ).

cnf(refute_0_0,plain,
    multiply(multiply(Y,Y),Z) = multiply(Y,multiply(Y,Z)),
    inference(subst,[],[associativity:[bind(X,$fot(Y))]]) ).

cnf(refute_0_1,plain,
    multiply(multiply(X_11,inverse(X_11)),X_13) = multiply(X_11,multiply(inverse(X_11),X_13)),
    inference(subst,[],[associativity:[bind(X,$fot(X_11)),bind(Y,$fot(inverse(X_11))),bind(Z,$fot(X_13))]]) ).

cnf(refute_0_2,plain,
    multiply(X_11,inverse(X_11)) = identity,
    inference(subst,[],[right_inverse:[bind(X,$fot(X_11))]]) ).

cnf(refute_0_3,plain,
    ( multiply(X_11,inverse(X_11)) != identity
    | multiply(multiply(X_11,inverse(X_11)),X_13) != multiply(X_11,multiply(inverse(X_11),X_13))
    | multiply(identity,X_13) = multiply(X_11,multiply(inverse(X_11),X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,inverse(X_11)),X_13),multiply(X_11,multiply(inverse(X_11),X_13))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_4,plain,
    ( multiply(multiply(X_11,inverse(X_11)),X_13) != multiply(X_11,multiply(inverse(X_11),X_13))
    | multiply(identity,X_13) = multiply(X_11,multiply(inverse(X_11),X_13)) ),
    inference(resolve,[$cnf( $equal(multiply(X_11,inverse(X_11)),identity) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    multiply(identity,X_13) = multiply(X_11,multiply(inverse(X_11),X_13)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_11,inverse(X_11)),X_13),multiply(X_11,multiply(inverse(X_11),X_13))) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    multiply(identity,X_13) = X_13,
    inference(subst,[],[left_identity:[bind(X,$fot(X_13))]]) ).

cnf(refute_0_7,plain,
    ( multiply(identity,X_13) != X_13
    | multiply(identity,X_13) != multiply(X_11,multiply(inverse(X_11),X_13))
    | X_13 = multiply(X_11,multiply(inverse(X_11),X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_13),multiply(X_11,multiply(inverse(X_11),X_13))) ),[0],$fot(X_13)]]) ).

cnf(refute_0_8,plain,
    ( multiply(identity,X_13) != multiply(X_11,multiply(inverse(X_11),X_13))
    | X_13 = multiply(X_11,multiply(inverse(X_11),X_13)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_13),X_13) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    X_13 = multiply(X_11,multiply(inverse(X_11),X_13)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_13),multiply(X_11,multiply(inverse(X_11),X_13))) )],[refute_0_5,refute_0_8]) ).

cnf(refute_0_10,plain,
    inverse(X_11) = multiply(X_11,multiply(inverse(X_11),inverse(X_11))),
    inference(subst,[],[refute_0_9:[bind(X_13,$fot(inverse(X_11)))]]) ).

cnf(refute_0_11,plain,
    multiply(inverse(X_14),inverse(X_14)) = multiply(X_14,multiply(inverse(X_14),multiply(inverse(X_14),inverse(X_14)))),
    inference(subst,[],[refute_0_9:[bind(X_11,$fot(X_14)),bind(X_13,$fot(multiply(inverse(X_14),inverse(X_14))))]]) ).

cnf(refute_0_12,plain,
    multiply(inverse(X_14),multiply(inverse(X_14),inverse(X_14))) = identity,
    inference(subst,[],[x_cubed_is_identity:[bind(X,$fot(inverse(X_14)))]]) ).

cnf(refute_0_13,plain,
    ( multiply(inverse(X_14),multiply(inverse(X_14),inverse(X_14))) != identity
    | multiply(inverse(X_14),inverse(X_14)) != multiply(X_14,multiply(inverse(X_14),multiply(inverse(X_14),inverse(X_14))))
    | multiply(inverse(X_14),inverse(X_14)) = multiply(X_14,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_14),inverse(X_14)),multiply(X_14,multiply(inverse(X_14),multiply(inverse(X_14),inverse(X_14))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_14,plain,
    ( multiply(inverse(X_14),inverse(X_14)) != multiply(X_14,multiply(inverse(X_14),multiply(inverse(X_14),inverse(X_14))))
    | multiply(inverse(X_14),inverse(X_14)) = multiply(X_14,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(inverse(X_14),inverse(X_14))),identity) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    multiply(inverse(X_14),inverse(X_14)) = multiply(X_14,identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_14),inverse(X_14)),multiply(X_14,multiply(inverse(X_14),multiply(inverse(X_14),inverse(X_14))))) )],[refute_0_11,refute_0_14]) ).

cnf(refute_0_16,plain,
    multiply(X_14,identity) = X_14,
    inference(subst,[],[right_identity:[bind(X,$fot(X_14))]]) ).

cnf(refute_0_17,plain,
    ( multiply(X_14,identity) != X_14
    | multiply(inverse(X_14),inverse(X_14)) != multiply(X_14,identity)
    | multiply(inverse(X_14),inverse(X_14)) = X_14 ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_14),inverse(X_14)),multiply(X_14,identity)) ),[1],$fot(X_14)]]) ).

cnf(refute_0_18,plain,
    ( multiply(inverse(X_14),inverse(X_14)) != multiply(X_14,identity)
    | multiply(inverse(X_14),inverse(X_14)) = X_14 ),
    inference(resolve,[$cnf( $equal(multiply(X_14,identity),X_14) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    multiply(inverse(X_14),inverse(X_14)) = X_14,
    inference(resolve,[$cnf( $equal(multiply(inverse(X_14),inverse(X_14)),multiply(X_14,identity)) )],[refute_0_15,refute_0_18]) ).

cnf(refute_0_20,plain,
    multiply(inverse(X_11),inverse(X_11)) = X_11,
    inference(subst,[],[refute_0_19:[bind(X_14,$fot(X_11))]]) ).

cnf(refute_0_21,plain,
    ( multiply(inverse(X_11),inverse(X_11)) != X_11
    | inverse(X_11) != multiply(X_11,multiply(inverse(X_11),inverse(X_11)))
    | inverse(X_11) = multiply(X_11,X_11) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(X_11),multiply(X_11,multiply(inverse(X_11),inverse(X_11)))) ),[1,1],$fot(X_11)]]) ).

cnf(refute_0_22,plain,
    ( inverse(X_11) != multiply(X_11,multiply(inverse(X_11),inverse(X_11)))
    | inverse(X_11) = multiply(X_11,X_11) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_11),inverse(X_11)),X_11) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    inverse(X_11) = multiply(X_11,X_11),
    inference(resolve,[$cnf( $equal(inverse(X_11),multiply(X_11,multiply(inverse(X_11),inverse(X_11)))) )],[refute_0_10,refute_0_22]) ).

cnf(refute_0_24,plain,
    inverse(Y) = multiply(Y,Y),
    inference(subst,[],[refute_0_23:[bind(X_11,$fot(Y))]]) ).

cnf(refute_0_25,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_26,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_27,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_25,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( inverse(Y) != multiply(Y,Y)
    | multiply(Y,Y) = inverse(Y) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(Y))),bind(Y0,$fot(multiply(Y,Y)))]]) ).

cnf(refute_0_29,plain,
    multiply(Y,Y) = inverse(Y),
    inference(resolve,[$cnf( $equal(inverse(Y),multiply(Y,Y)) )],[refute_0_24,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( multiply(Y,Y) != inverse(Y)
    | multiply(multiply(Y,Y),Z) != multiply(Y,multiply(Y,Z))
    | multiply(inverse(Y),Z) = multiply(Y,multiply(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(Y,Y),Z),multiply(Y,multiply(Y,Z))) ),[0,0],$fot(inverse(Y))]]) ).

cnf(refute_0_31,plain,
    ( multiply(multiply(Y,Y),Z) != multiply(Y,multiply(Y,Z))
    | multiply(inverse(Y),Z) = multiply(Y,multiply(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(Y,Y),inverse(Y)) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    multiply(inverse(Y),Z) = multiply(Y,multiply(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(Y,Y),Z),multiply(Y,multiply(Y,Z))) )],[refute_0_0,refute_0_31]) ).

cnf(refute_0_33,plain,
    multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) = multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y)))))),
    inference(subst,[],[refute_0_32:[bind(Z,$fot(multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))]]) ).

cnf(refute_0_34,plain,
    commutator(X,multiply(X_11,X_12)) = multiply(X,multiply(multiply(X_11,X_12),multiply(inverse(X),inverse(multiply(X_11,X_12))))),
    inference(subst,[],[commutator:[bind(Y,$fot(multiply(X_11,X_12)))]]) ).

cnf(refute_0_35,plain,
    multiply(multiply(X_11,X_12),multiply(inverse(X),inverse(multiply(X_11,X_12)))) = multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))),
    inference(subst,[],[associativity:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(multiply(inverse(X),inverse(multiply(X_11,X_12)))))]]) ).

cnf(refute_0_36,plain,
    ( multiply(multiply(X_11,X_12),multiply(inverse(X),inverse(multiply(X_11,X_12)))) != multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))
    | commutator(X,multiply(X_11,X_12)) != multiply(X,multiply(multiply(X_11,X_12),multiply(inverse(X),inverse(multiply(X_11,X_12)))))
    | commutator(X,multiply(X_11,X_12)) = multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X,multiply(X_11,X_12)),multiply(X,multiply(multiply(X_11,X_12),multiply(inverse(X),inverse(multiply(X_11,X_12)))))) ),[1,1],$fot(multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))]]) ).

cnf(refute_0_37,plain,
    ( commutator(X,multiply(X_11,X_12)) != multiply(X,multiply(multiply(X_11,X_12),multiply(inverse(X),inverse(multiply(X_11,X_12)))))
    | commutator(X,multiply(X_11,X_12)) = multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_11,X_12),multiply(inverse(X),inverse(multiply(X_11,X_12)))),multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) )],[refute_0_35,refute_0_36]) ).

cnf(refute_0_38,plain,
    commutator(X,multiply(X_11,X_12)) = multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))),
    inference(resolve,[$cnf( $equal(commutator(X,multiply(X_11,X_12)),multiply(X,multiply(multiply(X_11,X_12),multiply(inverse(X),inverse(multiply(X_11,X_12)))))) )],[refute_0_34,refute_0_37]) ).

cnf(refute_0_39,plain,
    multiply(multiply(X_11,X_12),X) = multiply(X_11,multiply(X_12,X)),
    inference(subst,[],[associativity:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(X))]]) ).

cnf(refute_0_40,plain,
    inverse(multiply(multiply(X_11,X_12),X)) = inverse(multiply(multiply(X_11,X_12),X)),
    introduced(tautology,[refl,[$fot(inverse(multiply(multiply(X_11,X_12),X)))]]) ).

cnf(refute_0_41,plain,
    ( multiply(multiply(X_11,X_12),X) != multiply(X_11,multiply(X_12,X))
    | inverse(multiply(multiply(X_11,X_12),X)) != inverse(multiply(multiply(X_11,X_12),X))
    | inverse(multiply(multiply(X_11,X_12),X)) = inverse(multiply(X_11,multiply(X_12,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(X_11,X_12),X)),inverse(multiply(multiply(X_11,X_12),X))) ),[1,0],$fot(multiply(X_11,multiply(X_12,X)))]]) ).

cnf(refute_0_42,plain,
    ( multiply(multiply(X_11,X_12),X) != multiply(X_11,multiply(X_12,X))
    | inverse(multiply(multiply(X_11,X_12),X)) = inverse(multiply(X_11,multiply(X_12,X))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_11,X_12),X)),inverse(multiply(multiply(X_11,X_12),X))) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    inverse(multiply(multiply(X_11,X_12),X)) = inverse(multiply(X_11,multiply(X_12,X))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_11,X_12),X),multiply(X_11,multiply(X_12,X))) )],[refute_0_39,refute_0_42]) ).

cnf(refute_0_44,plain,
    multiply(multiply(inverse(X_12),X_12),X_13) = multiply(inverse(X_12),multiply(X_12,X_13)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_12))),bind(Y,$fot(X_12)),bind(Z,$fot(X_13))]]) ).

cnf(refute_0_45,plain,
    multiply(inverse(X_12),X_12) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_12))]]) ).

cnf(refute_0_46,plain,
    ( multiply(multiply(inverse(X_12),X_12),X_13) != multiply(inverse(X_12),multiply(X_12,X_13))
    | multiply(inverse(X_12),X_12) != identity
    | multiply(identity,X_13) = multiply(inverse(X_12),multiply(X_12,X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_12),X_12),X_13),multiply(inverse(X_12),multiply(X_12,X_13))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_47,plain,
    ( multiply(multiply(inverse(X_12),X_12),X_13) != multiply(inverse(X_12),multiply(X_12,X_13))
    | multiply(identity,X_13) = multiply(inverse(X_12),multiply(X_12,X_13)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_12),X_12),identity) )],[refute_0_45,refute_0_46]) ).

cnf(refute_0_48,plain,
    multiply(identity,X_13) = multiply(inverse(X_12),multiply(X_12,X_13)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_12),X_12),X_13),multiply(inverse(X_12),multiply(X_12,X_13))) )],[refute_0_44,refute_0_47]) ).

cnf(refute_0_49,plain,
    ( multiply(identity,X_13) != X_13
    | multiply(identity,X_13) != multiply(inverse(X_12),multiply(X_12,X_13))
    | X_13 = multiply(inverse(X_12),multiply(X_12,X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_13),multiply(inverse(X_12),multiply(X_12,X_13))) ),[0],$fot(X_13)]]) ).

cnf(refute_0_50,plain,
    ( multiply(identity,X_13) != multiply(inverse(X_12),multiply(X_12,X_13))
    | X_13 = multiply(inverse(X_12),multiply(X_12,X_13)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_13),X_13) )],[refute_0_6,refute_0_49]) ).

cnf(refute_0_51,plain,
    X_13 = multiply(inverse(X_12),multiply(X_12,X_13)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_13),multiply(inverse(X_12),multiply(X_12,X_13))) )],[refute_0_48,refute_0_50]) ).

cnf(refute_0_52,plain,
    inverse(multiply(X_34,X_12)) = multiply(inverse(X_12),multiply(X_12,inverse(multiply(X_34,X_12)))),
    inference(subst,[],[refute_0_51:[bind(X_13,$fot(inverse(multiply(X_34,X_12))))]]) ).

cnf(refute_0_53,plain,
    multiply(X_27,inverse(multiply(X_12,X_27))) = multiply(inverse(X_12),multiply(X_12,multiply(X_27,inverse(multiply(X_12,X_27))))),
    inference(subst,[],[refute_0_51:[bind(X_13,$fot(multiply(X_27,inverse(multiply(X_12,X_27)))))]]) ).

cnf(refute_0_54,plain,
    multiply(multiply(X_11,X_12),inverse(multiply(X_11,X_12))) = identity,
    inference(subst,[],[right_inverse:[bind(X,$fot(multiply(X_11,X_12)))]]) ).

cnf(refute_0_55,plain,
    multiply(multiply(X_11,X_12),inverse(multiply(X_11,X_12))) = multiply(X_11,multiply(X_12,inverse(multiply(X_11,X_12)))),
    inference(subst,[],[associativity:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(inverse(multiply(X_11,X_12))))]]) ).

cnf(refute_0_56,plain,
    ( multiply(multiply(X_11,X_12),inverse(multiply(X_11,X_12))) != multiply(X_11,multiply(X_12,inverse(multiply(X_11,X_12))))
    | multiply(multiply(X_11,X_12),inverse(multiply(X_11,X_12))) != identity
    | multiply(X_11,multiply(X_12,inverse(multiply(X_11,X_12)))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,X_12),inverse(multiply(X_11,X_12))),identity) ),[0],$fot(multiply(X_11,multiply(X_12,inverse(multiply(X_11,X_12)))))]]) ).

cnf(refute_0_57,plain,
    ( multiply(multiply(X_11,X_12),inverse(multiply(X_11,X_12))) != identity
    | multiply(X_11,multiply(X_12,inverse(multiply(X_11,X_12)))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_11,X_12),inverse(multiply(X_11,X_12))),multiply(X_11,multiply(X_12,inverse(multiply(X_11,X_12))))) )],[refute_0_55,refute_0_56]) ).

cnf(refute_0_58,plain,
    multiply(X_11,multiply(X_12,inverse(multiply(X_11,X_12)))) = identity,
    inference(resolve,[$cnf( $equal(multiply(multiply(X_11,X_12),inverse(multiply(X_11,X_12))),identity) )],[refute_0_54,refute_0_57]) ).

cnf(refute_0_59,plain,
    multiply(X_12,multiply(X_27,inverse(multiply(X_12,X_27)))) = identity,
    inference(subst,[],[refute_0_58:[bind(X_11,$fot(X_12)),bind(X_12,$fot(X_27))]]) ).

cnf(refute_0_60,plain,
    ( multiply(X_12,multiply(X_27,inverse(multiply(X_12,X_27)))) != identity
    | multiply(X_27,inverse(multiply(X_12,X_27))) != multiply(inverse(X_12),multiply(X_12,multiply(X_27,inverse(multiply(X_12,X_27)))))
    | multiply(X_27,inverse(multiply(X_12,X_27))) = multiply(inverse(X_12),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,inverse(multiply(X_12,X_27))),multiply(inverse(X_12),multiply(X_12,multiply(X_27,inverse(multiply(X_12,X_27)))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_61,plain,
    ( multiply(X_27,inverse(multiply(X_12,X_27))) != multiply(inverse(X_12),multiply(X_12,multiply(X_27,inverse(multiply(X_12,X_27)))))
    | multiply(X_27,inverse(multiply(X_12,X_27))) = multiply(inverse(X_12),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_12,multiply(X_27,inverse(multiply(X_12,X_27)))),identity) )],[refute_0_59,refute_0_60]) ).

cnf(refute_0_62,plain,
    multiply(X_27,inverse(multiply(X_12,X_27))) = multiply(inverse(X_12),identity),
    inference(resolve,[$cnf( $equal(multiply(X_27,inverse(multiply(X_12,X_27))),multiply(inverse(X_12),multiply(X_12,multiply(X_27,inverse(multiply(X_12,X_27)))))) )],[refute_0_53,refute_0_61]) ).

cnf(refute_0_63,plain,
    multiply(inverse(X_12),identity) = inverse(X_12),
    inference(subst,[],[right_identity:[bind(X,$fot(inverse(X_12)))]]) ).

cnf(refute_0_64,plain,
    ( multiply(X_27,inverse(multiply(X_12,X_27))) != multiply(inverse(X_12),identity)
    | multiply(inverse(X_12),identity) != inverse(X_12)
    | multiply(X_27,inverse(multiply(X_12,X_27))) = inverse(X_12) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_27,inverse(multiply(X_12,X_27))),inverse(X_12)) ),[0],$fot(multiply(inverse(X_12),identity))]]) ).

cnf(refute_0_65,plain,
    ( multiply(X_27,inverse(multiply(X_12,X_27))) != multiply(inverse(X_12),identity)
    | multiply(X_27,inverse(multiply(X_12,X_27))) = inverse(X_12) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_12),identity),inverse(X_12)) )],[refute_0_63,refute_0_64]) ).

cnf(refute_0_66,plain,
    multiply(X_27,inverse(multiply(X_12,X_27))) = inverse(X_12),
    inference(resolve,[$cnf( $equal(multiply(X_27,inverse(multiply(X_12,X_27))),multiply(inverse(X_12),identity)) )],[refute_0_62,refute_0_65]) ).

cnf(refute_0_67,plain,
    multiply(X_12,inverse(multiply(X_34,X_12))) = inverse(X_34),
    inference(subst,[],[refute_0_66:[bind(X_12,$fot(X_34)),bind(X_27,$fot(X_12))]]) ).

cnf(refute_0_68,plain,
    ( multiply(X_12,inverse(multiply(X_34,X_12))) != inverse(X_34)
    | inverse(multiply(X_34,X_12)) != multiply(inverse(X_12),multiply(X_12,inverse(multiply(X_34,X_12))))
    | inverse(multiply(X_34,X_12)) = multiply(inverse(X_12),inverse(X_34)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_34,X_12)),multiply(inverse(X_12),multiply(X_12,inverse(multiply(X_34,X_12))))) ),[1,1],$fot(inverse(X_34))]]) ).

cnf(refute_0_69,plain,
    ( inverse(multiply(X_34,X_12)) != multiply(inverse(X_12),multiply(X_12,inverse(multiply(X_34,X_12))))
    | inverse(multiply(X_34,X_12)) = multiply(inverse(X_12),inverse(X_34)) ),
    inference(resolve,[$cnf( $equal(multiply(X_12,inverse(multiply(X_34,X_12))),inverse(X_34)) )],[refute_0_67,refute_0_68]) ).

cnf(refute_0_70,plain,
    inverse(multiply(X_34,X_12)) = multiply(inverse(X_12),inverse(X_34)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_34,X_12)),multiply(inverse(X_12),multiply(X_12,inverse(multiply(X_34,X_12))))) )],[refute_0_52,refute_0_69]) ).

cnf(refute_0_71,plain,
    ( inverse(multiply(X_34,X_12)) != multiply(inverse(X_12),inverse(X_34))
    | multiply(inverse(X_12),inverse(X_34)) = inverse(multiply(X_34,X_12)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X_34,X_12)))),bind(Y0,$fot(multiply(inverse(X_12),inverse(X_34))))]]) ).

cnf(refute_0_72,plain,
    multiply(inverse(X_12),inverse(X_34)) = inverse(multiply(X_34,X_12)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_34,X_12)),multiply(inverse(X_12),inverse(X_34))) )],[refute_0_70,refute_0_71]) ).

cnf(refute_0_73,plain,
    multiply(inverse(X),inverse(multiply(X_11,X_12))) = inverse(multiply(multiply(X_11,X_12),X)),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(X)),bind(X_34,$fot(multiply(X_11,X_12)))]]) ).

cnf(refute_0_74,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_75,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_27,refute_0_74]) ).

cnf(refute_0_76,plain,
    ( multiply(inverse(X),inverse(multiply(X_11,X_12))) != inverse(multiply(multiply(X_11,X_12),X))
    | inverse(multiply(multiply(X_11,X_12),X)) != inverse(multiply(X_11,multiply(X_12,X)))
    | multiply(inverse(X),inverse(multiply(X_11,X_12))) = inverse(multiply(X_11,multiply(X_12,X))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(inverse(X),inverse(multiply(X_11,X_12))))),bind(Y0,$fot(inverse(multiply(multiply(X_11,X_12),X)))),bind(Z0,$fot(inverse(multiply(X_11,multiply(X_12,X)))))]]) ).

cnf(refute_0_77,plain,
    ( inverse(multiply(multiply(X_11,X_12),X)) != inverse(multiply(X_11,multiply(X_12,X)))
    | multiply(inverse(X),inverse(multiply(X_11,X_12))) = inverse(multiply(X_11,multiply(X_12,X))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),inverse(multiply(X_11,X_12))),inverse(multiply(multiply(X_11,X_12),X))) )],[refute_0_73,refute_0_76]) ).

cnf(refute_0_78,plain,
    multiply(inverse(X),inverse(multiply(X_11,X_12))) = inverse(multiply(X_11,multiply(X_12,X))),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_11,X_12),X)),inverse(multiply(X_11,multiply(X_12,X)))) )],[refute_0_43,refute_0_77]) ).

cnf(refute_0_79,plain,
    multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))) = multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))),
    introduced(tautology,[refl,[$fot(multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))]]) ).

cnf(refute_0_80,plain,
    ( multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))) != multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))
    | multiply(inverse(X),inverse(multiply(X_11,X_12))) != inverse(multiply(X_11,multiply(X_12,X)))
    | multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))) = multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))),multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) ),[1,1],$fot(inverse(multiply(X_11,multiply(X_12,X))))]]) ).

cnf(refute_0_81,plain,
    ( multiply(inverse(X),inverse(multiply(X_11,X_12))) != inverse(multiply(X_11,multiply(X_12,X)))
    | multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))) = multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))),multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) )],[refute_0_79,refute_0_80]) ).

cnf(refute_0_82,plain,
    multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))) = multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),inverse(multiply(X_11,X_12))),inverse(multiply(X_11,multiply(X_12,X)))) )],[refute_0_78,refute_0_81]) ).

cnf(refute_0_83,plain,
    multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) = multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))),
    introduced(tautology,[refl,[$fot(multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))]]) ).

cnf(refute_0_84,plain,
    ( multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) != multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))
    | multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))) != multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))
    | multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) = multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))),multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) ),[1,1],$fot(multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))]]) ).

cnf(refute_0_85,plain,
    ( multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))) != multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))
    | multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) = multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))) ),
    inference(resolve,[$cnf( $equal(multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))),multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) )],[refute_0_83,refute_0_84]) ).

cnf(refute_0_86,plain,
    multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) = multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))),
    inference(resolve,[$cnf( $equal(multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))),multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))) )],[refute_0_82,refute_0_85]) ).

cnf(refute_0_87,plain,
    multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) = multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))),
    introduced(tautology,[refl,[$fot(multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))))]]) ).

cnf(refute_0_88,plain,
    ( multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) != multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))
    | multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) != multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))
    | multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) = multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))),multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))) ),[1,1],$fot(multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))))]]) ).

cnf(refute_0_89,plain,
    ( multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))) != multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))
    | multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) = multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))),multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))) )],[refute_0_87,refute_0_88]) ).

cnf(refute_0_90,plain,
    multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) = multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))),
    inference(resolve,[$cnf( $equal(multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))),multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))) )],[refute_0_86,refute_0_89]) ).

cnf(refute_0_91,plain,
    ( multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))) != multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))))
    | commutator(X,multiply(X_11,X_12)) != multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))
    | commutator(X,multiply(X_11,X_12)) = multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X,multiply(X_11,X_12)),multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))) ),[1],$fot(multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))))]]) ).

cnf(refute_0_92,plain,
    ( commutator(X,multiply(X_11,X_12)) != multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))
    | commutator(X,multiply(X_11,X_12)) = multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12)))))),multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X))))))) )],[refute_0_90,refute_0_91]) ).

cnf(refute_0_93,plain,
    commutator(X,multiply(X_11,X_12)) = multiply(X,multiply(X_11,multiply(X_12,inverse(multiply(X_11,multiply(X_12,X)))))),
    inference(resolve,[$cnf( $equal(commutator(X,multiply(X_11,X_12)),multiply(X,multiply(X_11,multiply(X_12,multiply(inverse(X),inverse(multiply(X_11,X_12))))))) )],[refute_0_38,refute_0_92]) ).

cnf(refute_0_94,plain,
    commutator(Y,multiply(Y,X_62)) = multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y)))))),
    inference(subst,[],[refute_0_93:[bind(X,$fot(Y)),bind(X_11,$fot(Y)),bind(X_12,$fot(X_62))]]) ).

cnf(refute_0_95,plain,
    ( commutator(Y,multiply(Y,X_62)) != multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))
    | multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y)))))) = commutator(Y,multiply(Y,X_62)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(Y,multiply(Y,X_62)))),bind(Y0,$fot(multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))))]]) ).

cnf(refute_0_96,plain,
    multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y)))))) = commutator(Y,multiply(Y,X_62)),
    inference(resolve,[$cnf( $equal(commutator(Y,multiply(Y,X_62)),multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    ( multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y)))))) != commutator(Y,multiply(Y,X_62))
    | multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) != multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))
    | multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) = commutator(Y,multiply(Y,X_62)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))),multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))) ),[1],$fot(commutator(Y,multiply(Y,X_62)))]]) ).

cnf(refute_0_98,plain,
    ( multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) != multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))
    | multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) = commutator(Y,multiply(Y,X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y)))))),commutator(Y,multiply(Y,X_62))) )],[refute_0_96,refute_0_97]) ).

cnf(refute_0_99,plain,
    multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) = commutator(Y,multiply(Y,X_62)),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))),multiply(Y,multiply(Y,multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))) )],[refute_0_33,refute_0_98]) ).

cnf(refute_0_100,plain,
    multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))))) = inverse(commutator(X_31,X_30)),
    inference(subst,[],[refute_0_66:[bind(X_12,$fot(commutator(X_31,X_30))),bind(X_27,$fot(multiply(X_30,multiply(X_31,inverse(X_30)))))]]) ).

cnf(refute_0_101,plain,
    multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) = multiply(inverse(inverse(X_31)),multiply(inverse(X_31),multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))))),
    inference(subst,[],[refute_0_51:[bind(X_12,$fot(inverse(X_31))),bind(X_13,$fot(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30))))))]]) ).

cnf(refute_0_102,plain,
    multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(inverse(X_20),commutator(X_20,Y))))) = identity,
    inference(subst,[],[refute_0_58:[bind(X_11,$fot(inverse(X_20))),bind(X_12,$fot(commutator(X_20,Y)))]]) ).

cnf(refute_0_103,plain,
    multiply(Y,multiply(inverse(X_20),inverse(Y))) = multiply(inverse(X_20),multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y))))),
    inference(subst,[],[refute_0_51:[bind(X_12,$fot(X_20)),bind(X_13,$fot(multiply(Y,multiply(inverse(X_20),inverse(Y)))))]]) ).

cnf(refute_0_104,plain,
    commutator(X_20,Y) = multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))),
    inference(subst,[],[commutator:[bind(X,$fot(X_20))]]) ).

cnf(refute_0_105,plain,
    ( commutator(X_20,Y) != multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y))))
    | multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))) = commutator(X_20,Y) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(X_20,Y))),bind(Y0,$fot(multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y))))))]]) ).

cnf(refute_0_106,plain,
    multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))) = commutator(X_20,Y),
    inference(resolve,[$cnf( $equal(commutator(X_20,Y),multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y))))) )],[refute_0_104,refute_0_105]) ).

cnf(refute_0_107,plain,
    ( multiply(Y,multiply(inverse(X_20),inverse(Y))) != multiply(inverse(X_20),multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))))
    | multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))) != commutator(X_20,Y)
    | multiply(Y,multiply(inverse(X_20),inverse(Y))) = multiply(inverse(X_20),commutator(X_20,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(Y,multiply(inverse(X_20),inverse(Y))),multiply(inverse(X_20),multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))))) ),[1,1],$fot(commutator(X_20,Y))]]) ).

cnf(refute_0_108,plain,
    ( multiply(Y,multiply(inverse(X_20),inverse(Y))) != multiply(inverse(X_20),multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))))
    | multiply(Y,multiply(inverse(X_20),inverse(Y))) = multiply(inverse(X_20),commutator(X_20,Y)) ),
    inference(resolve,[$cnf( $equal(multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))),commutator(X_20,Y)) )],[refute_0_106,refute_0_107]) ).

cnf(refute_0_109,plain,
    multiply(Y,multiply(inverse(X_20),inverse(Y))) = multiply(inverse(X_20),commutator(X_20,Y)),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(X_20),inverse(Y))),multiply(inverse(X_20),multiply(X_20,multiply(Y,multiply(inverse(X_20),inverse(Y)))))) )],[refute_0_103,refute_0_108]) ).

cnf(refute_0_110,plain,
    ( multiply(Y,multiply(inverse(X_20),inverse(Y))) != multiply(inverse(X_20),commutator(X_20,Y))
    | multiply(inverse(X_20),commutator(X_20,Y)) = multiply(Y,multiply(inverse(X_20),inverse(Y))) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(Y,multiply(inverse(X_20),inverse(Y))))),bind(Y0,$fot(multiply(inverse(X_20),commutator(X_20,Y))))]]) ).

cnf(refute_0_111,plain,
    multiply(inverse(X_20),commutator(X_20,Y)) = multiply(Y,multiply(inverse(X_20),inverse(Y))),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(X_20),inverse(Y))),multiply(inverse(X_20),commutator(X_20,Y))) )],[refute_0_109,refute_0_110]) ).

cnf(refute_0_112,plain,
    ( multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(inverse(X_20),commutator(X_20,Y))))) != identity
    | multiply(inverse(X_20),commutator(X_20,Y)) != multiply(Y,multiply(inverse(X_20),inverse(Y)))
    | multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(inverse(X_20),commutator(X_20,Y))))),identity) ),[0,1,1,0],$fot(multiply(Y,multiply(inverse(X_20),inverse(Y))))]]) ).

cnf(refute_0_113,plain,
    ( multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(inverse(X_20),commutator(X_20,Y))))) != identity
    | multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),commutator(X_20,Y)),multiply(Y,multiply(inverse(X_20),inverse(Y)))) )],[refute_0_111,refute_0_112]) ).

cnf(refute_0_114,plain,
    multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(inverse(X_20),commutator(X_20,Y))))),identity) )],[refute_0_102,refute_0_113]) ).

cnf(refute_0_115,plain,
    multiply(multiply(X,Y),multiply(X,Y)) = multiply(X,multiply(Y,multiply(X,Y))),
    inference(subst,[],[associativity:[bind(Z,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_116,plain,
    inverse(multiply(X,Y)) = multiply(multiply(X,Y),multiply(X,Y)),
    inference(subst,[],[refute_0_23:[bind(X_11,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_117,plain,
    ( inverse(multiply(X,Y)) != multiply(multiply(X,Y),multiply(X,Y))
    | multiply(multiply(X,Y),multiply(X,Y)) = inverse(multiply(X,Y)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(multiply(X,Y),multiply(X,Y))))]]) ).

cnf(refute_0_118,plain,
    multiply(multiply(X,Y),multiply(X,Y)) = inverse(multiply(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(multiply(X,Y),multiply(X,Y))) )],[refute_0_116,refute_0_117]) ).

cnf(refute_0_119,plain,
    ( multiply(multiply(X,Y),multiply(X,Y)) != multiply(X,multiply(Y,multiply(X,Y)))
    | multiply(multiply(X,Y),multiply(X,Y)) != inverse(multiply(X,Y))
    | inverse(multiply(X,Y)) = multiply(X,multiply(Y,multiply(X,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),multiply(X,Y)),multiply(X,multiply(Y,multiply(X,Y)))) ),[0],$fot(inverse(multiply(X,Y)))]]) ).

cnf(refute_0_120,plain,
    ( multiply(multiply(X,Y),multiply(X,Y)) != multiply(X,multiply(Y,multiply(X,Y)))
    | inverse(multiply(X,Y)) = multiply(X,multiply(Y,multiply(X,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),multiply(X,Y)),inverse(multiply(X,Y))) )],[refute_0_118,refute_0_119]) ).

cnf(refute_0_121,plain,
    inverse(multiply(X,Y)) = multiply(X,multiply(Y,multiply(X,Y))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),multiply(X,Y)),multiply(X,multiply(Y,multiply(X,Y)))) )],[refute_0_115,refute_0_120]) ).

cnf(refute_0_122,plain,
    inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) = multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(X_28,multiply(inverse(X_20),inverse(X_28))))),
    inference(subst,[],[refute_0_121:[bind(X,$fot(X_28)),bind(Y,$fot(multiply(inverse(X_20),inverse(X_28))))]]) ).

cnf(refute_0_123,plain,
    multiply(X_28,multiply(inverse(X_20),inverse(X_28))) = multiply(inverse(X_20),commutator(X_20,X_28)),
    inference(subst,[],[refute_0_109:[bind(Y,$fot(X_28))]]) ).

cnf(refute_0_124,plain,
    ( multiply(X_28,multiply(inverse(X_20),inverse(X_28))) != multiply(inverse(X_20),commutator(X_20,X_28))
    | inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) != multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(X_28,multiply(inverse(X_20),inverse(X_28)))))
    | inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) = multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))),multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(X_28,multiply(inverse(X_20),inverse(X_28)))))) ),[1,1,1],$fot(multiply(inverse(X_20),commutator(X_20,X_28)))]]) ).

cnf(refute_0_125,plain,
    ( inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) != multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(X_28,multiply(inverse(X_20),inverse(X_28)))))
    | inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) = multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_28,multiply(inverse(X_20),inverse(X_28))),multiply(inverse(X_20),commutator(X_20,X_28))) )],[refute_0_123,refute_0_124]) ).

cnf(refute_0_126,plain,
    inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) = multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))),multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(X_28,multiply(inverse(X_20),inverse(X_28)))))) )],[refute_0_122,refute_0_125]) ).

cnf(refute_0_127,plain,
    inverse(inverse(X_14)) = multiply(X_14,multiply(inverse(X_14),inverse(inverse(X_14)))),
    inference(subst,[],[refute_0_9:[bind(X_11,$fot(X_14)),bind(X_13,$fot(inverse(inverse(X_14))))]]) ).

cnf(refute_0_128,plain,
    multiply(inverse(X_14),inverse(inverse(X_14))) = identity,
    inference(subst,[],[right_inverse:[bind(X,$fot(inverse(X_14)))]]) ).

cnf(refute_0_129,plain,
    ( multiply(inverse(X_14),inverse(inverse(X_14))) != identity
    | inverse(inverse(X_14)) != multiply(X_14,multiply(inverse(X_14),inverse(inverse(X_14))))
    | inverse(inverse(X_14)) = multiply(X_14,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_14)),multiply(X_14,multiply(inverse(X_14),inverse(inverse(X_14))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_130,plain,
    ( inverse(inverse(X_14)) != multiply(X_14,multiply(inverse(X_14),inverse(inverse(X_14))))
    | inverse(inverse(X_14)) = multiply(X_14,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_14),inverse(inverse(X_14))),identity) )],[refute_0_128,refute_0_129]) ).

cnf(refute_0_131,plain,
    inverse(inverse(X_14)) = multiply(X_14,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_14)),multiply(X_14,multiply(inverse(X_14),inverse(inverse(X_14))))) )],[refute_0_127,refute_0_130]) ).

cnf(refute_0_132,plain,
    ( multiply(X_14,identity) != X_14
    | inverse(inverse(X_14)) != multiply(X_14,identity)
    | inverse(inverse(X_14)) = X_14 ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_14)),multiply(X_14,identity)) ),[1],$fot(X_14)]]) ).

cnf(refute_0_133,plain,
    ( inverse(inverse(X_14)) != multiply(X_14,identity)
    | inverse(inverse(X_14)) = X_14 ),
    inference(resolve,[$cnf( $equal(multiply(X_14,identity),X_14) )],[refute_0_16,refute_0_132]) ).

cnf(refute_0_134,plain,
    inverse(inverse(X_14)) = X_14,
    inference(resolve,[$cnf( $equal(inverse(inverse(X_14)),multiply(X_14,identity)) )],[refute_0_131,refute_0_133]) ).

cnf(refute_0_135,plain,
    inverse(inverse(X_20)) = X_20,
    inference(subst,[],[refute_0_134:[bind(X_14,$fot(X_20))]]) ).

cnf(refute_0_136,plain,
    multiply(inverse(inverse(X_20)),inverse(X_28)) = multiply(inverse(inverse(X_20)),inverse(X_28)),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_20)),inverse(X_28)))]]) ).

cnf(refute_0_137,plain,
    ( multiply(inverse(inverse(X_20)),inverse(X_28)) != multiply(inverse(inverse(X_20)),inverse(X_28))
    | inverse(inverse(X_20)) != X_20
    | multiply(inverse(inverse(X_20)),inverse(X_28)) = multiply(X_20,inverse(X_28)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_20)),inverse(X_28)),multiply(inverse(inverse(X_20)),inverse(X_28))) ),[1,0],$fot(X_20)]]) ).

cnf(refute_0_138,plain,
    ( inverse(inverse(X_20)) != X_20
    | multiply(inverse(inverse(X_20)),inverse(X_28)) = multiply(X_20,inverse(X_28)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_20)),inverse(X_28)),multiply(inverse(inverse(X_20)),inverse(X_28))) )],[refute_0_136,refute_0_137]) ).

cnf(refute_0_139,plain,
    multiply(inverse(inverse(X_20)),inverse(X_28)) = multiply(X_20,inverse(X_28)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_20)),X_20) )],[refute_0_135,refute_0_138]) ).

cnf(refute_0_140,plain,
    ( multiply(inverse(Y),Z) != multiply(Y,multiply(Y,Z))
    | multiply(Y,multiply(Y,Z)) = multiply(inverse(Y),Z) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(inverse(Y),Z))),bind(Y0,$fot(multiply(Y,multiply(Y,Z))))]]) ).

cnf(refute_0_141,plain,
    multiply(Y,multiply(Y,Z)) = multiply(inverse(Y),Z),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),Z),multiply(Y,multiply(Y,Z))) )],[refute_0_32,refute_0_140]) ).

cnf(refute_0_142,plain,
    multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) = multiply(inverse(inverse(X_20)),inverse(X_28)),
    inference(subst,[],[refute_0_141:[bind(Y,$fot(inverse(X_20))),bind(Z,$fot(inverse(X_28)))]]) ).

cnf(refute_0_143,plain,
    ( multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) != multiply(inverse(inverse(X_20)),inverse(X_28))
    | multiply(inverse(inverse(X_20)),inverse(X_28)) != multiply(X_20,inverse(X_28))
    | multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) = multiply(X_20,inverse(X_28)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))))),bind(Y0,$fot(multiply(inverse(inverse(X_20)),inverse(X_28)))),bind(Z0,$fot(multiply(X_20,inverse(X_28))))]]) ).

cnf(refute_0_144,plain,
    ( multiply(inverse(inverse(X_20)),inverse(X_28)) != multiply(X_20,inverse(X_28))
    | multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) = multiply(X_20,inverse(X_28)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))),multiply(inverse(inverse(X_20)),inverse(X_28))) )],[refute_0_142,refute_0_143]) ).

cnf(refute_0_145,plain,
    multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) = multiply(X_20,inverse(X_28)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_20)),inverse(X_28)),multiply(X_20,inverse(X_28))) )],[refute_0_139,refute_0_144]) ).

cnf(refute_0_146,plain,
    multiply(inverse(X_23),inverse(X_12)) = multiply(inverse(X_12),multiply(X_12,multiply(inverse(X_23),inverse(X_12)))),
    inference(subst,[],[refute_0_51:[bind(X_13,$fot(multiply(inverse(X_23),inverse(X_12))))]]) ).

cnf(refute_0_147,plain,
    multiply(X_12,multiply(inverse(X_23),inverse(X_12))) = multiply(inverse(X_23),commutator(X_23,X_12)),
    inference(subst,[],[refute_0_109:[bind(Y,$fot(X_12)),bind(X_20,$fot(X_23))]]) ).

cnf(refute_0_148,plain,
    ( multiply(X_12,multiply(inverse(X_23),inverse(X_12))) != multiply(inverse(X_23),commutator(X_23,X_12))
    | multiply(inverse(X_23),inverse(X_12)) != multiply(inverse(X_12),multiply(X_12,multiply(inverse(X_23),inverse(X_12))))
    | multiply(inverse(X_23),inverse(X_12)) = multiply(inverse(X_12),multiply(inverse(X_23),commutator(X_23,X_12))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_23),inverse(X_12)),multiply(inverse(X_12),multiply(X_12,multiply(inverse(X_23),inverse(X_12))))) ),[1,1],$fot(multiply(inverse(X_23),commutator(X_23,X_12)))]]) ).

cnf(refute_0_149,plain,
    ( multiply(inverse(X_23),inverse(X_12)) != multiply(inverse(X_12),multiply(X_12,multiply(inverse(X_23),inverse(X_12))))
    | multiply(inverse(X_23),inverse(X_12)) = multiply(inverse(X_12),multiply(inverse(X_23),commutator(X_23,X_12))) ),
    inference(resolve,[$cnf( $equal(multiply(X_12,multiply(inverse(X_23),inverse(X_12))),multiply(inverse(X_23),commutator(X_23,X_12))) )],[refute_0_147,refute_0_148]) ).

cnf(refute_0_150,plain,
    multiply(inverse(X_23),inverse(X_12)) = multiply(inverse(X_12),multiply(inverse(X_23),commutator(X_23,X_12))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_23),inverse(X_12)),multiply(inverse(X_12),multiply(X_12,multiply(inverse(X_23),inverse(X_12))))) )],[refute_0_146,refute_0_149]) ).

cnf(refute_0_151,plain,
    ( multiply(inverse(X_23),inverse(X_12)) != multiply(inverse(X_12),multiply(inverse(X_23),commutator(X_23,X_12)))
    | multiply(inverse(X_12),multiply(inverse(X_23),commutator(X_23,X_12))) = multiply(inverse(X_23),inverse(X_12)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(inverse(X_23),inverse(X_12)))),bind(Y0,$fot(multiply(inverse(X_12),multiply(inverse(X_23),commutator(X_23,X_12)))))]]) ).

cnf(refute_0_152,plain,
    multiply(inverse(X_12),multiply(inverse(X_23),commutator(X_23,X_12))) = multiply(inverse(X_23),inverse(X_12)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_23),inverse(X_12)),multiply(inverse(X_12),multiply(inverse(X_23),commutator(X_23,X_12)))) )],[refute_0_150,refute_0_151]) ).

cnf(refute_0_153,plain,
    multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))) = multiply(inverse(X_20),inverse(X_28)),
    inference(subst,[],[refute_0_152:[bind(X_12,$fot(X_28)),bind(X_23,$fot(X_20))]]) ).

cnf(refute_0_154,plain,
    multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))),
    introduced(tautology,[refl,[$fot(multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))))]]) ).

cnf(refute_0_155,plain,
    ( multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) != multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))))
    | multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))) != multiply(inverse(X_20),inverse(X_28))
    | multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))),multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))))) ),[1,1],$fot(multiply(inverse(X_20),inverse(X_28)))]]) ).

cnf(refute_0_156,plain,
    ( multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))) != multiply(inverse(X_20),inverse(X_28))
    | multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))),multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))))) )],[refute_0_154,refute_0_155]) ).

cnf(refute_0_157,plain,
    multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))),multiply(inverse(X_20),inverse(X_28))) )],[refute_0_153,refute_0_156]) ).

cnf(refute_0_158,plain,
    ( multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) != multiply(X_20,inverse(X_28))
    | multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) != multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28)))
    | multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(X_20,inverse(X_28)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))))),bind(Y0,$fot(multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))))),bind(Z0,$fot(multiply(X_20,inverse(X_28))))]]) ).

cnf(refute_0_159,plain,
    ( multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))) != multiply(X_20,inverse(X_28))
    | multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(X_20,inverse(X_28)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))),multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28)))) )],[refute_0_157,refute_0_158]) ).

cnf(refute_0_160,plain,
    multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(X_20,inverse(X_28)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(inverse(X_20),inverse(X_28))),multiply(X_20,inverse(X_28))) )],[refute_0_145,refute_0_159]) ).

cnf(refute_0_161,plain,
    multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))) = multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_20))),bind(Y,$fot(inverse(X_28))),bind(Z,$fot(multiply(inverse(X_20),commutator(X_20,X_28))))]]) ).

cnf(refute_0_162,plain,
    ( multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))) != multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))))
    | multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) != multiply(X_20,inverse(X_28))
    | multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))) = multiply(X_20,inverse(X_28)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))))),bind(Y0,$fot(multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))))),bind(Z0,$fot(multiply(X_20,inverse(X_28))))]]) ).

cnf(refute_0_163,plain,
    ( multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))) != multiply(X_20,inverse(X_28))
    | multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))) = multiply(X_20,inverse(X_28)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))),multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28))))) )],[refute_0_161,refute_0_162]) ).

cnf(refute_0_164,plain,
    multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))) = multiply(X_20,inverse(X_28)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(inverse(X_28),multiply(inverse(X_20),commutator(X_20,X_28)))),multiply(X_20,inverse(X_28))) )],[refute_0_160,refute_0_163]) ).

cnf(refute_0_165,plain,
    multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))),
    introduced(tautology,[refl,[$fot(multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))))]]) ).

cnf(refute_0_166,plain,
    ( multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))) != multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))))
    | multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))) != multiply(X_20,inverse(X_28))
    | multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(X_28,multiply(X_20,inverse(X_28))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))),multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))))) ),[1,1],$fot(multiply(X_20,inverse(X_28)))]]) ).

cnf(refute_0_167,plain,
    ( multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))) != multiply(X_20,inverse(X_28))
    | multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(X_28,multiply(X_20,inverse(X_28))) ),
    inference(resolve,[$cnf( $equal(multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))),multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))))) )],[refute_0_165,refute_0_166]) ).

cnf(refute_0_168,plain,
    multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))) = multiply(X_28,multiply(X_20,inverse(X_28))),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))),multiply(X_20,inverse(X_28))) )],[refute_0_164,refute_0_167]) ).

cnf(refute_0_169,plain,
    ( multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))) != multiply(X_28,multiply(X_20,inverse(X_28)))
    | inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) != multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))))
    | inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) = multiply(X_28,multiply(X_20,inverse(X_28))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))),multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))))) ),[1],$fot(multiply(X_28,multiply(X_20,inverse(X_28))))]]) ).

cnf(refute_0_170,plain,
    ( inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) != multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))))
    | inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) = multiply(X_28,multiply(X_20,inverse(X_28))) ),
    inference(resolve,[$cnf( $equal(multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28)))),multiply(X_28,multiply(X_20,inverse(X_28)))) )],[refute_0_168,refute_0_169]) ).

cnf(refute_0_171,plain,
    inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))) = multiply(X_28,multiply(X_20,inverse(X_28))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_28,multiply(inverse(X_20),inverse(X_28)))),multiply(X_28,multiply(multiply(inverse(X_20),inverse(X_28)),multiply(inverse(X_20),commutator(X_20,X_28))))) )],[refute_0_126,refute_0_170]) ).

cnf(refute_0_172,plain,
    inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))) = multiply(Y,multiply(X_20,inverse(Y))),
    inference(subst,[],[refute_0_171:[bind(X_28,$fot(Y))]]) ).

cnf(refute_0_173,plain,
    multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))) = multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))),
    introduced(tautology,[refl,[$fot(multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))))]]) ).

cnf(refute_0_174,plain,
    ( multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))) != multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))
    | inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))) != multiply(Y,multiply(X_20,inverse(Y)))
    | multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))) = multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) ),[1,1],$fot(multiply(Y,multiply(X_20,inverse(Y))))]]) ).

cnf(refute_0_175,plain,
    ( inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))) != multiply(Y,multiply(X_20,inverse(Y)))
    | multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))) = multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y)))) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) )],[refute_0_173,refute_0_174]) ).

cnf(refute_0_176,plain,
    multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))) = multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y)))),
    inference(resolve,[$cnf( $equal(inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))),multiply(Y,multiply(X_20,inverse(Y)))) )],[refute_0_172,refute_0_175]) ).

cnf(refute_0_177,plain,
    multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) = multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))),
    introduced(tautology,[refl,[$fot(multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))))]]) ).

cnf(refute_0_178,plain,
    ( multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))) != multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))
    | multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) != multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))))
    | multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) = multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))),multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))))) ),[1,1],$fot(multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y)))))]]) ).

cnf(refute_0_179,plain,
    ( multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))) != multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))
    | multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) = multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))),multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))))) )],[refute_0_177,refute_0_178]) ).

cnf(refute_0_180,plain,
    multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) = multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y))))),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))) )],[refute_0_176,refute_0_179]) ).

cnf(refute_0_181,plain,
    ( multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) != multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y)))))
    | multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) != identity
    | multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))),identity) ),[0],$fot(multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))))]]) ).

cnf(refute_0_182,plain,
    ( multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))) != identity
    | multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))),multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y)))))) )],[refute_0_180,refute_0_181]) ).

cnf(refute_0_183,plain,
    multiply(inverse(X_20),multiply(commutator(X_20,Y),multiply(Y,multiply(X_20,inverse(Y))))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(commutator(X_20,Y),inverse(multiply(Y,multiply(inverse(X_20),inverse(Y)))))),identity) )],[refute_0_114,refute_0_182]) ).

cnf(refute_0_184,plain,
    multiply(inverse(X_31),multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30))))) = identity,
    inference(subst,[],[refute_0_183:[bind(Y,$fot(X_30)),bind(X_20,$fot(X_31))]]) ).

cnf(refute_0_185,plain,
    ( multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) != multiply(inverse(inverse(X_31)),multiply(inverse(X_31),multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30))))))
    | multiply(inverse(X_31),multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30))))) != identity
    | multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) = multiply(inverse(inverse(X_31)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))),multiply(inverse(inverse(X_31)),multiply(inverse(X_31),multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30))))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_186,plain,
    ( multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) != multiply(inverse(inverse(X_31)),multiply(inverse(X_31),multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30))))))
    | multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) = multiply(inverse(inverse(X_31)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_31),multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30))))),identity) )],[refute_0_184,refute_0_185]) ).

cnf(refute_0_187,plain,
    multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) = multiply(inverse(inverse(X_31)),identity),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))),multiply(inverse(inverse(X_31)),multiply(inverse(X_31),multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30))))))) )],[refute_0_101,refute_0_186]) ).

cnf(refute_0_188,plain,
    inverse(inverse(X_31)) = X_31,
    inference(subst,[],[refute_0_134:[bind(X_14,$fot(X_31))]]) ).

cnf(refute_0_189,plain,
    multiply(inverse(inverse(X_31)),identity) = inverse(inverse(X_31)),
    inference(subst,[],[right_identity:[bind(X,$fot(inverse(inverse(X_31))))]]) ).

cnf(refute_0_190,plain,
    ( multiply(inverse(inverse(X_31)),identity) != inverse(inverse(X_31))
    | inverse(inverse(X_31)) != X_31
    | multiply(inverse(inverse(X_31)),identity) = X_31 ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(inverse(inverse(X_31)),identity))),bind(Y0,$fot(inverse(inverse(X_31)))),bind(Z0,$fot(X_31))]]) ).

cnf(refute_0_191,plain,
    ( inverse(inverse(X_31)) != X_31
    | multiply(inverse(inverse(X_31)),identity) = X_31 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_31)),identity),inverse(inverse(X_31))) )],[refute_0_189,refute_0_190]) ).

cnf(refute_0_192,plain,
    multiply(inverse(inverse(X_31)),identity) = X_31,
    inference(resolve,[$cnf( $equal(inverse(inverse(X_31)),X_31) )],[refute_0_188,refute_0_191]) ).

cnf(refute_0_193,plain,
    ( multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) != multiply(inverse(inverse(X_31)),identity)
    | multiply(inverse(inverse(X_31)),identity) != X_31
    | multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) = X_31 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))),X_31) ),[0],$fot(multiply(inverse(inverse(X_31)),identity))]]) ).

cnf(refute_0_194,plain,
    ( multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) != multiply(inverse(inverse(X_31)),identity)
    | multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) = X_31 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_31)),identity),X_31) )],[refute_0_192,refute_0_193]) ).

cnf(refute_0_195,plain,
    multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) = X_31,
    inference(resolve,[$cnf( $equal(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))),multiply(inverse(inverse(X_31)),identity)) )],[refute_0_187,refute_0_194]) ).

cnf(refute_0_196,plain,
    ( multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))))) != inverse(commutator(X_31,X_30))
    | multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))) != X_31
    | multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) = inverse(commutator(X_31,X_30)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))))),inverse(commutator(X_31,X_30))) ),[0,1,0],$fot(X_31)]]) ).

cnf(refute_0_197,plain,
    ( multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))))) != inverse(commutator(X_31,X_30))
    | multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) = inverse(commutator(X_31,X_30)) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))),X_31) )],[refute_0_195,refute_0_196]) ).

cnf(refute_0_198,plain,
    multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) = inverse(commutator(X_31,X_30)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(multiply(commutator(X_31,X_30),multiply(X_30,multiply(X_31,inverse(X_30)))))),inverse(commutator(X_31,X_30))) )],[refute_0_100,refute_0_197]) ).

cnf(refute_0_199,plain,
    multiply(inverse(X_30),inverse(X_31)) = inverse(multiply(X_31,X_30)),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(X_30)),bind(X_34,$fot(X_31))]]) ).

cnf(refute_0_200,plain,
    multiply(X_31,multiply(inverse(X_30),inverse(X_31))) = multiply(X_31,multiply(inverse(X_30),inverse(X_31))),
    introduced(tautology,[refl,[$fot(multiply(X_31,multiply(inverse(X_30),inverse(X_31))))]]) ).

cnf(refute_0_201,plain,
    ( multiply(X_31,multiply(inverse(X_30),inverse(X_31))) != multiply(X_31,multiply(inverse(X_30),inverse(X_31)))
    | multiply(inverse(X_30),inverse(X_31)) != inverse(multiply(X_31,X_30))
    | multiply(X_31,multiply(inverse(X_30),inverse(X_31))) = multiply(X_31,inverse(multiply(X_31,X_30))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_31,multiply(inverse(X_30),inverse(X_31))),multiply(X_31,multiply(inverse(X_30),inverse(X_31)))) ),[1,1],$fot(inverse(multiply(X_31,X_30)))]]) ).

cnf(refute_0_202,plain,
    ( multiply(inverse(X_30),inverse(X_31)) != inverse(multiply(X_31,X_30))
    | multiply(X_31,multiply(inverse(X_30),inverse(X_31))) = multiply(X_31,inverse(multiply(X_31,X_30))) ),
    inference(resolve,[$cnf( $equal(multiply(X_31,multiply(inverse(X_30),inverse(X_31))),multiply(X_31,multiply(inverse(X_30),inverse(X_31)))) )],[refute_0_200,refute_0_201]) ).

cnf(refute_0_203,plain,
    multiply(X_31,multiply(inverse(X_30),inverse(X_31))) = multiply(X_31,inverse(multiply(X_31,X_30))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_30),inverse(X_31)),inverse(multiply(X_31,X_30))) )],[refute_0_199,refute_0_202]) ).

cnf(refute_0_204,plain,
    multiply(multiply(X_31,inverse(X_30)),inverse(X_31)) = multiply(X_31,multiply(inverse(X_30),inverse(X_31))),
    inference(subst,[],[associativity:[bind(X,$fot(X_31)),bind(Y,$fot(inverse(X_30))),bind(Z,$fot(inverse(X_31)))]]) ).

cnf(refute_0_205,plain,
    ( multiply(X_31,multiply(inverse(X_30),inverse(X_31))) != multiply(X_31,inverse(multiply(X_31,X_30)))
    | multiply(multiply(X_31,inverse(X_30)),inverse(X_31)) != multiply(X_31,multiply(inverse(X_30),inverse(X_31)))
    | multiply(multiply(X_31,inverse(X_30)),inverse(X_31)) = multiply(X_31,inverse(multiply(X_31,X_30))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(X_31,inverse(X_30)),inverse(X_31)))),bind(Y0,$fot(multiply(X_31,multiply(inverse(X_30),inverse(X_31))))),bind(Z0,$fot(multiply(X_31,inverse(multiply(X_31,X_30)))))]]) ).

cnf(refute_0_206,plain,
    ( multiply(X_31,multiply(inverse(X_30),inverse(X_31))) != multiply(X_31,inverse(multiply(X_31,X_30)))
    | multiply(multiply(X_31,inverse(X_30)),inverse(X_31)) = multiply(X_31,inverse(multiply(X_31,X_30))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_31,inverse(X_30)),inverse(X_31)),multiply(X_31,multiply(inverse(X_30),inverse(X_31)))) )],[refute_0_204,refute_0_205]) ).

cnf(refute_0_207,plain,
    multiply(multiply(X_31,inverse(X_30)),inverse(X_31)) = multiply(X_31,inverse(multiply(X_31,X_30))),
    inference(resolve,[$cnf( $equal(multiply(X_31,multiply(inverse(X_30),inverse(X_31))),multiply(X_31,inverse(multiply(X_31,X_30)))) )],[refute_0_203,refute_0_206]) ).

cnf(refute_0_208,plain,
    multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))) = multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))),
    introduced(tautology,[refl,[$fot(multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))))]]) ).

cnf(refute_0_209,plain,
    ( multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))) != multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31)))
    | multiply(multiply(X_31,inverse(X_30)),inverse(X_31)) != multiply(X_31,inverse(multiply(X_31,X_30)))
    | multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))) = multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))),multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31)))) ),[1,1],$fot(multiply(X_31,inverse(multiply(X_31,X_30))))]]) ).

cnf(refute_0_210,plain,
    ( multiply(multiply(X_31,inverse(X_30)),inverse(X_31)) != multiply(X_31,inverse(multiply(X_31,X_30)))
    | multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))) = multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))),multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31)))) )],[refute_0_208,refute_0_209]) ).

cnf(refute_0_211,plain,
    multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))) = multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_31,inverse(X_30)),inverse(X_31)),multiply(X_31,inverse(multiply(X_31,X_30)))) )],[refute_0_207,refute_0_210]) ).

cnf(refute_0_212,plain,
    multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) = multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))),
    inference(subst,[],[associativity:[bind(X,$fot(X_30)),bind(Y,$fot(multiply(X_31,inverse(X_30)))),bind(Z,$fot(inverse(X_31)))]]) ).

cnf(refute_0_213,plain,
    ( multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))) != multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30))))
    | multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) != multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31)))
    | multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) = multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)))),bind(Y0,$fot(multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))))),bind(Z0,$fot(multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30))))))]]) ).

cnf(refute_0_214,plain,
    ( multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))) != multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30))))
    | multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) = multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)),multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31)))) )],[refute_0_212,refute_0_213]) ).

cnf(refute_0_215,plain,
    multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) = multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))),
    inference(resolve,[$cnf( $equal(multiply(X_30,multiply(multiply(X_31,inverse(X_30)),inverse(X_31))),multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30))))) )],[refute_0_211,refute_0_214]) ).

cnf(refute_0_216,plain,
    ( multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) != multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30))))
    | multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) != inverse(commutator(X_31,X_30))
    | multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) = inverse(commutator(X_31,X_30)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)),inverse(commutator(X_31,X_30))) ),[0],$fot(multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))))]]) ).

cnf(refute_0_217,plain,
    ( multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)) != inverse(commutator(X_31,X_30))
    | multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) = inverse(commutator(X_31,X_30)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)),multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30))))) )],[refute_0_215,refute_0_216]) ).

cnf(refute_0_218,plain,
    multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) = inverse(commutator(X_31,X_30)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_30,multiply(X_31,inverse(X_30))),inverse(X_31)),inverse(commutator(X_31,X_30))) )],[refute_0_198,refute_0_217]) ).

cnf(refute_0_219,plain,
    multiply(X,multiply(Y,inverse(multiply(Y,X)))) = inverse(commutator(Y,X)),
    inference(subst,[],[refute_0_218:[bind(X_30,$fot(X)),bind(X_31,$fot(Y))]]) ).

cnf(refute_0_220,plain,
    multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(X)),bind(X_34,$fot(Y))]]) ).

cnf(refute_0_221,plain,
    multiply(Y,multiply(inverse(X),inverse(Y))) = multiply(Y,multiply(inverse(X),inverse(Y))),
    introduced(tautology,[refl,[$fot(multiply(Y,multiply(inverse(X),inverse(Y))))]]) ).

cnf(refute_0_222,plain,
    ( multiply(Y,multiply(inverse(X),inverse(Y))) != multiply(Y,multiply(inverse(X),inverse(Y)))
    | multiply(inverse(X),inverse(Y)) != inverse(multiply(Y,X))
    | multiply(Y,multiply(inverse(X),inverse(Y))) = multiply(Y,inverse(multiply(Y,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(Y,multiply(inverse(X),inverse(Y))),multiply(Y,multiply(inverse(X),inverse(Y)))) ),[1,1],$fot(inverse(multiply(Y,X)))]]) ).

cnf(refute_0_223,plain,
    ( multiply(inverse(X),inverse(Y)) != inverse(multiply(Y,X))
    | multiply(Y,multiply(inverse(X),inverse(Y))) = multiply(Y,inverse(multiply(Y,X))) ),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(X),inverse(Y))),multiply(Y,multiply(inverse(X),inverse(Y)))) )],[refute_0_221,refute_0_222]) ).

cnf(refute_0_224,plain,
    multiply(Y,multiply(inverse(X),inverse(Y))) = multiply(Y,inverse(multiply(Y,X))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),inverse(Y)),inverse(multiply(Y,X))) )],[refute_0_220,refute_0_223]) ).

cnf(refute_0_225,plain,
    multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),
    introduced(tautology,[refl,[$fot(multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))))]]) ).

cnf(refute_0_226,plain,
    ( multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) != multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))))
    | multiply(Y,multiply(inverse(X),inverse(Y))) != multiply(Y,inverse(multiply(Y,X)))
    | multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) = multiply(X,multiply(Y,inverse(multiply(Y,X)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))))) ),[1,1],$fot(multiply(Y,inverse(multiply(Y,X))))]]) ).

cnf(refute_0_227,plain,
    ( multiply(Y,multiply(inverse(X),inverse(Y))) != multiply(Y,inverse(multiply(Y,X)))
    | multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) = multiply(X,multiply(Y,inverse(multiply(Y,X)))) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))))) )],[refute_0_225,refute_0_226]) ).

cnf(refute_0_228,plain,
    multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) = multiply(X,multiply(Y,inverse(multiply(Y,X)))),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(X),inverse(Y))),multiply(Y,inverse(multiply(Y,X)))) )],[refute_0_224,refute_0_227]) ).

cnf(refute_0_229,plain,
    ( multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) != multiply(X,multiply(Y,inverse(multiply(Y,X))))
    | multiply(X,multiply(Y,inverse(multiply(Y,X)))) != inverse(commutator(Y,X))
    | multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) = inverse(commutator(Y,X)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))))),bind(Y0,$fot(multiply(X,multiply(Y,inverse(multiply(Y,X)))))),bind(Z0,$fot(inverse(commutator(Y,X))))]]) ).

cnf(refute_0_230,plain,
    ( multiply(X,multiply(Y,inverse(multiply(Y,X)))) != inverse(commutator(Y,X))
    | multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) = inverse(commutator(Y,X)) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),multiply(X,multiply(Y,inverse(multiply(Y,X))))) )],[refute_0_228,refute_0_229]) ).

cnf(refute_0_231,plain,
    multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) = inverse(commutator(Y,X)),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,inverse(multiply(Y,X)))),inverse(commutator(Y,X))) )],[refute_0_219,refute_0_230]) ).

cnf(refute_0_232,plain,
    ( multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) != inverse(commutator(Y,X))
    | commutator(X,Y) != multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))))
    | commutator(X,Y) = inverse(commutator(Y,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X,Y),multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))))) ),[1],$fot(inverse(commutator(Y,X)))]]) ).

cnf(refute_0_233,plain,
    ( commutator(X,Y) != multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))))
    | commutator(X,Y) = inverse(commutator(Y,X)) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),inverse(commutator(Y,X))) )],[refute_0_231,refute_0_232]) ).

cnf(refute_0_234,plain,
    commutator(X,Y) = inverse(commutator(Y,X)),
    inference(resolve,[$cnf( $equal(commutator(X,Y),multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))))) )],[commutator,refute_0_233]) ).

cnf(refute_0_235,plain,
    ( commutator(X,Y) != inverse(commutator(Y,X))
    | inverse(commutator(Y,X)) = commutator(X,Y) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(X,Y))),bind(Y0,$fot(inverse(commutator(Y,X))))]]) ).

cnf(refute_0_236,plain,
    inverse(commutator(Y,X)) = commutator(X,Y),
    inference(resolve,[$cnf( $equal(commutator(X,Y),inverse(commutator(Y,X))) )],[refute_0_234,refute_0_235]) ).

cnf(refute_0_237,plain,
    inverse(commutator(Y,inverse(X_62))) = commutator(inverse(X_62),Y),
    inference(subst,[],[refute_0_236:[bind(X,$fot(inverse(X_62)))]]) ).

cnf(refute_0_238,plain,
    commutator(X,inverse(X_17)) = multiply(X,multiply(inverse(X_17),multiply(inverse(X),inverse(inverse(X_17))))),
    inference(subst,[],[commutator:[bind(Y,$fot(inverse(X_17)))]]) ).

cnf(refute_0_239,plain,
    inverse(inverse(X_17)) = X_17,
    inference(subst,[],[refute_0_134:[bind(X_14,$fot(X_17))]]) ).

cnf(refute_0_240,plain,
    ( commutator(X,inverse(X_17)) != multiply(X,multiply(inverse(X_17),multiply(inverse(X),inverse(inverse(X_17)))))
    | inverse(inverse(X_17)) != X_17
    | commutator(X,inverse(X_17)) = multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X,inverse(X_17)),multiply(X,multiply(inverse(X_17),multiply(inverse(X),inverse(inverse(X_17)))))) ),[1,1,1,1],$fot(X_17)]]) ).

cnf(refute_0_241,plain,
    ( commutator(X,inverse(X_17)) != multiply(X,multiply(inverse(X_17),multiply(inverse(X),inverse(inverse(X_17)))))
    | commutator(X,inverse(X_17)) = multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_17)),X_17) )],[refute_0_239,refute_0_240]) ).

cnf(refute_0_242,plain,
    commutator(X,inverse(X_17)) = multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))),
    inference(resolve,[$cnf( $equal(commutator(X,inverse(X_17)),multiply(X,multiply(inverse(X_17),multiply(inverse(X),inverse(inverse(X_17)))))) )],[refute_0_238,refute_0_241]) ).

cnf(refute_0_243,plain,
    multiply(multiply(inverse(X_38),inverse(X_39)),Z) = multiply(inverse(X_38),multiply(inverse(X_39),Z)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_38))),bind(Y,$fot(inverse(X_39)))]]) ).

cnf(refute_0_244,plain,
    inverse(multiply(X_39,X_38)) = multiply(inverse(X_38),inverse(X_39)),
    inference(subst,[],[refute_0_70:[bind(X_12,$fot(X_38)),bind(X_34,$fot(X_39))]]) ).

cnf(refute_0_245,plain,
    ( inverse(multiply(X_39,X_38)) != multiply(inverse(X_38),inverse(X_39))
    | multiply(inverse(X_38),inverse(X_39)) = inverse(multiply(X_39,X_38)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X_39,X_38)))),bind(Y0,$fot(multiply(inverse(X_38),inverse(X_39))))]]) ).

cnf(refute_0_246,plain,
    multiply(inverse(X_38),inverse(X_39)) = inverse(multiply(X_39,X_38)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_39,X_38)),multiply(inverse(X_38),inverse(X_39))) )],[refute_0_244,refute_0_245]) ).

cnf(refute_0_247,plain,
    ( multiply(multiply(inverse(X_38),inverse(X_39)),Z) != multiply(inverse(X_38),multiply(inverse(X_39),Z))
    | multiply(inverse(X_38),inverse(X_39)) != inverse(multiply(X_39,X_38))
    | multiply(inverse(multiply(X_39,X_38)),Z) = multiply(inverse(X_38),multiply(inverse(X_39),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_38),inverse(X_39)),Z),multiply(inverse(X_38),multiply(inverse(X_39),Z))) ),[0,0],$fot(inverse(multiply(X_39,X_38)))]]) ).

cnf(refute_0_248,plain,
    ( multiply(multiply(inverse(X_38),inverse(X_39)),Z) != multiply(inverse(X_38),multiply(inverse(X_39),Z))
    | multiply(inverse(multiply(X_39,X_38)),Z) = multiply(inverse(X_38),multiply(inverse(X_39),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_38),inverse(X_39)),inverse(multiply(X_39,X_38))) )],[refute_0_246,refute_0_247]) ).

cnf(refute_0_249,plain,
    multiply(inverse(multiply(X_39,X_38)),Z) = multiply(inverse(X_38),multiply(inverse(X_39),Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_38),inverse(X_39)),Z),multiply(inverse(X_38),multiply(inverse(X_39),Z))) )],[refute_0_243,refute_0_248]) ).

cnf(refute_0_250,plain,
    ( multiply(inverse(multiply(X_39,X_38)),Z) != multiply(inverse(X_38),multiply(inverse(X_39),Z))
    | multiply(inverse(X_38),multiply(inverse(X_39),Z)) = multiply(inverse(multiply(X_39,X_38)),Z) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(inverse(multiply(X_39,X_38)),Z))),bind(Y0,$fot(multiply(inverse(X_38),multiply(inverse(X_39),Z))))]]) ).

cnf(refute_0_251,plain,
    multiply(inverse(X_38),multiply(inverse(X_39),Z)) = multiply(inverse(multiply(X_39,X_38)),Z),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_39,X_38)),Z),multiply(inverse(X_38),multiply(inverse(X_39),Z))) )],[refute_0_249,refute_0_250]) ).

cnf(refute_0_252,plain,
    multiply(inverse(X_17),multiply(inverse(X),X_17)) = multiply(inverse(multiply(X,X_17)),X_17),
    inference(subst,[],[refute_0_251:[bind(Z,$fot(X_17)),bind(X_38,$fot(X_17)),bind(X_39,$fot(X))]]) ).

cnf(refute_0_253,plain,
    multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))) = multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))),
    introduced(tautology,[refl,[$fot(multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))))]]) ).

cnf(refute_0_254,plain,
    ( multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))) != multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17)))
    | multiply(inverse(X_17),multiply(inverse(X),X_17)) != multiply(inverse(multiply(X,X_17)),X_17)
    | multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))) = multiply(X,multiply(inverse(multiply(X,X_17)),X_17)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))),multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17)))) ),[1,1],$fot(multiply(inverse(multiply(X,X_17)),X_17))]]) ).

cnf(refute_0_255,plain,
    ( multiply(inverse(X_17),multiply(inverse(X),X_17)) != multiply(inverse(multiply(X,X_17)),X_17)
    | multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))) = multiply(X,multiply(inverse(multiply(X,X_17)),X_17)) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))),multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17)))) )],[refute_0_253,refute_0_254]) ).

cnf(refute_0_256,plain,
    multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))) = multiply(X,multiply(inverse(multiply(X,X_17)),X_17)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_17),multiply(inverse(X),X_17)),multiply(inverse(multiply(X,X_17)),X_17)) )],[refute_0_252,refute_0_255]) ).

cnf(refute_0_257,plain,
    ( multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))) != multiply(X,multiply(inverse(multiply(X,X_17)),X_17))
    | commutator(X,inverse(X_17)) != multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17)))
    | commutator(X,inverse(X_17)) = multiply(X,multiply(inverse(multiply(X,X_17)),X_17)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X,inverse(X_17)),multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17)))) ),[1],$fot(multiply(X,multiply(inverse(multiply(X,X_17)),X_17)))]]) ).

cnf(refute_0_258,plain,
    ( commutator(X,inverse(X_17)) != multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17)))
    | commutator(X,inverse(X_17)) = multiply(X,multiply(inverse(multiply(X,X_17)),X_17)) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17))),multiply(X,multiply(inverse(multiply(X,X_17)),X_17))) )],[refute_0_256,refute_0_257]) ).

cnf(refute_0_259,plain,
    commutator(X,inverse(X_17)) = multiply(X,multiply(inverse(multiply(X,X_17)),X_17)),
    inference(resolve,[$cnf( $equal(commutator(X,inverse(X_17)),multiply(X,multiply(inverse(X_17),multiply(inverse(X),X_17)))) )],[refute_0_242,refute_0_258]) ).

cnf(refute_0_260,plain,
    ( commutator(X,inverse(X_17)) != multiply(X,multiply(inverse(multiply(X,X_17)),X_17))
    | multiply(X,multiply(inverse(multiply(X,X_17)),X_17)) = commutator(X,inverse(X_17)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(X,inverse(X_17)))),bind(Y0,$fot(multiply(X,multiply(inverse(multiply(X,X_17)),X_17))))]]) ).

cnf(refute_0_261,plain,
    multiply(X,multiply(inverse(multiply(X,X_17)),X_17)) = commutator(X,inverse(X_17)),
    inference(resolve,[$cnf( $equal(commutator(X,inverse(X_17)),multiply(X,multiply(inverse(multiply(X,X_17)),X_17))) )],[refute_0_259,refute_0_260]) ).

cnf(refute_0_262,plain,
    multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62)) = commutator(Y,inverse(X_62)),
    inference(subst,[],[refute_0_261:[bind(X,$fot(Y)),bind(X_17,$fot(X_62))]]) ).

cnf(refute_0_263,plain,
    multiply(X_29,multiply(X_12,X_29)) = multiply(inverse(X_12),multiply(X_12,multiply(X_29,multiply(X_12,X_29)))),
    inference(subst,[],[refute_0_51:[bind(X_13,$fot(multiply(X_29,multiply(X_12,X_29))))]]) ).

cnf(refute_0_264,plain,
    inverse(multiply(X_12,X_29)) = multiply(X_12,multiply(X_29,multiply(X_12,X_29))),
    inference(subst,[],[refute_0_121:[bind(X,$fot(X_12)),bind(Y,$fot(X_29))]]) ).

cnf(refute_0_265,plain,
    ( inverse(multiply(X_12,X_29)) != multiply(X_12,multiply(X_29,multiply(X_12,X_29)))
    | multiply(X_12,multiply(X_29,multiply(X_12,X_29))) = inverse(multiply(X_12,X_29)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X_12,X_29)))),bind(Y0,$fot(multiply(X_12,multiply(X_29,multiply(X_12,X_29)))))]]) ).

cnf(refute_0_266,plain,
    multiply(X_12,multiply(X_29,multiply(X_12,X_29))) = inverse(multiply(X_12,X_29)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_12,X_29)),multiply(X_12,multiply(X_29,multiply(X_12,X_29)))) )],[refute_0_264,refute_0_265]) ).

cnf(refute_0_267,plain,
    ( multiply(X_12,multiply(X_29,multiply(X_12,X_29))) != inverse(multiply(X_12,X_29))
    | multiply(X_29,multiply(X_12,X_29)) != multiply(inverse(X_12),multiply(X_12,multiply(X_29,multiply(X_12,X_29))))
    | multiply(X_29,multiply(X_12,X_29)) = multiply(inverse(X_12),inverse(multiply(X_12,X_29))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_29,multiply(X_12,X_29)),multiply(inverse(X_12),multiply(X_12,multiply(X_29,multiply(X_12,X_29))))) ),[1,1],$fot(inverse(multiply(X_12,X_29)))]]) ).

cnf(refute_0_268,plain,
    ( multiply(X_29,multiply(X_12,X_29)) != multiply(inverse(X_12),multiply(X_12,multiply(X_29,multiply(X_12,X_29))))
    | multiply(X_29,multiply(X_12,X_29)) = multiply(inverse(X_12),inverse(multiply(X_12,X_29))) ),
    inference(resolve,[$cnf( $equal(multiply(X_12,multiply(X_29,multiply(X_12,X_29))),inverse(multiply(X_12,X_29))) )],[refute_0_266,refute_0_267]) ).

cnf(refute_0_269,plain,
    multiply(X_29,multiply(X_12,X_29)) = multiply(inverse(X_12),inverse(multiply(X_12,X_29))),
    inference(resolve,[$cnf( $equal(multiply(X_29,multiply(X_12,X_29)),multiply(inverse(X_12),multiply(X_12,multiply(X_29,multiply(X_12,X_29))))) )],[refute_0_263,refute_0_268]) ).

cnf(refute_0_270,plain,
    multiply(multiply(X_12,X_29),X_12) = multiply(X_12,multiply(X_29,X_12)),
    inference(subst,[],[associativity:[bind(X,$fot(X_12)),bind(Y,$fot(X_29)),bind(Z,$fot(X_12))]]) ).

cnf(refute_0_271,plain,
    inverse(multiply(multiply(X_12,X_29),X_12)) = inverse(multiply(multiply(X_12,X_29),X_12)),
    introduced(tautology,[refl,[$fot(inverse(multiply(multiply(X_12,X_29),X_12)))]]) ).

cnf(refute_0_272,plain,
    ( multiply(multiply(X_12,X_29),X_12) != multiply(X_12,multiply(X_29,X_12))
    | inverse(multiply(multiply(X_12,X_29),X_12)) != inverse(multiply(multiply(X_12,X_29),X_12))
    | inverse(multiply(multiply(X_12,X_29),X_12)) = inverse(multiply(X_12,multiply(X_29,X_12))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(X_12,X_29),X_12)),inverse(multiply(multiply(X_12,X_29),X_12))) ),[1,0],$fot(multiply(X_12,multiply(X_29,X_12)))]]) ).

cnf(refute_0_273,plain,
    ( multiply(multiply(X_12,X_29),X_12) != multiply(X_12,multiply(X_29,X_12))
    | inverse(multiply(multiply(X_12,X_29),X_12)) = inverse(multiply(X_12,multiply(X_29,X_12))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_12,X_29),X_12)),inverse(multiply(multiply(X_12,X_29),X_12))) )],[refute_0_271,refute_0_272]) ).

cnf(refute_0_274,plain,
    inverse(multiply(multiply(X_12,X_29),X_12)) = inverse(multiply(X_12,multiply(X_29,X_12))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_12,X_29),X_12),multiply(X_12,multiply(X_29,X_12))) )],[refute_0_270,refute_0_273]) ).

cnf(refute_0_275,plain,
    multiply(inverse(X_12),inverse(multiply(X_12,X_29))) = inverse(multiply(multiply(X_12,X_29),X_12)),
    inference(subst,[],[refute_0_72:[bind(X_34,$fot(multiply(X_12,X_29)))]]) ).

cnf(refute_0_276,plain,
    ( multiply(inverse(X_12),inverse(multiply(X_12,X_29))) != inverse(multiply(multiply(X_12,X_29),X_12))
    | inverse(multiply(multiply(X_12,X_29),X_12)) != inverse(multiply(X_12,multiply(X_29,X_12)))
    | multiply(inverse(X_12),inverse(multiply(X_12,X_29))) = inverse(multiply(X_12,multiply(X_29,X_12))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(inverse(X_12),inverse(multiply(X_12,X_29))))),bind(Y0,$fot(inverse(multiply(multiply(X_12,X_29),X_12)))),bind(Z0,$fot(inverse(multiply(X_12,multiply(X_29,X_12)))))]]) ).

cnf(refute_0_277,plain,
    ( inverse(multiply(multiply(X_12,X_29),X_12)) != inverse(multiply(X_12,multiply(X_29,X_12)))
    | multiply(inverse(X_12),inverse(multiply(X_12,X_29))) = inverse(multiply(X_12,multiply(X_29,X_12))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_12),inverse(multiply(X_12,X_29))),inverse(multiply(multiply(X_12,X_29),X_12))) )],[refute_0_275,refute_0_276]) ).

cnf(refute_0_278,plain,
    multiply(inverse(X_12),inverse(multiply(X_12,X_29))) = inverse(multiply(X_12,multiply(X_29,X_12))),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_12,X_29),X_12)),inverse(multiply(X_12,multiply(X_29,X_12)))) )],[refute_0_274,refute_0_277]) ).

cnf(refute_0_279,plain,
    ( multiply(X_29,multiply(X_12,X_29)) != multiply(inverse(X_12),inverse(multiply(X_12,X_29)))
    | multiply(inverse(X_12),inverse(multiply(X_12,X_29))) != inverse(multiply(X_12,multiply(X_29,X_12)))
    | multiply(X_29,multiply(X_12,X_29)) = inverse(multiply(X_12,multiply(X_29,X_12))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_29,multiply(X_12,X_29)),inverse(multiply(X_12,multiply(X_29,X_12)))) ),[0],$fot(multiply(inverse(X_12),inverse(multiply(X_12,X_29))))]]) ).

cnf(refute_0_280,plain,
    ( multiply(X_29,multiply(X_12,X_29)) != multiply(inverse(X_12),inverse(multiply(X_12,X_29)))
    | multiply(X_29,multiply(X_12,X_29)) = inverse(multiply(X_12,multiply(X_29,X_12))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_12),inverse(multiply(X_12,X_29))),inverse(multiply(X_12,multiply(X_29,X_12)))) )],[refute_0_278,refute_0_279]) ).

cnf(refute_0_281,plain,
    multiply(X_29,multiply(X_12,X_29)) = inverse(multiply(X_12,multiply(X_29,X_12))),
    inference(resolve,[$cnf( $equal(multiply(X_29,multiply(X_12,X_29)),multiply(inverse(X_12),inverse(multiply(X_12,X_29)))) )],[refute_0_269,refute_0_280]) ).

cnf(refute_0_282,plain,
    multiply(multiply(X_54,Z),multiply(X_54,multiply(X_54,Z))) = inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))),
    inference(subst,[],[refute_0_281:[bind(X_12,$fot(X_54)),bind(X_29,$fot(multiply(X_54,Z)))]]) ).

cnf(refute_0_283,plain,
    multiply(inverse(X_54),Z) = multiply(X_54,multiply(X_54,Z)),
    inference(subst,[],[refute_0_32:[bind(Y,$fot(X_54))]]) ).

cnf(refute_0_284,plain,
    ( multiply(inverse(X_54),Z) != multiply(X_54,multiply(X_54,Z))
    | multiply(X_54,multiply(X_54,Z)) = multiply(inverse(X_54),Z) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(inverse(X_54),Z))),bind(Y0,$fot(multiply(X_54,multiply(X_54,Z))))]]) ).

cnf(refute_0_285,plain,
    multiply(X_54,multiply(X_54,Z)) = multiply(inverse(X_54),Z),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_54),Z),multiply(X_54,multiply(X_54,Z))) )],[refute_0_283,refute_0_284]) ).

cnf(refute_0_286,plain,
    ( multiply(X_54,multiply(X_54,Z)) != multiply(inverse(X_54),Z)
    | multiply(multiply(X_54,Z),multiply(X_54,multiply(X_54,Z))) != inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))
    | multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)) = inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_54,Z),multiply(X_54,multiply(X_54,Z))),inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))) ),[0,1],$fot(multiply(inverse(X_54),Z))]]) ).

cnf(refute_0_287,plain,
    ( multiply(multiply(X_54,Z),multiply(X_54,multiply(X_54,Z))) != inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))
    | multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)) = inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) ),
    inference(resolve,[$cnf( $equal(multiply(X_54,multiply(X_54,Z)),multiply(inverse(X_54),Z)) )],[refute_0_285,refute_0_286]) ).

cnf(refute_0_288,plain,
    multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)) = inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_54,Z),multiply(X_54,multiply(X_54,Z))),inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))) )],[refute_0_282,refute_0_287]) ).

cnf(refute_0_289,plain,
    multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)) = multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))),
    inference(subst,[],[associativity:[bind(X,$fot(X_54)),bind(Y,$fot(Z)),bind(Z,$fot(multiply(inverse(X_54),Z)))]]) ).

cnf(refute_0_290,plain,
    ( multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)) != multiply(X_54,multiply(Z,multiply(inverse(X_54),Z)))
    | multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)) != inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))
    | multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))) = inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)),inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))) ),[0],$fot(multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))))]]) ).

cnf(refute_0_291,plain,
    ( multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)) != inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))
    | multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))) = inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)),multiply(X_54,multiply(Z,multiply(inverse(X_54),Z)))) )],[refute_0_289,refute_0_290]) ).

cnf(refute_0_292,plain,
    inverse(multiply(inverse(X_14),X_38)) = multiply(inverse(X_38),inverse(inverse(X_14))),
    inference(subst,[],[refute_0_70:[bind(X_12,$fot(X_38)),bind(X_34,$fot(inverse(X_14)))]]) ).

cnf(refute_0_293,plain,
    ( inverse(multiply(inverse(X_14),X_38)) != multiply(inverse(X_38),inverse(inverse(X_14)))
    | inverse(inverse(X_14)) != X_14
    | inverse(multiply(inverse(X_14),X_38)) = multiply(inverse(X_38),X_14) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_14),X_38)),multiply(inverse(X_38),inverse(inverse(X_14)))) ),[1,1],$fot(X_14)]]) ).

cnf(refute_0_294,plain,
    ( inverse(multiply(inverse(X_14),X_38)) != multiply(inverse(X_38),inverse(inverse(X_14)))
    | inverse(multiply(inverse(X_14),X_38)) = multiply(inverse(X_38),X_14) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_14)),X_14) )],[refute_0_134,refute_0_293]) ).

cnf(refute_0_295,plain,
    inverse(multiply(inverse(X_14),X_38)) = multiply(inverse(X_38),X_14),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_14),X_38)),multiply(inverse(X_38),inverse(inverse(X_14)))) )],[refute_0_292,refute_0_294]) ).

cnf(refute_0_296,plain,
    inverse(multiply(inverse(X_54),multiply(Z,X_54))) = multiply(inverse(multiply(Z,X_54)),X_54),
    inference(subst,[],[refute_0_295:[bind(X_14,$fot(X_54)),bind(X_38,$fot(multiply(Z,X_54)))]]) ).

cnf(refute_0_297,plain,
    multiply(X_54,multiply(X_54,multiply(Z,X_54))) = multiply(inverse(X_54),multiply(Z,X_54)),
    inference(subst,[],[refute_0_141:[bind(Y,$fot(X_54)),bind(Z,$fot(multiply(Z,X_54)))]]) ).

cnf(refute_0_298,plain,
    multiply(multiply(X_54,Z),X_54) = multiply(X_54,multiply(Z,X_54)),
    inference(subst,[],[associativity:[bind(X,$fot(X_54)),bind(Y,$fot(Z)),bind(Z,$fot(X_54))]]) ).

cnf(refute_0_299,plain,
    multiply(X_54,multiply(multiply(X_54,Z),X_54)) = multiply(X_54,multiply(multiply(X_54,Z),X_54)),
    introduced(tautology,[refl,[$fot(multiply(X_54,multiply(multiply(X_54,Z),X_54)))]]) ).

cnf(refute_0_300,plain,
    ( multiply(X_54,multiply(multiply(X_54,Z),X_54)) != multiply(X_54,multiply(multiply(X_54,Z),X_54))
    | multiply(multiply(X_54,Z),X_54) != multiply(X_54,multiply(Z,X_54))
    | multiply(X_54,multiply(multiply(X_54,Z),X_54)) = multiply(X_54,multiply(X_54,multiply(Z,X_54))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_54,multiply(multiply(X_54,Z),X_54)),multiply(X_54,multiply(multiply(X_54,Z),X_54))) ),[1,1],$fot(multiply(X_54,multiply(Z,X_54)))]]) ).

cnf(refute_0_301,plain,
    ( multiply(multiply(X_54,Z),X_54) != multiply(X_54,multiply(Z,X_54))
    | multiply(X_54,multiply(multiply(X_54,Z),X_54)) = multiply(X_54,multiply(X_54,multiply(Z,X_54))) ),
    inference(resolve,[$cnf( $equal(multiply(X_54,multiply(multiply(X_54,Z),X_54)),multiply(X_54,multiply(multiply(X_54,Z),X_54))) )],[refute_0_299,refute_0_300]) ).

cnf(refute_0_302,plain,
    multiply(X_54,multiply(multiply(X_54,Z),X_54)) = multiply(X_54,multiply(X_54,multiply(Z,X_54))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_54,Z),X_54),multiply(X_54,multiply(Z,X_54))) )],[refute_0_298,refute_0_301]) ).

cnf(refute_0_303,plain,
    ( multiply(X_54,multiply(X_54,multiply(Z,X_54))) != multiply(inverse(X_54),multiply(Z,X_54))
    | multiply(X_54,multiply(multiply(X_54,Z),X_54)) != multiply(X_54,multiply(X_54,multiply(Z,X_54)))
    | multiply(X_54,multiply(multiply(X_54,Z),X_54)) = multiply(inverse(X_54),multiply(Z,X_54)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(X_54,multiply(multiply(X_54,Z),X_54)))),bind(Y0,$fot(multiply(X_54,multiply(X_54,multiply(Z,X_54))))),bind(Z0,$fot(multiply(inverse(X_54),multiply(Z,X_54))))]]) ).

cnf(refute_0_304,plain,
    ( multiply(X_54,multiply(X_54,multiply(Z,X_54))) != multiply(inverse(X_54),multiply(Z,X_54))
    | multiply(X_54,multiply(multiply(X_54,Z),X_54)) = multiply(inverse(X_54),multiply(Z,X_54)) ),
    inference(resolve,[$cnf( $equal(multiply(X_54,multiply(multiply(X_54,Z),X_54)),multiply(X_54,multiply(X_54,multiply(Z,X_54)))) )],[refute_0_302,refute_0_303]) ).

cnf(refute_0_305,plain,
    multiply(X_54,multiply(multiply(X_54,Z),X_54)) = multiply(inverse(X_54),multiply(Z,X_54)),
    inference(resolve,[$cnf( $equal(multiply(X_54,multiply(X_54,multiply(Z,X_54))),multiply(inverse(X_54),multiply(Z,X_54))) )],[refute_0_297,refute_0_304]) ).

cnf(refute_0_306,plain,
    inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) = inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))),
    introduced(tautology,[refl,[$fot(inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))))]]) ).

cnf(refute_0_307,plain,
    ( multiply(X_54,multiply(multiply(X_54,Z),X_54)) != multiply(inverse(X_54),multiply(Z,X_54))
    | inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) != inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))
    | inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) = inverse(multiply(inverse(X_54),multiply(Z,X_54))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))),inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))) ),[1,0],$fot(multiply(inverse(X_54),multiply(Z,X_54)))]]) ).

cnf(refute_0_308,plain,
    ( multiply(X_54,multiply(multiply(X_54,Z),X_54)) != multiply(inverse(X_54),multiply(Z,X_54))
    | inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) = inverse(multiply(inverse(X_54),multiply(Z,X_54))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))),inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))) )],[refute_0_306,refute_0_307]) ).

cnf(refute_0_309,plain,
    inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) = inverse(multiply(inverse(X_54),multiply(Z,X_54))),
    inference(resolve,[$cnf( $equal(multiply(X_54,multiply(multiply(X_54,Z),X_54)),multiply(inverse(X_54),multiply(Z,X_54))) )],[refute_0_305,refute_0_308]) ).

cnf(refute_0_310,plain,
    ( inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) != inverse(multiply(inverse(X_54),multiply(Z,X_54)))
    | inverse(multiply(inverse(X_54),multiply(Z,X_54))) != multiply(inverse(multiply(Z,X_54)),X_54)
    | inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) = multiply(inverse(multiply(Z,X_54)),X_54) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))))),bind(Y0,$fot(inverse(multiply(inverse(X_54),multiply(Z,X_54))))),bind(Z0,$fot(multiply(inverse(multiply(Z,X_54)),X_54)))]]) ).

cnf(refute_0_311,plain,
    ( inverse(multiply(inverse(X_54),multiply(Z,X_54))) != multiply(inverse(multiply(Z,X_54)),X_54)
    | inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) = multiply(inverse(multiply(Z,X_54)),X_54) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))),inverse(multiply(inverse(X_54),multiply(Z,X_54)))) )],[refute_0_309,refute_0_310]) ).

cnf(refute_0_312,plain,
    inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) = multiply(inverse(multiply(Z,X_54)),X_54),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_54),multiply(Z,X_54))),multiply(inverse(multiply(Z,X_54)),X_54)) )],[refute_0_296,refute_0_311]) ).

cnf(refute_0_313,plain,
    ( multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))) != inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))
    | inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))) != multiply(inverse(multiply(Z,X_54)),X_54)
    | multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))) = multiply(inverse(multiply(Z,X_54)),X_54) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))),multiply(inverse(multiply(Z,X_54)),X_54)) ),[0],$fot(inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))))]]) ).

cnf(refute_0_314,plain,
    ( multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))) != inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))
    | multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))) = multiply(inverse(multiply(Z,X_54)),X_54) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54))),multiply(inverse(multiply(Z,X_54)),X_54)) )],[refute_0_312,refute_0_313]) ).

cnf(refute_0_315,plain,
    ( multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)) != inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))
    | multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))) = multiply(inverse(multiply(Z,X_54)),X_54) ),
    inference(resolve,[$cnf( $equal(multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))),inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))) )],[refute_0_291,refute_0_314]) ).

cnf(refute_0_316,plain,
    multiply(X_54,multiply(Z,multiply(inverse(X_54),Z))) = multiply(inverse(multiply(Z,X_54)),X_54),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_54,Z),multiply(inverse(X_54),Z)),inverse(multiply(X_54,multiply(multiply(X_54,Z),X_54)))) )],[refute_0_288,refute_0_315]) ).

cnf(refute_0_317,plain,
    multiply(X_62,multiply(Y,multiply(inverse(X_62),Y))) = multiply(inverse(multiply(Y,X_62)),X_62),
    inference(subst,[],[refute_0_316:[bind(Z,$fot(Y)),bind(X_54,$fot(X_62))]]) ).

cnf(refute_0_318,plain,
    multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)) = multiply(X_62,multiply(Y,multiply(inverse(X_62),Y))),
    inference(subst,[],[associativity:[bind(X,$fot(X_62)),bind(Z,$fot(multiply(inverse(X_62),Y)))]]) ).

cnf(refute_0_319,plain,
    ( multiply(X_62,multiply(Y,multiply(inverse(X_62),Y))) != multiply(inverse(multiply(Y,X_62)),X_62)
    | multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)) != multiply(X_62,multiply(Y,multiply(inverse(X_62),Y)))
    | multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)) = multiply(inverse(multiply(Y,X_62)),X_62) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)))),bind(Y0,$fot(multiply(X_62,multiply(Y,multiply(inverse(X_62),Y))))),bind(Z0,$fot(multiply(inverse(multiply(Y,X_62)),X_62)))]]) ).

cnf(refute_0_320,plain,
    ( multiply(X_62,multiply(Y,multiply(inverse(X_62),Y))) != multiply(inverse(multiply(Y,X_62)),X_62)
    | multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)) = multiply(inverse(multiply(Y,X_62)),X_62) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)),multiply(X_62,multiply(Y,multiply(inverse(X_62),Y)))) )],[refute_0_318,refute_0_319]) ).

cnf(refute_0_321,plain,
    multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)) = multiply(inverse(multiply(Y,X_62)),X_62),
    inference(resolve,[$cnf( $equal(multiply(X_62,multiply(Y,multiply(inverse(X_62),Y))),multiply(inverse(multiply(Y,X_62)),X_62)) )],[refute_0_317,refute_0_320]) ).

cnf(refute_0_322,plain,
    multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) = multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))),
    introduced(tautology,[refl,[$fot(multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))))]]) ).

cnf(refute_0_323,plain,
    ( multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) != multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)))
    | multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)) != multiply(inverse(multiply(Y,X_62)),X_62)
    | multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) = multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))),multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)))) ),[1,1],$fot(multiply(inverse(multiply(Y,X_62)),X_62))]]) ).

cnf(refute_0_324,plain,
    ( multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)) != multiply(inverse(multiply(Y,X_62)),X_62)
    | multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) = multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))),multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)))) )],[refute_0_322,refute_0_323]) ).

cnf(refute_0_325,plain,
    multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) = multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)),multiply(inverse(multiply(Y,X_62)),X_62)) )],[refute_0_321,refute_0_324]) ).

cnf(refute_0_326,plain,
    ( multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) != multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62))
    | multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62)) != commutator(Y,inverse(X_62))
    | multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) = commutator(Y,inverse(X_62)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))))),bind(Y0,$fot(multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62)))),bind(Z0,$fot(commutator(Y,inverse(X_62))))]]) ).

cnf(refute_0_327,plain,
    ( multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62)) != commutator(Y,inverse(X_62))
    | multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) = commutator(Y,inverse(X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))),multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62))) )],[refute_0_325,refute_0_326]) ).

cnf(refute_0_328,plain,
    multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) = commutator(Y,inverse(X_62)),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(multiply(Y,X_62)),X_62)),commutator(Y,inverse(X_62))) )],[refute_0_262,refute_0_327]) ).

cnf(refute_0_329,plain,
    multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)) = multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))),
    inference(subst,[],[associativity:[bind(X,$fot(Y)),bind(Y,$fot(multiply(X_62,Y))),bind(Z,$fot(multiply(inverse(X_62),Y)))]]) ).

cnf(refute_0_330,plain,
    ( multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) != commutator(Y,inverse(X_62))
    | multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)) != multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)))
    | multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)) = commutator(Y,inverse(X_62)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)))),bind(Y0,$fot(multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))))),bind(Z0,$fot(commutator(Y,inverse(X_62))))]]) ).

cnf(refute_0_331,plain,
    ( multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))) != commutator(Y,inverse(X_62))
    | multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)) = commutator(Y,inverse(X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)),multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y)))) )],[refute_0_329,refute_0_330]) ).

cnf(refute_0_332,plain,
    multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)) = commutator(Y,inverse(X_62)),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(multiply(X_62,Y),multiply(inverse(X_62),Y))),commutator(Y,inverse(X_62))) )],[refute_0_328,refute_0_331]) ).

cnf(refute_0_333,plain,
    inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) = inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))),
    introduced(tautology,[refl,[$fot(inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))))]]) ).

cnf(refute_0_334,plain,
    ( multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)) != commutator(Y,inverse(X_62))
    | inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) != inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)))
    | inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) = inverse(commutator(Y,inverse(X_62))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))),inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)))) ),[1,0],$fot(commutator(Y,inverse(X_62)))]]) ).

cnf(refute_0_335,plain,
    ( multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)) != commutator(Y,inverse(X_62))
    | inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) = inverse(commutator(Y,inverse(X_62))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))),inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)))) )],[refute_0_333,refute_0_334]) ).

cnf(refute_0_336,plain,
    inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) = inverse(commutator(Y,inverse(X_62))),
    inference(resolve,[$cnf( $equal(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)),commutator(Y,inverse(X_62))) )],[refute_0_332,refute_0_335]) ).

cnf(refute_0_337,plain,
    ( inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) != inverse(commutator(Y,inverse(X_62)))
    | inverse(commutator(Y,inverse(X_62))) != commutator(inverse(X_62),Y)
    | inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) = commutator(inverse(X_62),Y) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))))),bind(Y0,$fot(inverse(commutator(Y,inverse(X_62))))),bind(Z0,$fot(commutator(inverse(X_62),Y)))]]) ).

cnf(refute_0_338,plain,
    ( inverse(commutator(Y,inverse(X_62))) != commutator(inverse(X_62),Y)
    | inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) = commutator(inverse(X_62),Y) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))),inverse(commutator(Y,inverse(X_62)))) )],[refute_0_336,refute_0_337]) ).

cnf(refute_0_339,plain,
    inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) = commutator(inverse(X_62),Y),
    inference(resolve,[$cnf( $equal(inverse(commutator(Y,inverse(X_62))),commutator(inverse(X_62),Y)) )],[refute_0_237,refute_0_338]) ).

cnf(refute_0_340,plain,
    inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) = multiply(inverse(X_38),inverse(multiply(X_34,inverse(X_11)))),
    inference(subst,[],[refute_0_70:[bind(X_12,$fot(X_38)),bind(X_34,$fot(multiply(X_34,inverse(X_11))))]]) ).

cnf(refute_0_341,plain,
    inverse(multiply(X_34,inverse(X_11))) = multiply(X_11,multiply(inverse(X_11),inverse(multiply(X_34,inverse(X_11))))),
    inference(subst,[],[refute_0_9:[bind(X_13,$fot(inverse(multiply(X_34,inverse(X_11)))))]]) ).

cnf(refute_0_342,plain,
    multiply(inverse(X_11),inverse(multiply(X_34,inverse(X_11)))) = inverse(X_34),
    inference(subst,[],[refute_0_66:[bind(X_12,$fot(X_34)),bind(X_27,$fot(inverse(X_11)))]]) ).

cnf(refute_0_343,plain,
    ( multiply(inverse(X_11),inverse(multiply(X_34,inverse(X_11)))) != inverse(X_34)
    | inverse(multiply(X_34,inverse(X_11))) != multiply(X_11,multiply(inverse(X_11),inverse(multiply(X_34,inverse(X_11)))))
    | inverse(multiply(X_34,inverse(X_11))) = multiply(X_11,inverse(X_34)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_34,inverse(X_11))),multiply(X_11,multiply(inverse(X_11),inverse(multiply(X_34,inverse(X_11)))))) ),[1,1],$fot(inverse(X_34))]]) ).

cnf(refute_0_344,plain,
    ( inverse(multiply(X_34,inverse(X_11))) != multiply(X_11,multiply(inverse(X_11),inverse(multiply(X_34,inverse(X_11)))))
    | inverse(multiply(X_34,inverse(X_11))) = multiply(X_11,inverse(X_34)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_11),inverse(multiply(X_34,inverse(X_11)))),inverse(X_34)) )],[refute_0_342,refute_0_343]) ).

cnf(refute_0_345,plain,
    inverse(multiply(X_34,inverse(X_11))) = multiply(X_11,inverse(X_34)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_34,inverse(X_11))),multiply(X_11,multiply(inverse(X_11),inverse(multiply(X_34,inverse(X_11)))))) )],[refute_0_341,refute_0_344]) ).

cnf(refute_0_346,plain,
    ( inverse(multiply(X_34,inverse(X_11))) != multiply(X_11,inverse(X_34))
    | inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) != multiply(inverse(X_38),inverse(multiply(X_34,inverse(X_11))))
    | inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) = multiply(inverse(X_38),multiply(X_11,inverse(X_34))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(X_34,inverse(X_11)),X_38)),multiply(inverse(X_38),inverse(multiply(X_34,inverse(X_11))))) ),[1,1],$fot(multiply(X_11,inverse(X_34)))]]) ).

cnf(refute_0_347,plain,
    ( inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) != multiply(inverse(X_38),inverse(multiply(X_34,inverse(X_11))))
    | inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) = multiply(inverse(X_38),multiply(X_11,inverse(X_34))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_34,inverse(X_11))),multiply(X_11,inverse(X_34))) )],[refute_0_345,refute_0_346]) ).

cnf(refute_0_348,plain,
    inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) = multiply(inverse(X_38),multiply(X_11,inverse(X_34))),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_34,inverse(X_11)),X_38)),multiply(inverse(X_38),inverse(multiply(X_34,inverse(X_11))))) )],[refute_0_340,refute_0_347]) ).

cnf(refute_0_349,plain,
    multiply(multiply(X_34,inverse(X_11)),X_38) = multiply(X_34,multiply(inverse(X_11),X_38)),
    inference(subst,[],[associativity:[bind(X,$fot(X_34)),bind(Y,$fot(inverse(X_11))),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_350,plain,
    inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) = inverse(multiply(multiply(X_34,inverse(X_11)),X_38)),
    introduced(tautology,[refl,[$fot(inverse(multiply(multiply(X_34,inverse(X_11)),X_38)))]]) ).

cnf(refute_0_351,plain,
    ( multiply(multiply(X_34,inverse(X_11)),X_38) != multiply(X_34,multiply(inverse(X_11),X_38))
    | inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) != inverse(multiply(multiply(X_34,inverse(X_11)),X_38))
    | inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) = inverse(multiply(X_34,multiply(inverse(X_11),X_38))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(X_34,inverse(X_11)),X_38)),inverse(multiply(multiply(X_34,inverse(X_11)),X_38))) ),[1,0],$fot(multiply(X_34,multiply(inverse(X_11),X_38)))]]) ).

cnf(refute_0_352,plain,
    ( multiply(multiply(X_34,inverse(X_11)),X_38) != multiply(X_34,multiply(inverse(X_11),X_38))
    | inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) = inverse(multiply(X_34,multiply(inverse(X_11),X_38))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_34,inverse(X_11)),X_38)),inverse(multiply(multiply(X_34,inverse(X_11)),X_38))) )],[refute_0_350,refute_0_351]) ).

cnf(refute_0_353,plain,
    inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) = inverse(multiply(X_34,multiply(inverse(X_11),X_38))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_34,inverse(X_11)),X_38),multiply(X_34,multiply(inverse(X_11),X_38))) )],[refute_0_349,refute_0_352]) ).

cnf(refute_0_354,plain,
    ( inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) != multiply(inverse(X_38),multiply(X_11,inverse(X_34)))
    | inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) != inverse(multiply(X_34,multiply(inverse(X_11),X_38)))
    | inverse(multiply(X_34,multiply(inverse(X_11),X_38))) = multiply(inverse(X_38),multiply(X_11,inverse(X_34))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(X_34,inverse(X_11)),X_38)),multiply(inverse(X_38),multiply(X_11,inverse(X_34)))) ),[0],$fot(inverse(multiply(X_34,multiply(inverse(X_11),X_38))))]]) ).

cnf(refute_0_355,plain,
    ( inverse(multiply(multiply(X_34,inverse(X_11)),X_38)) != multiply(inverse(X_38),multiply(X_11,inverse(X_34)))
    | inverse(multiply(X_34,multiply(inverse(X_11),X_38))) = multiply(inverse(X_38),multiply(X_11,inverse(X_34))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_34,inverse(X_11)),X_38)),inverse(multiply(X_34,multiply(inverse(X_11),X_38)))) )],[refute_0_353,refute_0_354]) ).

cnf(refute_0_356,plain,
    inverse(multiply(X_34,multiply(inverse(X_11),X_38))) = multiply(inverse(X_38),multiply(X_11,inverse(X_34))),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_34,inverse(X_11)),X_38)),multiply(inverse(X_38),multiply(X_11,inverse(X_34)))) )],[refute_0_348,refute_0_355]) ).

cnf(refute_0_357,plain,
    ( inverse(multiply(X_34,multiply(inverse(X_11),X_38))) != multiply(inverse(X_38),multiply(X_11,inverse(X_34)))
    | multiply(inverse(X_38),multiply(X_11,inverse(X_34))) = inverse(multiply(X_34,multiply(inverse(X_11),X_38))) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X_34,multiply(inverse(X_11),X_38))))),bind(Y0,$fot(multiply(inverse(X_38),multiply(X_11,inverse(X_34)))))]]) ).

cnf(refute_0_358,plain,
    multiply(inverse(X_38),multiply(X_11,inverse(X_34))) = inverse(multiply(X_34,multiply(inverse(X_11),X_38))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_34,multiply(inverse(X_11),X_38))),multiply(inverse(X_38),multiply(X_11,inverse(X_34)))) )],[refute_0_356,refute_0_357]) ).

cnf(refute_0_359,plain,
    multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) = inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))),
    inference(subst,[],[refute_0_358:[bind(X_11,$fot(X_62)),bind(X_34,$fot(multiply(Y,multiply(X_62,Y)))),bind(X_38,$fot(Y))]]) ).

cnf(refute_0_360,plain,
    ( multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) != inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)))
    | inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) != commutator(inverse(X_62),Y)
    | multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) = commutator(inverse(X_62),Y) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))))),bind(Y0,$fot(inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))))),bind(Z0,$fot(commutator(inverse(X_62),Y)))]]) ).

cnf(refute_0_361,plain,
    ( inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))) != commutator(inverse(X_62),Y)
    | multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) = commutator(inverse(X_62),Y) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))),inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y)))) )],[refute_0_359,refute_0_360]) ).

cnf(refute_0_362,plain,
    multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) = commutator(inverse(X_62),Y),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(Y,multiply(X_62,Y)),multiply(inverse(X_62),Y))),commutator(inverse(X_62),Y)) )],[refute_0_339,refute_0_361]) ).

cnf(refute_0_363,plain,
    ( multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) != commutator(Y,multiply(Y,X_62))
    | multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) != commutator(inverse(X_62),Y)
    | commutator(inverse(X_62),Y) = commutator(Y,multiply(Y,X_62)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))),commutator(Y,multiply(Y,X_62))) ),[0],$fot(commutator(inverse(X_62),Y))]]) ).

cnf(refute_0_364,plain,
    ( multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))) != commutator(Y,multiply(Y,X_62))
    | commutator(inverse(X_62),Y) = commutator(Y,multiply(Y,X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))),commutator(inverse(X_62),Y)) )],[refute_0_362,refute_0_363]) ).

cnf(refute_0_365,plain,
    commutator(inverse(X_62),Y) = commutator(Y,multiply(Y,X_62)),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),multiply(X_62,inverse(multiply(Y,multiply(X_62,Y))))),commutator(Y,multiply(Y,X_62))) )],[refute_0_99,refute_0_364]) ).

cnf(refute_0_366,plain,
    commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) = commutator(X_65,multiply(X_65,multiply(Y,multiply(X_65,Y)))),
    inference(subst,[],[refute_0_365:[bind(Y,$fot(X_65)),bind(X_62,$fot(multiply(Y,multiply(X_65,Y))))]]) ).

cnf(refute_0_367,plain,
    inverse(multiply(X_65,Y)) = multiply(X_65,multiply(Y,multiply(X_65,Y))),
    inference(subst,[],[refute_0_121:[bind(X,$fot(X_65))]]) ).

cnf(refute_0_368,plain,
    ( inverse(multiply(X_65,Y)) != multiply(X_65,multiply(Y,multiply(X_65,Y)))
    | multiply(X_65,multiply(Y,multiply(X_65,Y))) = inverse(multiply(X_65,Y)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X_65,Y)))),bind(Y0,$fot(multiply(X_65,multiply(Y,multiply(X_65,Y)))))]]) ).

cnf(refute_0_369,plain,
    multiply(X_65,multiply(Y,multiply(X_65,Y))) = inverse(multiply(X_65,Y)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_65,Y)),multiply(X_65,multiply(Y,multiply(X_65,Y)))) )],[refute_0_367,refute_0_368]) ).

cnf(refute_0_370,plain,
    ( multiply(X_65,multiply(Y,multiply(X_65,Y))) != inverse(multiply(X_65,Y))
    | commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) != commutator(X_65,multiply(X_65,multiply(Y,multiply(X_65,Y))))
    | commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) = commutator(X_65,inverse(multiply(X_65,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65),commutator(X_65,multiply(X_65,multiply(Y,multiply(X_65,Y))))) ),[1,1],$fot(inverse(multiply(X_65,Y)))]]) ).

cnf(refute_0_371,plain,
    ( commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) != commutator(X_65,multiply(X_65,multiply(Y,multiply(X_65,Y))))
    | commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) = commutator(X_65,inverse(multiply(X_65,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(X_65,multiply(Y,multiply(X_65,Y))),inverse(multiply(X_65,Y))) )],[refute_0_369,refute_0_370]) ).

cnf(refute_0_372,plain,
    commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) = commutator(X_65,inverse(multiply(X_65,Y))),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65),commutator(X_65,multiply(X_65,multiply(Y,multiply(X_65,Y))))) )],[refute_0_366,refute_0_371]) ).

cnf(refute_0_373,plain,
    commutator(X_60,multiply(multiply(X_62,X_60),X_62)) = multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(multiply(multiply(X_62,X_60),multiply(X_62,X_60)))))),
    inference(subst,[],[refute_0_93:[bind(X,$fot(X_60)),bind(X_11,$fot(multiply(X_62,X_60))),bind(X_12,$fot(X_62))]]) ).

cnf(refute_0_374,plain,
    inverse(multiply(X_62,X_60)) = multiply(multiply(X_62,X_60),multiply(X_62,X_60)),
    inference(subst,[],[refute_0_23:[bind(X_11,$fot(multiply(X_62,X_60)))]]) ).

cnf(refute_0_375,plain,
    ( inverse(multiply(X_62,X_60)) != multiply(multiply(X_62,X_60),multiply(X_62,X_60))
    | multiply(multiply(X_62,X_60),multiply(X_62,X_60)) = inverse(multiply(X_62,X_60)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X_62,X_60)))),bind(Y0,$fot(multiply(multiply(X_62,X_60),multiply(X_62,X_60))))]]) ).

cnf(refute_0_376,plain,
    multiply(multiply(X_62,X_60),multiply(X_62,X_60)) = inverse(multiply(X_62,X_60)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_62,X_60)),multiply(multiply(X_62,X_60),multiply(X_62,X_60))) )],[refute_0_374,refute_0_375]) ).

cnf(refute_0_377,plain,
    ( multiply(multiply(X_62,X_60),multiply(X_62,X_60)) != inverse(multiply(X_62,X_60))
    | commutator(X_60,multiply(multiply(X_62,X_60),X_62)) != multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(multiply(multiply(X_62,X_60),multiply(X_62,X_60))))))
    | commutator(X_60,multiply(multiply(X_62,X_60),X_62)) = multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X_60,multiply(multiply(X_62,X_60),X_62)),multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(multiply(multiply(X_62,X_60),multiply(X_62,X_60))))))) ),[1,1,1,1,0],$fot(inverse(multiply(X_62,X_60)))]]) ).

cnf(refute_0_378,plain,
    ( commutator(X_60,multiply(multiply(X_62,X_60),X_62)) != multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(multiply(multiply(X_62,X_60),multiply(X_62,X_60))))))
    | commutator(X_60,multiply(multiply(X_62,X_60),X_62)) = multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_62,X_60),multiply(X_62,X_60)),inverse(multiply(X_62,X_60))) )],[refute_0_376,refute_0_377]) ).

cnf(refute_0_379,plain,
    commutator(X_60,multiply(multiply(X_62,X_60),X_62)) = multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),
    inference(resolve,[$cnf( $equal(commutator(X_60,multiply(multiply(X_62,X_60),X_62)),multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(multiply(multiply(X_62,X_60),multiply(X_62,X_60))))))) )],[refute_0_373,refute_0_378]) ).

cnf(refute_0_380,plain,
    multiply(multiply(X_62,X_60),X_62) = multiply(X_62,multiply(X_60,X_62)),
    inference(subst,[],[associativity:[bind(X,$fot(X_62)),bind(Y,$fot(X_60)),bind(Z,$fot(X_62))]]) ).

cnf(refute_0_381,plain,
    commutator(X_60,multiply(multiply(X_62,X_60),X_62)) = commutator(X_60,multiply(multiply(X_62,X_60),X_62)),
    introduced(tautology,[refl,[$fot(commutator(X_60,multiply(multiply(X_62,X_60),X_62)))]]) ).

cnf(refute_0_382,plain,
    ( multiply(multiply(X_62,X_60),X_62) != multiply(X_62,multiply(X_60,X_62))
    | commutator(X_60,multiply(multiply(X_62,X_60),X_62)) != commutator(X_60,multiply(multiply(X_62,X_60),X_62))
    | commutator(X_60,multiply(multiply(X_62,X_60),X_62)) = commutator(X_60,multiply(X_62,multiply(X_60,X_62))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X_60,multiply(multiply(X_62,X_60),X_62)),commutator(X_60,multiply(multiply(X_62,X_60),X_62))) ),[1,1],$fot(multiply(X_62,multiply(X_60,X_62)))]]) ).

cnf(refute_0_383,plain,
    ( multiply(multiply(X_62,X_60),X_62) != multiply(X_62,multiply(X_60,X_62))
    | commutator(X_60,multiply(multiply(X_62,X_60),X_62)) = commutator(X_60,multiply(X_62,multiply(X_60,X_62))) ),
    inference(resolve,[$cnf( $equal(commutator(X_60,multiply(multiply(X_62,X_60),X_62)),commutator(X_60,multiply(multiply(X_62,X_60),X_62))) )],[refute_0_381,refute_0_382]) ).

cnf(refute_0_384,plain,
    commutator(X_60,multiply(multiply(X_62,X_60),X_62)) = commutator(X_60,multiply(X_62,multiply(X_60,X_62))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_62,X_60),X_62),multiply(X_62,multiply(X_60,X_62))) )],[refute_0_380,refute_0_383]) ).

cnf(refute_0_385,plain,
    ( commutator(X_60,multiply(multiply(X_62,X_60),X_62)) != multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))
    | commutator(X_60,multiply(multiply(X_62,X_60),X_62)) != commutator(X_60,multiply(X_62,multiply(X_60,X_62)))
    | commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X_60,multiply(multiply(X_62,X_60),X_62)),multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) ),[0],$fot(commutator(X_60,multiply(X_62,multiply(X_60,X_62))))]]) ).

cnf(refute_0_386,plain,
    ( commutator(X_60,multiply(multiply(X_62,X_60),X_62)) != multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))
    | commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) ),
    inference(resolve,[$cnf( $equal(commutator(X_60,multiply(multiply(X_62,X_60),X_62)),commutator(X_60,multiply(X_62,multiply(X_60,X_62)))) )],[refute_0_384,refute_0_385]) ).

cnf(refute_0_387,plain,
    multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62)) = commutator(X_60,inverse(X_62)),
    inference(subst,[],[refute_0_261:[bind(X,$fot(X_60)),bind(X_17,$fot(X_62))]]) ).

cnf(refute_0_388,plain,
    multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60))) = multiply(inverse(multiply(X_60,X_62)),X_62),
    inference(subst,[],[refute_0_316:[bind(Z,$fot(X_60)),bind(X_54,$fot(X_62))]]) ).

cnf(refute_0_389,plain,
    multiply(X_62,multiply(X_62,X_60)) = multiply(inverse(X_62),X_60),
    inference(subst,[],[refute_0_141:[bind(Y,$fot(X_62)),bind(Z,$fot(X_60))]]) ).

cnf(refute_0_390,plain,
    inverse(inverse(multiply(X_62,X_60))) = multiply(X_62,X_60),
    inference(subst,[],[refute_0_134:[bind(X_14,$fot(multiply(X_62,X_60)))]]) ).

cnf(refute_0_391,plain,
    multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) = multiply(X_62,inverse(inverse(multiply(X_62,X_60)))),
    introduced(tautology,[refl,[$fot(multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))]]) ).

cnf(refute_0_392,plain,
    ( multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) != multiply(X_62,inverse(inverse(multiply(X_62,X_60))))
    | inverse(inverse(multiply(X_62,X_60))) != multiply(X_62,X_60)
    | multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) = multiply(X_62,multiply(X_62,X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_62,inverse(inverse(multiply(X_62,X_60)))),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) ),[1,1],$fot(multiply(X_62,X_60))]]) ).

cnf(refute_0_393,plain,
    ( inverse(inverse(multiply(X_62,X_60))) != multiply(X_62,X_60)
    | multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) = multiply(X_62,multiply(X_62,X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(X_62,inverse(inverse(multiply(X_62,X_60)))),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) )],[refute_0_391,refute_0_392]) ).

cnf(refute_0_394,plain,
    multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) = multiply(X_62,multiply(X_62,X_60)),
    inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_62,X_60))),multiply(X_62,X_60)) )],[refute_0_390,refute_0_393]) ).

cnf(refute_0_395,plain,
    ( multiply(X_62,multiply(X_62,X_60)) != multiply(inverse(X_62),X_60)
    | multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) != multiply(X_62,multiply(X_62,X_60))
    | multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) = multiply(inverse(X_62),X_60) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),bind(Y0,$fot(multiply(X_62,multiply(X_62,X_60)))),bind(Z0,$fot(multiply(inverse(X_62),X_60)))]]) ).

cnf(refute_0_396,plain,
    ( multiply(X_62,multiply(X_62,X_60)) != multiply(inverse(X_62),X_60)
    | multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) = multiply(inverse(X_62),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(X_62,inverse(inverse(multiply(X_62,X_60)))),multiply(X_62,multiply(X_62,X_60))) )],[refute_0_394,refute_0_395]) ).

cnf(refute_0_397,plain,
    multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) = multiply(inverse(X_62),X_60),
    inference(resolve,[$cnf( $equal(multiply(X_62,multiply(X_62,X_60)),multiply(inverse(X_62),X_60)) )],[refute_0_389,refute_0_396]) ).

cnf(refute_0_398,plain,
    multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) = multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))),
    introduced(tautology,[refl,[$fot(multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))]]) ).

cnf(refute_0_399,plain,
    ( multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) != multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))
    | multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) != multiply(inverse(X_62),X_60)
    | multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) = multiply(X_60,multiply(inverse(X_62),X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))),multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) ),[1,1],$fot(multiply(inverse(X_62),X_60))]]) ).

cnf(refute_0_400,plain,
    ( multiply(X_62,inverse(inverse(multiply(X_62,X_60)))) != multiply(inverse(X_62),X_60)
    | multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) = multiply(X_60,multiply(inverse(X_62),X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))),multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) )],[refute_0_398,refute_0_399]) ).

cnf(refute_0_401,plain,
    multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) = multiply(X_60,multiply(inverse(X_62),X_60)),
    inference(resolve,[$cnf( $equal(multiply(X_62,inverse(inverse(multiply(X_62,X_60)))),multiply(inverse(X_62),X_60)) )],[refute_0_397,refute_0_400]) ).

cnf(refute_0_402,plain,
    multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),
    introduced(tautology,[refl,[$fot(multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))))]]) ).

cnf(refute_0_403,plain,
    ( multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) != multiply(X_60,multiply(inverse(X_62),X_60))
    | multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) != multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))
    | multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) ),[1,1],$fot(multiply(X_60,multiply(inverse(X_62),X_60)))]]) ).

cnf(refute_0_404,plain,
    ( multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) != multiply(X_60,multiply(inverse(X_62),X_60))
    | multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60))) ),
    inference(resolve,[$cnf( $equal(multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) )],[refute_0_402,refute_0_403]) ).

cnf(refute_0_405,plain,
    multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60))),
    inference(resolve,[$cnf( $equal(multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))),multiply(X_60,multiply(inverse(X_62),X_60))) )],[refute_0_401,refute_0_404]) ).

cnf(refute_0_406,plain,
    ( multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) != multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60)))
    | multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60))) != multiply(inverse(multiply(X_60,X_62)),X_62)
    | multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(inverse(multiply(X_60,X_62)),X_62) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))))),bind(Y0,$fot(multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60))))),bind(Z0,$fot(multiply(inverse(multiply(X_60,X_62)),X_62)))]]) ).

cnf(refute_0_407,plain,
    ( multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60))) != multiply(inverse(multiply(X_60,X_62)),X_62)
    | multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(inverse(multiply(X_60,X_62)),X_62) ),
    inference(resolve,[$cnf( $equal(multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60)))) )],[refute_0_405,refute_0_406]) ).

cnf(refute_0_408,plain,
    multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(inverse(multiply(X_60,X_62)),X_62),
    inference(resolve,[$cnf( $equal(multiply(X_62,multiply(X_60,multiply(inverse(X_62),X_60))),multiply(inverse(multiply(X_60,X_62)),X_62)) )],[refute_0_388,refute_0_407]) ).

cnf(refute_0_409,plain,
    multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) = multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),
    inference(subst,[],[associativity:[bind(X,$fot(X_62)),bind(Y,$fot(X_60)),bind(Z,$fot(multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))]]) ).

cnf(refute_0_410,plain,
    ( multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) != multiply(inverse(multiply(X_60,X_62)),X_62)
    | multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) != multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))
    | multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) = multiply(inverse(multiply(X_60,X_62)),X_62) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))),bind(Y0,$fot(multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))))),bind(Z0,$fot(multiply(inverse(multiply(X_60,X_62)),X_62)))]]) ).

cnf(refute_0_411,plain,
    ( multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) != multiply(inverse(multiply(X_60,X_62)),X_62)
    | multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) = multiply(inverse(multiply(X_60,X_62)),X_62) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))),multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) = multiply(inverse(multiply(X_60,X_62)),X_62),
    inference(resolve,[$cnf( $equal(multiply(X_62,multiply(X_60,multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),multiply(inverse(multiply(X_60,X_62)),X_62)) )],[refute_0_408,refute_0_411]) ).

cnf(refute_0_413,plain,
    multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),
    introduced(tautology,[refl,[$fot(multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))))]]) ).

cnf(refute_0_414,plain,
    ( multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) != multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))
    | multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) != multiply(inverse(multiply(X_60,X_62)),X_62)
    | multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) ),[1,1],$fot(multiply(inverse(multiply(X_60,X_62)),X_62))]]) ).

cnf(refute_0_415,plain,
    ( multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))) != multiply(inverse(multiply(X_60,X_62)),X_62)
    | multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) )],[refute_0_413,refute_0_414]) ).

cnf(refute_0_416,plain,
    multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))),multiply(inverse(multiply(X_60,X_62)),X_62)) )],[refute_0_412,refute_0_415]) ).

cnf(refute_0_417,plain,
    ( multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) != multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62))
    | multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62)) != commutator(X_60,inverse(X_62))
    | multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = commutator(X_60,inverse(X_62)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))))),bind(Y0,$fot(multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62)))),bind(Z0,$fot(commutator(X_60,inverse(X_62))))]]) ).

cnf(refute_0_418,plain,
    ( multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62)) != commutator(X_60,inverse(X_62))
    | multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = commutator(X_60,inverse(X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62))) )],[refute_0_416,refute_0_417]) ).

cnf(refute_0_419,plain,
    multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) = commutator(X_60,inverse(X_62)),
    inference(resolve,[$cnf( $equal(multiply(X_60,multiply(inverse(multiply(X_60,X_62)),X_62)),commutator(X_60,inverse(X_62))) )],[refute_0_387,refute_0_418]) ).

cnf(refute_0_420,plain,
    ( multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))) != commutator(X_60,inverse(X_62))
    | commutator(X_60,multiply(X_62,multiply(X_60,X_62))) != multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))
    | commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = commutator(X_60,inverse(X_62)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X_60,multiply(X_62,multiply(X_60,X_62))),multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) ),[1],$fot(commutator(X_60,inverse(X_62)))]]) ).

cnf(refute_0_421,plain,
    ( commutator(X_60,multiply(X_62,multiply(X_60,X_62))) != multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))
    | commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = commutator(X_60,inverse(X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60)))))),commutator(X_60,inverse(X_62))) )],[refute_0_419,refute_0_420]) ).

cnf(refute_0_422,plain,
    ( commutator(X_60,multiply(multiply(X_62,X_60),X_62)) != multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))
    | commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = commutator(X_60,inverse(X_62)) ),
    inference(resolve,[$cnf( $equal(commutator(X_60,multiply(X_62,multiply(X_60,X_62))),multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) )],[refute_0_386,refute_0_421]) ).

cnf(refute_0_423,plain,
    commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = commutator(X_60,inverse(X_62)),
    inference(resolve,[$cnf( $equal(commutator(X_60,multiply(multiply(X_62,X_60),X_62)),multiply(X_60,multiply(multiply(X_62,X_60),multiply(X_62,inverse(inverse(multiply(X_62,X_60))))))) )],[refute_0_379,refute_0_422]) ).

cnf(refute_0_424,plain,
    commutator(X_65,multiply(Y,multiply(X_65,Y))) = commutator(X_65,inverse(Y)),
    inference(subst,[],[refute_0_423:[bind(X_60,$fot(X_65)),bind(X_62,$fot(Y))]]) ).

cnf(refute_0_425,plain,
    commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(X_65,multiply(X_65,multiply(inverse(X_65),X_13))),
    inference(subst,[],[refute_0_365:[bind(Y,$fot(X_65)),bind(X_62,$fot(multiply(inverse(X_65),X_13)))]]) ).

cnf(refute_0_426,plain,
    X_13 = multiply(X_65,multiply(inverse(X_65),X_13)),
    inference(subst,[],[refute_0_9:[bind(X_11,$fot(X_65))]]) ).

cnf(refute_0_427,plain,
    ( X_13 != multiply(X_65,multiply(inverse(X_65),X_13))
    | multiply(X_65,multiply(inverse(X_65),X_13)) = X_13 ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(X_13)),bind(Y0,$fot(multiply(X_65,multiply(inverse(X_65),X_13))))]]) ).

cnf(refute_0_428,plain,
    multiply(X_65,multiply(inverse(X_65),X_13)) = X_13,
    inference(resolve,[$cnf( $equal(X_13,multiply(X_65,multiply(inverse(X_65),X_13))) )],[refute_0_426,refute_0_427]) ).

cnf(refute_0_429,plain,
    ( multiply(X_65,multiply(inverse(X_65),X_13)) != X_13
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) != commutator(X_65,multiply(X_65,multiply(inverse(X_65),X_13)))
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(X_65,X_13) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(multiply(inverse(X_65),X_13)),X_65),commutator(X_65,multiply(X_65,multiply(inverse(X_65),X_13)))) ),[1,1],$fot(X_13)]]) ).

cnf(refute_0_430,plain,
    ( commutator(inverse(multiply(inverse(X_65),X_13)),X_65) != commutator(X_65,multiply(X_65,multiply(inverse(X_65),X_13)))
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(X_65,X_13) ),
    inference(resolve,[$cnf( $equal(multiply(X_65,multiply(inverse(X_65),X_13)),X_13) )],[refute_0_428,refute_0_429]) ).

cnf(refute_0_431,plain,
    commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(X_65,X_13),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(inverse(X_65),X_13)),X_65),commutator(X_65,multiply(X_65,multiply(inverse(X_65),X_13)))) )],[refute_0_425,refute_0_430]) ).

cnf(refute_0_432,plain,
    multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(multiply(commutator(X_56,multiply(X_57,X_56)),multiply(X_57,multiply(X_56,inverse(X_57)))))) = inverse(commutator(X_56,multiply(X_57,X_56))),
    inference(subst,[],[refute_0_66:[bind(X_12,$fot(commutator(X_56,multiply(X_57,X_56)))),bind(X_27,$fot(multiply(X_57,multiply(X_56,inverse(X_57)))))]]) ).

cnf(refute_0_433,plain,
    multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),multiply(X_31,inverse(multiply(X_34,X_31))))) = X_31,
    inference(subst,[],[refute_0_195:[bind(X_30,$fot(multiply(X_34,X_31)))]]) ).

cnf(refute_0_434,plain,
    multiply(X_31,inverse(multiply(X_34,X_31))) = inverse(X_34),
    inference(subst,[],[refute_0_66:[bind(X_12,$fot(X_34)),bind(X_27,$fot(X_31))]]) ).

cnf(refute_0_435,plain,
    ( multiply(X_31,inverse(multiply(X_34,X_31))) != inverse(X_34)
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),multiply(X_31,inverse(multiply(X_34,X_31))))) != X_31
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) = X_31 ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),multiply(X_31,inverse(multiply(X_34,X_31))))),X_31) ),[0,1,1],$fot(inverse(X_34))]]) ).

cnf(refute_0_436,plain,
    ( multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),multiply(X_31,inverse(multiply(X_34,X_31))))) != X_31
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) = X_31 ),
    inference(resolve,[$cnf( $equal(multiply(X_31,inverse(multiply(X_34,X_31))),inverse(X_34)) )],[refute_0_434,refute_0_435]) ).

cnf(refute_0_437,plain,
    multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) = X_31,
    inference(resolve,[$cnf( $equal(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),multiply(X_31,inverse(multiply(X_34,X_31))))),X_31) )],[refute_0_433,refute_0_436]) ).

cnf(refute_0_438,plain,
    multiply(multiply(X_34,X_31),inverse(X_34)) = multiply(X_34,multiply(X_31,inverse(X_34))),
    inference(subst,[],[associativity:[bind(X,$fot(X_34)),bind(Y,$fot(X_31)),bind(Z,$fot(inverse(X_34)))]]) ).

cnf(refute_0_439,plain,
    multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) = multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))),
    introduced(tautology,[refl,[$fot(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))))]]) ).

cnf(refute_0_440,plain,
    ( multiply(multiply(X_34,X_31),inverse(X_34)) != multiply(X_34,multiply(X_31,inverse(X_34)))
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) != multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34)))
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) = multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))),multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34)))) ),[1,1],$fot(multiply(X_34,multiply(X_31,inverse(X_34))))]]) ).

cnf(refute_0_441,plain,
    ( multiply(multiply(X_34,X_31),inverse(X_34)) != multiply(X_34,multiply(X_31,inverse(X_34)))
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) = multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34)))) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))),multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34)))) )],[refute_0_439,refute_0_440]) ).

cnf(refute_0_442,plain,
    multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) = multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_34,X_31),inverse(X_34)),multiply(X_34,multiply(X_31,inverse(X_34)))) )],[refute_0_438,refute_0_441]) ).

cnf(refute_0_443,plain,
    ( multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) != X_31
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) != multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34))))
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34)))) = X_31 ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))),X_31) ),[0],$fot(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34)))))]]) ).

cnf(refute_0_444,plain,
    ( multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))) != X_31
    | multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34)))) = X_31 ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))),multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34))))) )],[refute_0_442,refute_0_443]) ).

cnf(refute_0_445,plain,
    multiply(commutator(X_31,multiply(X_34,X_31)),multiply(X_34,multiply(X_31,inverse(X_34)))) = X_31,
    inference(resolve,[$cnf( $equal(multiply(commutator(X_31,multiply(X_34,X_31)),multiply(multiply(X_34,X_31),inverse(X_34))),X_31) )],[refute_0_437,refute_0_444]) ).

cnf(refute_0_446,plain,
    multiply(commutator(X_56,multiply(X_57,X_56)),multiply(X_57,multiply(X_56,inverse(X_57)))) = X_56,
    inference(subst,[],[refute_0_445:[bind(X_31,$fot(X_56)),bind(X_34,$fot(X_57))]]) ).

cnf(refute_0_447,plain,
    ( multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(multiply(commutator(X_56,multiply(X_57,X_56)),multiply(X_57,multiply(X_56,inverse(X_57)))))) != inverse(commutator(X_56,multiply(X_57,X_56)))
    | multiply(commutator(X_56,multiply(X_57,X_56)),multiply(X_57,multiply(X_56,inverse(X_57)))) != X_56
    | multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) = inverse(commutator(X_56,multiply(X_57,X_56))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(multiply(commutator(X_56,multiply(X_57,X_56)),multiply(X_57,multiply(X_56,inverse(X_57)))))),inverse(commutator(X_56,multiply(X_57,X_56)))) ),[0,1,0],$fot(X_56)]]) ).

cnf(refute_0_448,plain,
    ( multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(multiply(commutator(X_56,multiply(X_57,X_56)),multiply(X_57,multiply(X_56,inverse(X_57)))))) != inverse(commutator(X_56,multiply(X_57,X_56)))
    | multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) = inverse(commutator(X_56,multiply(X_57,X_56))) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_56,multiply(X_57,X_56)),multiply(X_57,multiply(X_56,inverse(X_57)))),X_56) )],[refute_0_446,refute_0_447]) ).

cnf(refute_0_449,plain,
    multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) = inverse(commutator(X_56,multiply(X_57,X_56))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(multiply(commutator(X_56,multiply(X_57,X_56)),multiply(X_57,multiply(X_56,inverse(X_57)))))),inverse(commutator(X_56,multiply(X_57,X_56)))) )],[refute_0_432,refute_0_448]) ).

cnf(refute_0_450,plain,
    inverse(commutator(X_31,X_30)) = commutator(X_30,X_31),
    inference(subst,[],[refute_0_236:[bind(X,$fot(X_30)),bind(Y,$fot(X_31))]]) ).

cnf(refute_0_451,plain,
    ( multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) != inverse(commutator(X_31,X_30))
    | inverse(commutator(X_31,X_30)) != commutator(X_30,X_31)
    | multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) = commutator(X_30,X_31) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))),commutator(X_30,X_31)) ),[0],$fot(inverse(commutator(X_31,X_30)))]]) ).

cnf(refute_0_452,plain,
    ( multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) != inverse(commutator(X_31,X_30))
    | multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) = commutator(X_30,X_31) ),
    inference(resolve,[$cnf( $equal(inverse(commutator(X_31,X_30)),commutator(X_30,X_31)) )],[refute_0_450,refute_0_451]) ).

cnf(refute_0_453,plain,
    multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))) = commutator(X_30,X_31),
    inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_31,inverse(multiply(X_31,X_30)))),inverse(commutator(X_31,X_30))) )],[refute_0_218,refute_0_452]) ).

cnf(refute_0_454,plain,
    multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57)))) = commutator(X_57,X_56),
    inference(subst,[],[refute_0_453:[bind(X_30,$fot(X_57)),bind(X_31,$fot(X_56))]]) ).

cnf(refute_0_455,plain,
    multiply(inverse(X_57),inverse(X_56)) = inverse(multiply(X_56,X_57)),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(X_57)),bind(X_34,$fot(X_56))]]) ).

cnf(refute_0_456,plain,
    multiply(X_56,multiply(inverse(X_57),inverse(X_56))) = multiply(X_56,multiply(inverse(X_57),inverse(X_56))),
    introduced(tautology,[refl,[$fot(multiply(X_56,multiply(inverse(X_57),inverse(X_56))))]]) ).

cnf(refute_0_457,plain,
    ( multiply(X_56,multiply(inverse(X_57),inverse(X_56))) != multiply(X_56,multiply(inverse(X_57),inverse(X_56)))
    | multiply(inverse(X_57),inverse(X_56)) != inverse(multiply(X_56,X_57))
    | multiply(X_56,multiply(inverse(X_57),inverse(X_56))) = multiply(X_56,inverse(multiply(X_56,X_57))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_56,multiply(inverse(X_57),inverse(X_56))),multiply(X_56,multiply(inverse(X_57),inverse(X_56)))) ),[1,1],$fot(inverse(multiply(X_56,X_57)))]]) ).

cnf(refute_0_458,plain,
    ( multiply(inverse(X_57),inverse(X_56)) != inverse(multiply(X_56,X_57))
    | multiply(X_56,multiply(inverse(X_57),inverse(X_56))) = multiply(X_56,inverse(multiply(X_56,X_57))) ),
    inference(resolve,[$cnf( $equal(multiply(X_56,multiply(inverse(X_57),inverse(X_56))),multiply(X_56,multiply(inverse(X_57),inverse(X_56)))) )],[refute_0_456,refute_0_457]) ).

cnf(refute_0_459,plain,
    multiply(X_56,multiply(inverse(X_57),inverse(X_56))) = multiply(X_56,inverse(multiply(X_56,X_57))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_57),inverse(X_56)),inverse(multiply(X_56,X_57))) )],[refute_0_455,refute_0_458]) ).

cnf(refute_0_460,plain,
    multiply(multiply(X_56,inverse(X_57)),inverse(X_56)) = multiply(X_56,multiply(inverse(X_57),inverse(X_56))),
    inference(subst,[],[associativity:[bind(X,$fot(X_56)),bind(Y,$fot(inverse(X_57))),bind(Z,$fot(inverse(X_56)))]]) ).

cnf(refute_0_461,plain,
    ( multiply(X_56,multiply(inverse(X_57),inverse(X_56))) != multiply(X_56,inverse(multiply(X_56,X_57)))
    | multiply(multiply(X_56,inverse(X_57)),inverse(X_56)) != multiply(X_56,multiply(inverse(X_57),inverse(X_56)))
    | multiply(multiply(X_56,inverse(X_57)),inverse(X_56)) = multiply(X_56,inverse(multiply(X_56,X_57))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(X_56,inverse(X_57)),inverse(X_56)))),bind(Y0,$fot(multiply(X_56,multiply(inverse(X_57),inverse(X_56))))),bind(Z0,$fot(multiply(X_56,inverse(multiply(X_56,X_57)))))]]) ).

cnf(refute_0_462,plain,
    ( multiply(X_56,multiply(inverse(X_57),inverse(X_56))) != multiply(X_56,inverse(multiply(X_56,X_57)))
    | multiply(multiply(X_56,inverse(X_57)),inverse(X_56)) = multiply(X_56,inverse(multiply(X_56,X_57))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_56,inverse(X_57)),inverse(X_56)),multiply(X_56,multiply(inverse(X_57),inverse(X_56)))) )],[refute_0_460,refute_0_461]) ).

cnf(refute_0_463,plain,
    multiply(multiply(X_56,inverse(X_57)),inverse(X_56)) = multiply(X_56,inverse(multiply(X_56,X_57))),
    inference(resolve,[$cnf( $equal(multiply(X_56,multiply(inverse(X_57),inverse(X_56))),multiply(X_56,inverse(multiply(X_56,X_57)))) )],[refute_0_459,refute_0_462]) ).

cnf(refute_0_464,plain,
    multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) = multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))),
    introduced(tautology,[refl,[$fot(multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))))]]) ).

cnf(refute_0_465,plain,
    ( multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) != multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56)))
    | multiply(multiply(X_56,inverse(X_57)),inverse(X_56)) != multiply(X_56,inverse(multiply(X_56,X_57)))
    | multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) = multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))),multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56)))) ),[1,1],$fot(multiply(X_56,inverse(multiply(X_56,X_57))))]]) ).

cnf(refute_0_466,plain,
    ( multiply(multiply(X_56,inverse(X_57)),inverse(X_56)) != multiply(X_56,inverse(multiply(X_56,X_57)))
    | multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) = multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))),multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56)))) )],[refute_0_464,refute_0_465]) ).

cnf(refute_0_467,plain,
    multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) = multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_56,inverse(X_57)),inverse(X_56)),multiply(X_56,inverse(multiply(X_56,X_57)))) )],[refute_0_463,refute_0_466]) ).

cnf(refute_0_468,plain,
    ( multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57)))) != commutator(X_57,X_56)
    | multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) != multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57))))
    | multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) = commutator(X_57,X_56) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))))),bind(Y0,$fot(multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57)))))),bind(Z0,$fot(commutator(X_57,X_56)))]]) ).

cnf(refute_0_469,plain,
    ( multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57)))) != commutator(X_57,X_56)
    | multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) = commutator(X_57,X_56) ),
    inference(resolve,[$cnf( $equal(multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))),multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57))))) )],[refute_0_467,refute_0_468]) ).

cnf(refute_0_470,plain,
    multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) = commutator(X_57,X_56),
    inference(resolve,[$cnf( $equal(multiply(X_57,multiply(X_56,inverse(multiply(X_56,X_57)))),commutator(X_57,X_56)) )],[refute_0_454,refute_0_469]) ).

cnf(refute_0_471,plain,
    multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) = multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))),
    inference(subst,[],[associativity:[bind(X,$fot(X_57)),bind(Y,$fot(multiply(X_56,inverse(X_57)))),bind(Z,$fot(inverse(X_56)))]]) ).

cnf(refute_0_472,plain,
    ( multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) != commutator(X_57,X_56)
    | multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) != multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56)))
    | multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) = commutator(X_57,X_56) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)))),bind(Y0,$fot(multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))))),bind(Z0,$fot(commutator(X_57,X_56)))]]) ).

cnf(refute_0_473,plain,
    ( multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))) != commutator(X_57,X_56)
    | multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) = commutator(X_57,X_56) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)),multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56)))) )],[refute_0_471,refute_0_472]) ).

cnf(refute_0_474,plain,
    multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) = commutator(X_57,X_56),
    inference(resolve,[$cnf( $equal(multiply(X_57,multiply(multiply(X_56,inverse(X_57)),inverse(X_56))),commutator(X_57,X_56)) )],[refute_0_470,refute_0_473]) ).

cnf(refute_0_475,plain,
    ( multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) != commutator(X_57,X_56)
    | multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) != inverse(commutator(X_56,multiply(X_57,X_56)))
    | commutator(X_57,X_56) = inverse(commutator(X_56,multiply(X_57,X_56))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)),inverse(commutator(X_56,multiply(X_57,X_56)))) ),[0],$fot(commutator(X_57,X_56))]]) ).

cnf(refute_0_476,plain,
    ( multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) != inverse(commutator(X_56,multiply(X_57,X_56)))
    | commutator(X_57,X_56) = inverse(commutator(X_56,multiply(X_57,X_56))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)),commutator(X_57,X_56)) )],[refute_0_474,refute_0_475]) ).

cnf(refute_0_477,plain,
    inverse(commutator(X_56,multiply(X_57,X_56))) = commutator(multiply(X_57,X_56),X_56),
    inference(subst,[],[refute_0_236:[bind(X,$fot(multiply(X_57,X_56))),bind(Y,$fot(X_56))]]) ).

cnf(refute_0_478,plain,
    ( commutator(X_57,X_56) != inverse(commutator(X_56,multiply(X_57,X_56)))
    | inverse(commutator(X_56,multiply(X_57,X_56))) != commutator(multiply(X_57,X_56),X_56)
    | commutator(X_57,X_56) = commutator(multiply(X_57,X_56),X_56) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(commutator(X_57,X_56),commutator(multiply(X_57,X_56),X_56)) ),[0],$fot(inverse(commutator(X_56,multiply(X_57,X_56))))]]) ).

cnf(refute_0_479,plain,
    ( commutator(X_57,X_56) != inverse(commutator(X_56,multiply(X_57,X_56)))
    | commutator(X_57,X_56) = commutator(multiply(X_57,X_56),X_56) ),
    inference(resolve,[$cnf( $equal(inverse(commutator(X_56,multiply(X_57,X_56))),commutator(multiply(X_57,X_56),X_56)) )],[refute_0_477,refute_0_478]) ).

cnf(refute_0_480,plain,
    ( multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)) != inverse(commutator(X_56,multiply(X_57,X_56)))
    | commutator(X_57,X_56) = commutator(multiply(X_57,X_56),X_56) ),
    inference(resolve,[$cnf( $equal(commutator(X_57,X_56),inverse(commutator(X_56,multiply(X_57,X_56)))) )],[refute_0_476,refute_0_479]) ).

cnf(refute_0_481,plain,
    commutator(X_57,X_56) = commutator(multiply(X_57,X_56),X_56),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_57,multiply(X_56,inverse(X_57))),inverse(X_56)),inverse(commutator(X_56,multiply(X_57,X_56)))) )],[refute_0_449,refute_0_480]) ).

cnf(refute_0_482,plain,
    ( commutator(X_57,X_56) != commutator(multiply(X_57,X_56),X_56)
    | commutator(multiply(X_57,X_56),X_56) = commutator(X_57,X_56) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(X_57,X_56))),bind(Y0,$fot(commutator(multiply(X_57,X_56),X_56)))]]) ).

cnf(refute_0_483,plain,
    commutator(multiply(X_57,X_56),X_56) = commutator(X_57,X_56),
    inference(resolve,[$cnf( $equal(commutator(X_57,X_56),commutator(multiply(X_57,X_56),X_56)) )],[refute_0_481,refute_0_482]) ).

cnf(refute_0_484,plain,
    commutator(multiply(inverse(X_13),X_65),X_65) = commutator(inverse(X_13),X_65),
    inference(subst,[],[refute_0_483:[bind(X_56,$fot(X_65)),bind(X_57,$fot(inverse(X_13)))]]) ).

cnf(refute_0_485,plain,
    inverse(multiply(inverse(X_65),X_13)) = multiply(inverse(X_13),X_65),
    inference(subst,[],[refute_0_295:[bind(X_14,$fot(X_65)),bind(X_38,$fot(X_13))]]) ).

cnf(refute_0_486,plain,
    commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(inverse(multiply(inverse(X_65),X_13)),X_65),
    introduced(tautology,[refl,[$fot(commutator(inverse(multiply(inverse(X_65),X_13)),X_65))]]) ).

cnf(refute_0_487,plain,
    ( commutator(inverse(multiply(inverse(X_65),X_13)),X_65) != commutator(inverse(multiply(inverse(X_65),X_13)),X_65)
    | inverse(multiply(inverse(X_65),X_13)) != multiply(inverse(X_13),X_65)
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(multiply(inverse(X_13),X_65),X_65) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(multiply(inverse(X_65),X_13)),X_65),commutator(inverse(multiply(inverse(X_65),X_13)),X_65)) ),[1,0],$fot(multiply(inverse(X_13),X_65))]]) ).

cnf(refute_0_488,plain,
    ( inverse(multiply(inverse(X_65),X_13)) != multiply(inverse(X_13),X_65)
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(multiply(inverse(X_13),X_65),X_65) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(inverse(X_65),X_13)),X_65),commutator(inverse(multiply(inverse(X_65),X_13)),X_65)) )],[refute_0_486,refute_0_487]) ).

cnf(refute_0_489,plain,
    commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(multiply(inverse(X_13),X_65),X_65),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_65),X_13)),multiply(inverse(X_13),X_65)) )],[refute_0_485,refute_0_488]) ).

cnf(refute_0_490,plain,
    ( commutator(multiply(inverse(X_13),X_65),X_65) != commutator(inverse(X_13),X_65)
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) != commutator(multiply(inverse(X_13),X_65),X_65)
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(inverse(X_13),X_65) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(commutator(inverse(multiply(inverse(X_65),X_13)),X_65))),bind(Y0,$fot(commutator(multiply(inverse(X_13),X_65),X_65))),bind(Z0,$fot(commutator(inverse(X_13),X_65)))]]) ).

cnf(refute_0_491,plain,
    ( commutator(multiply(inverse(X_13),X_65),X_65) != commutator(inverse(X_13),X_65)
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(inverse(X_13),X_65) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(inverse(X_65),X_13)),X_65),commutator(multiply(inverse(X_13),X_65),X_65)) )],[refute_0_489,refute_0_490]) ).

cnf(refute_0_492,plain,
    commutator(inverse(multiply(inverse(X_65),X_13)),X_65) = commutator(inverse(X_13),X_65),
    inference(resolve,[$cnf( $equal(commutator(multiply(inverse(X_13),X_65),X_65),commutator(inverse(X_13),X_65)) )],[refute_0_484,refute_0_491]) ).

cnf(refute_0_493,plain,
    ( commutator(inverse(multiply(inverse(X_65),X_13)),X_65) != commutator(X_65,X_13)
    | commutator(inverse(multiply(inverse(X_65),X_13)),X_65) != commutator(inverse(X_13),X_65)
    | commutator(inverse(X_13),X_65) = commutator(X_65,X_13) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(multiply(inverse(X_65),X_13)),X_65),commutator(X_65,X_13)) ),[0],$fot(commutator(inverse(X_13),X_65))]]) ).

cnf(refute_0_494,plain,
    ( commutator(inverse(multiply(inverse(X_65),X_13)),X_65) != commutator(X_65,X_13)
    | commutator(inverse(X_13),X_65) = commutator(X_65,X_13) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(inverse(X_65),X_13)),X_65),commutator(inverse(X_13),X_65)) )],[refute_0_492,refute_0_493]) ).

cnf(refute_0_495,plain,
    commutator(inverse(X_13),X_65) = commutator(X_65,X_13),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(inverse(X_65),X_13)),X_65),commutator(X_65,X_13)) )],[refute_0_431,refute_0_494]) ).

cnf(refute_0_496,plain,
    commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) = commutator(X_65,multiply(Y,multiply(X_65,Y))),
    inference(subst,[],[refute_0_495:[bind(X_13,$fot(multiply(Y,multiply(X_65,Y))))]]) ).

cnf(refute_0_497,plain,
    ( commutator(X_65,multiply(Y,multiply(X_65,Y))) != commutator(X_65,inverse(Y))
    | commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) != commutator(X_65,multiply(Y,multiply(X_65,Y)))
    | commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) = commutator(X_65,inverse(Y)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65))),bind(Y0,$fot(commutator(X_65,multiply(Y,multiply(X_65,Y))))),bind(Z0,$fot(commutator(X_65,inverse(Y))))]]) ).

cnf(refute_0_498,plain,
    ( commutator(X_65,multiply(Y,multiply(X_65,Y))) != commutator(X_65,inverse(Y))
    | commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) = commutator(X_65,inverse(Y)) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65),commutator(X_65,multiply(Y,multiply(X_65,Y)))) )],[refute_0_496,refute_0_497]) ).

cnf(refute_0_499,plain,
    commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) = commutator(X_65,inverse(Y)),
    inference(resolve,[$cnf( $equal(commutator(X_65,multiply(Y,multiply(X_65,Y))),commutator(X_65,inverse(Y))) )],[refute_0_424,refute_0_498]) ).

cnf(refute_0_500,plain,
    ( commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) != commutator(X_65,inverse(Y))
    | commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) != commutator(X_65,inverse(multiply(X_65,Y)))
    | commutator(X_65,inverse(Y)) = commutator(X_65,inverse(multiply(X_65,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65),commutator(X_65,inverse(multiply(X_65,Y)))) ),[0],$fot(commutator(X_65,inverse(Y)))]]) ).

cnf(refute_0_501,plain,
    ( commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) != commutator(X_65,inverse(multiply(X_65,Y)))
    | commutator(X_65,inverse(Y)) = commutator(X_65,inverse(multiply(X_65,Y))) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65),commutator(X_65,inverse(Y))) )],[refute_0_499,refute_0_500]) ).

cnf(refute_0_502,plain,
    commutator(inverse(X_65),Y) = commutator(Y,X_65),
    inference(subst,[],[refute_0_495:[bind(X_13,$fot(X_65)),bind(X_65,$fot(Y))]]) ).

cnf(refute_0_503,plain,
    commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) = commutator(inverse(X_12),multiply(inverse(X_12),multiply(X_12,X_13))),
    inference(subst,[],[refute_0_365:[bind(Y,$fot(inverse(X_12))),bind(X_62,$fot(multiply(X_12,X_13)))]]) ).

cnf(refute_0_504,plain,
    ( X_13 != multiply(inverse(X_12),multiply(X_12,X_13))
    | multiply(inverse(X_12),multiply(X_12,X_13)) = X_13 ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(X_13)),bind(Y0,$fot(multiply(inverse(X_12),multiply(X_12,X_13))))]]) ).

cnf(refute_0_505,plain,
    multiply(inverse(X_12),multiply(X_12,X_13)) = X_13,
    inference(resolve,[$cnf( $equal(X_13,multiply(inverse(X_12),multiply(X_12,X_13))) )],[refute_0_51,refute_0_504]) ).

cnf(refute_0_506,plain,
    ( multiply(inverse(X_12),multiply(X_12,X_13)) != X_13
    | commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) != commutator(inverse(X_12),multiply(inverse(X_12),multiply(X_12,X_13)))
    | commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) = commutator(inverse(X_12),X_13) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(multiply(X_12,X_13)),inverse(X_12)),commutator(inverse(X_12),multiply(inverse(X_12),multiply(X_12,X_13)))) ),[1,1],$fot(X_13)]]) ).

cnf(refute_0_507,plain,
    ( commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) != commutator(inverse(X_12),multiply(inverse(X_12),multiply(X_12,X_13)))
    | commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) = commutator(inverse(X_12),X_13) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(X_12,X_13)),X_13) )],[refute_0_505,refute_0_506]) ).

cnf(refute_0_508,plain,
    commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) = commutator(inverse(X_12),X_13),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(X_12,X_13)),inverse(X_12)),commutator(inverse(X_12),multiply(inverse(X_12),multiply(X_12,X_13)))) )],[refute_0_503,refute_0_507]) ).

cnf(refute_0_509,plain,
    commutator(multiply(Y,X_66),Y) = inverse(commutator(Y,multiply(Y,X_66))),
    inference(subst,[],[refute_0_234:[bind(X,$fot(multiply(Y,X_66)))]]) ).

cnf(refute_0_510,plain,
    commutator(inverse(X_66),Y) = commutator(Y,multiply(Y,X_66)),
    inference(subst,[],[refute_0_365:[bind(X_62,$fot(X_66))]]) ).

cnf(refute_0_511,plain,
    ( commutator(inverse(X_66),Y) != commutator(Y,multiply(Y,X_66))
    | commutator(Y,multiply(Y,X_66)) = commutator(inverse(X_66),Y) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(inverse(X_66),Y))),bind(Y0,$fot(commutator(Y,multiply(Y,X_66))))]]) ).

cnf(refute_0_512,plain,
    commutator(Y,multiply(Y,X_66)) = commutator(inverse(X_66),Y),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_66),Y),commutator(Y,multiply(Y,X_66))) )],[refute_0_510,refute_0_511]) ).

cnf(refute_0_513,plain,
    ( commutator(Y,multiply(Y,X_66)) != commutator(inverse(X_66),Y)
    | commutator(multiply(Y,X_66),Y) != inverse(commutator(Y,multiply(Y,X_66)))
    | commutator(multiply(Y,X_66),Y) = inverse(commutator(inverse(X_66),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(multiply(Y,X_66),Y),inverse(commutator(Y,multiply(Y,X_66)))) ),[1,0],$fot(commutator(inverse(X_66),Y))]]) ).

cnf(refute_0_514,plain,
    ( commutator(multiply(Y,X_66),Y) != inverse(commutator(Y,multiply(Y,X_66)))
    | commutator(multiply(Y,X_66),Y) = inverse(commutator(inverse(X_66),Y)) ),
    inference(resolve,[$cnf( $equal(commutator(Y,multiply(Y,X_66)),commutator(inverse(X_66),Y)) )],[refute_0_512,refute_0_513]) ).

cnf(refute_0_515,plain,
    commutator(multiply(Y,X_66),Y) = inverse(commutator(inverse(X_66),Y)),
    inference(resolve,[$cnf( $equal(commutator(multiply(Y,X_66),Y),inverse(commutator(Y,multiply(Y,X_66)))) )],[refute_0_509,refute_0_514]) ).

cnf(refute_0_516,plain,
    multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))),
    inference(subst,[],[refute_0_51:[bind(X_13,$fot(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))))]]) ).

cnf(refute_0_517,plain,
    commutator(inverse(X_12),multiply(X_12,X_62)) = multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))),
    inference(subst,[],[refute_0_93:[bind(X,$fot(inverse(X_12))),bind(X_11,$fot(X_12)),bind(X_12,$fot(X_62))]]) ).

cnf(refute_0_518,plain,
    ( commutator(inverse(X_12),multiply(X_12,X_62)) != multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))))
    | multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))) = commutator(inverse(X_12),multiply(X_12,X_62)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(inverse(X_12),multiply(X_12,X_62)))),bind(Y0,$fot(multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))))))]]) ).

cnf(refute_0_519,plain,
    multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))) = commutator(inverse(X_12),multiply(X_12,X_62)),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_12),multiply(X_12,X_62)),multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))))) )],[refute_0_517,refute_0_518]) ).

cnf(refute_0_520,plain,
    ( multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) != multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))))
    | multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))) != commutator(inverse(X_12),multiply(X_12,X_62))
    | multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = commutator(inverse(X_12),multiply(X_12,X_62)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),commutator(inverse(X_12),multiply(X_12,X_62))) ),[0],$fot(multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))))]]) ).

cnf(refute_0_521,plain,
    ( multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) != multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))))
    | multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = commutator(inverse(X_12),multiply(X_12,X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))),commutator(inverse(X_12),multiply(X_12,X_62))) )],[refute_0_519,refute_0_520]) ).

cnf(refute_0_522,plain,
    multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = commutator(inverse(X_12),multiply(X_12,X_62)),
    inference(resolve,[$cnf( $equal(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),multiply(inverse(X_12),multiply(X_12,multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))))) )],[refute_0_516,refute_0_521]) ).

cnf(refute_0_523,plain,
    multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62)))) = commutator(X_62,X_12),
    inference(subst,[],[refute_0_453:[bind(X_30,$fot(X_62)),bind(X_31,$fot(X_12))]]) ).

cnf(refute_0_524,plain,
    inverse(multiply(X_34,inverse(multiply(X_37,inverse(X_36))))) = multiply(multiply(X_37,inverse(X_36)),inverse(X_34)),
    inference(subst,[],[refute_0_345:[bind(X_11,$fot(multiply(X_37,inverse(X_36))))]]) ).

cnf(refute_0_525,plain,
    inverse(multiply(X_37,inverse(X_36))) = multiply(X_36,inverse(X_37)),
    inference(subst,[],[refute_0_345:[bind(X_11,$fot(X_36)),bind(X_34,$fot(X_37))]]) ).

cnf(refute_0_526,plain,
    ( inverse(multiply(X_34,inverse(multiply(X_37,inverse(X_36))))) != multiply(multiply(X_37,inverse(X_36)),inverse(X_34))
    | inverse(multiply(X_37,inverse(X_36))) != multiply(X_36,inverse(X_37))
    | inverse(multiply(X_34,multiply(X_36,inverse(X_37)))) = multiply(multiply(X_37,inverse(X_36)),inverse(X_34)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_34,inverse(multiply(X_37,inverse(X_36))))),multiply(multiply(X_37,inverse(X_36)),inverse(X_34))) ),[0,0,1],$fot(multiply(X_36,inverse(X_37)))]]) ).

cnf(refute_0_527,plain,
    ( inverse(multiply(X_34,inverse(multiply(X_37,inverse(X_36))))) != multiply(multiply(X_37,inverse(X_36)),inverse(X_34))
    | inverse(multiply(X_34,multiply(X_36,inverse(X_37)))) = multiply(multiply(X_37,inverse(X_36)),inverse(X_34)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_37,inverse(X_36))),multiply(X_36,inverse(X_37))) )],[refute_0_525,refute_0_526]) ).

cnf(refute_0_528,plain,
    inverse(multiply(X_34,multiply(X_36,inverse(X_37)))) = multiply(multiply(X_37,inverse(X_36)),inverse(X_34)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_34,inverse(multiply(X_37,inverse(X_36))))),multiply(multiply(X_37,inverse(X_36)),inverse(X_34))) )],[refute_0_524,refute_0_527]) ).

cnf(refute_0_529,plain,
    multiply(inverse(X_36),inverse(X_34)) = inverse(multiply(X_34,X_36)),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(X_36))]]) ).

cnf(refute_0_530,plain,
    multiply(X_37,multiply(inverse(X_36),inverse(X_34))) = multiply(X_37,multiply(inverse(X_36),inverse(X_34))),
    introduced(tautology,[refl,[$fot(multiply(X_37,multiply(inverse(X_36),inverse(X_34))))]]) ).

cnf(refute_0_531,plain,
    ( multiply(X_37,multiply(inverse(X_36),inverse(X_34))) != multiply(X_37,multiply(inverse(X_36),inverse(X_34)))
    | multiply(inverse(X_36),inverse(X_34)) != inverse(multiply(X_34,X_36))
    | multiply(X_37,multiply(inverse(X_36),inverse(X_34))) = multiply(X_37,inverse(multiply(X_34,X_36))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,multiply(inverse(X_36),inverse(X_34))),multiply(X_37,multiply(inverse(X_36),inverse(X_34)))) ),[1,1],$fot(inverse(multiply(X_34,X_36)))]]) ).

cnf(refute_0_532,plain,
    ( multiply(inverse(X_36),inverse(X_34)) != inverse(multiply(X_34,X_36))
    | multiply(X_37,multiply(inverse(X_36),inverse(X_34))) = multiply(X_37,inverse(multiply(X_34,X_36))) ),
    inference(resolve,[$cnf( $equal(multiply(X_37,multiply(inverse(X_36),inverse(X_34))),multiply(X_37,multiply(inverse(X_36),inverse(X_34)))) )],[refute_0_530,refute_0_531]) ).

cnf(refute_0_533,plain,
    multiply(X_37,multiply(inverse(X_36),inverse(X_34))) = multiply(X_37,inverse(multiply(X_34,X_36))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_36),inverse(X_34)),inverse(multiply(X_34,X_36))) )],[refute_0_529,refute_0_532]) ).

cnf(refute_0_534,plain,
    multiply(multiply(X_37,inverse(X_36)),inverse(X_34)) = multiply(X_37,multiply(inverse(X_36),inverse(X_34))),
    inference(subst,[],[associativity:[bind(X,$fot(X_37)),bind(Y,$fot(inverse(X_36))),bind(Z,$fot(inverse(X_34)))]]) ).

cnf(refute_0_535,plain,
    ( multiply(X_37,multiply(inverse(X_36),inverse(X_34))) != multiply(X_37,inverse(multiply(X_34,X_36)))
    | multiply(multiply(X_37,inverse(X_36)),inverse(X_34)) != multiply(X_37,multiply(inverse(X_36),inverse(X_34)))
    | multiply(multiply(X_37,inverse(X_36)),inverse(X_34)) = multiply(X_37,inverse(multiply(X_34,X_36))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(multiply(X_37,inverse(X_36)),inverse(X_34)))),bind(Y0,$fot(multiply(X_37,multiply(inverse(X_36),inverse(X_34))))),bind(Z0,$fot(multiply(X_37,inverse(multiply(X_34,X_36)))))]]) ).

cnf(refute_0_536,plain,
    ( multiply(X_37,multiply(inverse(X_36),inverse(X_34))) != multiply(X_37,inverse(multiply(X_34,X_36)))
    | multiply(multiply(X_37,inverse(X_36)),inverse(X_34)) = multiply(X_37,inverse(multiply(X_34,X_36))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_37,inverse(X_36)),inverse(X_34)),multiply(X_37,multiply(inverse(X_36),inverse(X_34)))) )],[refute_0_534,refute_0_535]) ).

cnf(refute_0_537,plain,
    multiply(multiply(X_37,inverse(X_36)),inverse(X_34)) = multiply(X_37,inverse(multiply(X_34,X_36))),
    inference(resolve,[$cnf( $equal(multiply(X_37,multiply(inverse(X_36),inverse(X_34))),multiply(X_37,inverse(multiply(X_34,X_36)))) )],[refute_0_533,refute_0_536]) ).

cnf(refute_0_538,plain,
    ( multiply(multiply(X_37,inverse(X_36)),inverse(X_34)) != multiply(X_37,inverse(multiply(X_34,X_36)))
    | inverse(multiply(X_34,multiply(X_36,inverse(X_37)))) != multiply(multiply(X_37,inverse(X_36)),inverse(X_34))
    | inverse(multiply(X_34,multiply(X_36,inverse(X_37)))) = multiply(X_37,inverse(multiply(X_34,X_36))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_34,multiply(X_36,inverse(X_37)))),multiply(multiply(X_37,inverse(X_36)),inverse(X_34))) ),[1],$fot(multiply(X_37,inverse(multiply(X_34,X_36))))]]) ).

cnf(refute_0_539,plain,
    ( inverse(multiply(X_34,multiply(X_36,inverse(X_37)))) != multiply(multiply(X_37,inverse(X_36)),inverse(X_34))
    | inverse(multiply(X_34,multiply(X_36,inverse(X_37)))) = multiply(X_37,inverse(multiply(X_34,X_36))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_37,inverse(X_36)),inverse(X_34)),multiply(X_37,inverse(multiply(X_34,X_36)))) )],[refute_0_537,refute_0_538]) ).

cnf(refute_0_540,plain,
    inverse(multiply(X_34,multiply(X_36,inverse(X_37)))) = multiply(X_37,inverse(multiply(X_34,X_36))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_34,multiply(X_36,inverse(X_37)))),multiply(multiply(X_37,inverse(X_36)),inverse(X_34))) )],[refute_0_528,refute_0_539]) ).

cnf(refute_0_541,plain,
    inverse(multiply(X_12,multiply(X_62,inverse(X_12)))) = multiply(X_12,inverse(multiply(X_12,X_62))),
    inference(subst,[],[refute_0_540:[bind(X_34,$fot(X_12)),bind(X_36,$fot(X_62)),bind(X_37,$fot(X_12))]]) ).

cnf(refute_0_542,plain,
    multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),
    introduced(tautology,[refl,[$fot(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))]]) ).

cnf(refute_0_543,plain,
    ( multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) != multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))
    | inverse(multiply(X_12,multiply(X_62,inverse(X_12)))) != multiply(X_12,inverse(multiply(X_12,X_62)))
    | multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))) ),[1,1],$fot(multiply(X_12,inverse(multiply(X_12,X_62))))]]) ).

cnf(refute_0_544,plain,
    ( inverse(multiply(X_12,multiply(X_62,inverse(X_12)))) != multiply(X_12,inverse(multiply(X_12,X_62)))
    | multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12)))))) )],[refute_0_542,refute_0_543]) ).

cnf(refute_0_545,plain,
    multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62)))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_12,multiply(X_62,inverse(X_12)))),multiply(X_12,inverse(multiply(X_12,X_62)))) )],[refute_0_541,refute_0_544]) ).

cnf(refute_0_546,plain,
    ( multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62)))) != commutator(X_62,X_12)
    | multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) != multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62))))
    | multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = commutator(X_62,X_12) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))))),bind(Y0,$fot(multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62)))))),bind(Z0,$fot(commutator(X_62,X_12)))]]) ).

cnf(refute_0_547,plain,
    ( multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62)))) != commutator(X_62,X_12)
    | multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = commutator(X_62,X_12) ),
    inference(resolve,[$cnf( $equal(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62))))) )],[refute_0_545,refute_0_546]) ).

cnf(refute_0_548,plain,
    multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) = commutator(X_62,X_12),
    inference(resolve,[$cnf( $equal(multiply(X_62,multiply(X_12,inverse(multiply(X_12,X_62)))),commutator(X_62,X_12)) )],[refute_0_523,refute_0_547]) ).

cnf(refute_0_549,plain,
    ( multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) != commutator(X_62,X_12)
    | multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) != commutator(inverse(X_12),multiply(X_12,X_62))
    | commutator(X_62,X_12) = commutator(inverse(X_12),multiply(X_12,X_62)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),commutator(inverse(X_12),multiply(X_12,X_62))) ),[0],$fot(commutator(X_62,X_12))]]) ).

cnf(refute_0_550,plain,
    ( multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))) != commutator(inverse(X_12),multiply(X_12,X_62))
    | commutator(X_62,X_12) = commutator(inverse(X_12),multiply(X_12,X_62)) ),
    inference(resolve,[$cnf( $equal(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),commutator(X_62,X_12)) )],[refute_0_548,refute_0_549]) ).

cnf(refute_0_551,plain,
    commutator(X_62,X_12) = commutator(inverse(X_12),multiply(X_12,X_62)),
    inference(resolve,[$cnf( $equal(multiply(X_62,inverse(multiply(X_12,multiply(X_62,inverse(X_12))))),commutator(inverse(X_12),multiply(X_12,X_62))) )],[refute_0_522,refute_0_550]) ).

cnf(refute_0_552,plain,
    commutator(multiply(X_63,Z),X_63) = commutator(inverse(X_63),multiply(X_63,multiply(X_63,Z))),
    inference(subst,[],[refute_0_551:[bind(X_12,$fot(X_63)),bind(X_62,$fot(multiply(X_63,Z)))]]) ).

cnf(refute_0_553,plain,
    multiply(inverse(X_63),Z) = multiply(X_63,multiply(X_63,Z)),
    inference(subst,[],[refute_0_32:[bind(Y,$fot(X_63))]]) ).

cnf(refute_0_554,plain,
    ( multiply(inverse(X_63),Z) != multiply(X_63,multiply(X_63,Z))
    | multiply(X_63,multiply(X_63,Z)) = multiply(inverse(X_63),Z) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(inverse(X_63),Z))),bind(Y0,$fot(multiply(X_63,multiply(X_63,Z))))]]) ).

cnf(refute_0_555,plain,
    multiply(X_63,multiply(X_63,Z)) = multiply(inverse(X_63),Z),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_63),Z),multiply(X_63,multiply(X_63,Z))) )],[refute_0_553,refute_0_554]) ).

cnf(refute_0_556,plain,
    ( multiply(X_63,multiply(X_63,Z)) != multiply(inverse(X_63),Z)
    | commutator(multiply(X_63,Z),X_63) != commutator(inverse(X_63),multiply(X_63,multiply(X_63,Z)))
    | commutator(multiply(X_63,Z),X_63) = commutator(inverse(X_63),multiply(inverse(X_63),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(multiply(X_63,Z),X_63),commutator(inverse(X_63),multiply(X_63,multiply(X_63,Z)))) ),[1,1],$fot(multiply(inverse(X_63),Z))]]) ).

cnf(refute_0_557,plain,
    ( commutator(multiply(X_63,Z),X_63) != commutator(inverse(X_63),multiply(X_63,multiply(X_63,Z)))
    | commutator(multiply(X_63,Z),X_63) = commutator(inverse(X_63),multiply(inverse(X_63),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(X_63,multiply(X_63,Z)),multiply(inverse(X_63),Z)) )],[refute_0_555,refute_0_556]) ).

cnf(refute_0_558,plain,
    commutator(multiply(X_63,Z),X_63) = commutator(inverse(X_63),multiply(inverse(X_63),Z)),
    inference(resolve,[$cnf( $equal(commutator(multiply(X_63,Z),X_63),commutator(inverse(X_63),multiply(X_63,multiply(X_63,Z)))) )],[refute_0_552,refute_0_557]) ).

cnf(refute_0_559,plain,
    ( commutator(inverse(X_62),Y) != commutator(Y,multiply(Y,X_62))
    | commutator(Y,multiply(Y,X_62)) = commutator(inverse(X_62),Y) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(inverse(X_62),Y))),bind(Y0,$fot(commutator(Y,multiply(Y,X_62))))]]) ).

cnf(refute_0_560,plain,
    commutator(Y,multiply(Y,X_62)) = commutator(inverse(X_62),Y),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_62),Y),commutator(Y,multiply(Y,X_62))) )],[refute_0_365,refute_0_559]) ).

cnf(refute_0_561,plain,
    commutator(inverse(X_63),multiply(inverse(X_63),Z)) = commutator(inverse(Z),inverse(X_63)),
    inference(subst,[],[refute_0_560:[bind(Y,$fot(inverse(X_63))),bind(X_62,$fot(Z))]]) ).

cnf(refute_0_562,plain,
    ( commutator(multiply(X_63,Z),X_63) != commutator(inverse(X_63),multiply(inverse(X_63),Z))
    | commutator(inverse(X_63),multiply(inverse(X_63),Z)) != commutator(inverse(Z),inverse(X_63))
    | commutator(multiply(X_63,Z),X_63) = commutator(inverse(Z),inverse(X_63)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(commutator(multiply(X_63,Z),X_63),commutator(inverse(Z),inverse(X_63))) ),[0],$fot(commutator(inverse(X_63),multiply(inverse(X_63),Z)))]]) ).

cnf(refute_0_563,plain,
    ( commutator(multiply(X_63,Z),X_63) != commutator(inverse(X_63),multiply(inverse(X_63),Z))
    | commutator(multiply(X_63,Z),X_63) = commutator(inverse(Z),inverse(X_63)) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_63),multiply(inverse(X_63),Z)),commutator(inverse(Z),inverse(X_63))) )],[refute_0_561,refute_0_562]) ).

cnf(refute_0_564,plain,
    commutator(multiply(X_63,Z),X_63) = commutator(inverse(Z),inverse(X_63)),
    inference(resolve,[$cnf( $equal(commutator(multiply(X_63,Z),X_63),commutator(inverse(X_63),multiply(inverse(X_63),Z))) )],[refute_0_558,refute_0_563]) ).

cnf(refute_0_565,plain,
    commutator(multiply(Y,X_66),Y) = commutator(inverse(X_66),inverse(Y)),
    inference(subst,[],[refute_0_564:[bind(Z,$fot(X_66)),bind(X_63,$fot(Y))]]) ).

cnf(refute_0_566,plain,
    ( commutator(multiply(Y,X_66),Y) != commutator(inverse(X_66),inverse(Y))
    | commutator(multiply(Y,X_66),Y) != inverse(commutator(inverse(X_66),Y))
    | commutator(inverse(X_66),inverse(Y)) = inverse(commutator(inverse(X_66),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(multiply(Y,X_66),Y),inverse(commutator(inverse(X_66),Y))) ),[0],$fot(commutator(inverse(X_66),inverse(Y)))]]) ).

cnf(refute_0_567,plain,
    ( commutator(multiply(Y,X_66),Y) != inverse(commutator(inverse(X_66),Y))
    | commutator(inverse(X_66),inverse(Y)) = inverse(commutator(inverse(X_66),Y)) ),
    inference(resolve,[$cnf( $equal(commutator(multiply(Y,X_66),Y),commutator(inverse(X_66),inverse(Y))) )],[refute_0_565,refute_0_566]) ).

cnf(refute_0_568,plain,
    inverse(commutator(inverse(X_66),Y)) = commutator(Y,inverse(X_66)),
    inference(subst,[],[refute_0_236:[bind(X,$fot(Y)),bind(Y,$fot(inverse(X_66)))]]) ).

cnf(refute_0_569,plain,
    ( commutator(inverse(X_66),inverse(Y)) != inverse(commutator(inverse(X_66),Y))
    | inverse(commutator(inverse(X_66),Y)) != commutator(Y,inverse(X_66))
    | commutator(inverse(X_66),inverse(Y)) = commutator(Y,inverse(X_66)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(commutator(inverse(X_66),inverse(Y)),commutator(Y,inverse(X_66))) ),[0],$fot(inverse(commutator(inverse(X_66),Y)))]]) ).

cnf(refute_0_570,plain,
    ( commutator(inverse(X_66),inverse(Y)) != inverse(commutator(inverse(X_66),Y))
    | commutator(inverse(X_66),inverse(Y)) = commutator(Y,inverse(X_66)) ),
    inference(resolve,[$cnf( $equal(inverse(commutator(inverse(X_66),Y)),commutator(Y,inverse(X_66))) )],[refute_0_568,refute_0_569]) ).

cnf(refute_0_571,plain,
    ( commutator(multiply(Y,X_66),Y) != inverse(commutator(inverse(X_66),Y))
    | commutator(inverse(X_66),inverse(Y)) = commutator(Y,inverse(X_66)) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_66),inverse(Y)),inverse(commutator(inverse(X_66),Y))) )],[refute_0_567,refute_0_570]) ).

cnf(refute_0_572,plain,
    commutator(inverse(X_66),inverse(Y)) = commutator(Y,inverse(X_66)),
    inference(resolve,[$cnf( $equal(commutator(multiply(Y,X_66),Y),inverse(commutator(inverse(X_66),Y))) )],[refute_0_515,refute_0_571]) ).

cnf(refute_0_573,plain,
    commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) = commutator(X_12,inverse(multiply(X_12,X_13))),
    inference(subst,[],[refute_0_572:[bind(Y,$fot(X_12)),bind(X_66,$fot(multiply(X_12,X_13)))]]) ).

cnf(refute_0_574,plain,
    ( commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) != commutator(X_12,inverse(multiply(X_12,X_13)))
    | commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) != commutator(inverse(X_12),X_13)
    | commutator(X_12,inverse(multiply(X_12,X_13))) = commutator(inverse(X_12),X_13) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(multiply(X_12,X_13)),inverse(X_12)),commutator(inverse(X_12),X_13)) ),[0],$fot(commutator(X_12,inverse(multiply(X_12,X_13))))]]) ).

cnf(refute_0_575,plain,
    ( commutator(inverse(multiply(X_12,X_13)),inverse(X_12)) != commutator(inverse(X_12),X_13)
    | commutator(X_12,inverse(multiply(X_12,X_13))) = commutator(inverse(X_12),X_13) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(X_12,X_13)),inverse(X_12)),commutator(X_12,inverse(multiply(X_12,X_13)))) )],[refute_0_573,refute_0_574]) ).

cnf(refute_0_576,plain,
    commutator(X_12,inverse(multiply(X_12,X_13))) = commutator(inverse(X_12),X_13),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(X_12,X_13)),inverse(X_12)),commutator(inverse(X_12),X_13)) )],[refute_0_508,refute_0_575]) ).

cnf(refute_0_577,plain,
    commutator(X_65,inverse(multiply(X_65,Y))) = commutator(inverse(X_65),Y),
    inference(subst,[],[refute_0_576:[bind(X_12,$fot(X_65)),bind(X_13,$fot(Y))]]) ).

cnf(refute_0_578,plain,
    ( commutator(X_65,inverse(multiply(X_65,Y))) != commutator(inverse(X_65),Y)
    | commutator(inverse(X_65),Y) != commutator(Y,X_65)
    | commutator(X_65,inverse(multiply(X_65,Y))) = commutator(Y,X_65) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(commutator(X_65,inverse(multiply(X_65,Y))))),bind(Y0,$fot(commutator(inverse(X_65),Y))),bind(Z0,$fot(commutator(Y,X_65)))]]) ).

cnf(refute_0_579,plain,
    ( commutator(inverse(X_65),Y) != commutator(Y,X_65)
    | commutator(X_65,inverse(multiply(X_65,Y))) = commutator(Y,X_65) ),
    inference(resolve,[$cnf( $equal(commutator(X_65,inverse(multiply(X_65,Y))),commutator(inverse(X_65),Y)) )],[refute_0_577,refute_0_578]) ).

cnf(refute_0_580,plain,
    commutator(X_65,inverse(multiply(X_65,Y))) = commutator(Y,X_65),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_65),Y),commutator(Y,X_65)) )],[refute_0_502,refute_0_579]) ).

cnf(refute_0_581,plain,
    ( commutator(X_65,inverse(Y)) != commutator(X_65,inverse(multiply(X_65,Y)))
    | commutator(X_65,inverse(multiply(X_65,Y))) != commutator(Y,X_65)
    | commutator(X_65,inverse(Y)) = commutator(Y,X_65) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(commutator(X_65,inverse(Y)),commutator(Y,X_65)) ),[0],$fot(commutator(X_65,inverse(multiply(X_65,Y))))]]) ).

cnf(refute_0_582,plain,
    ( commutator(X_65,inverse(Y)) != commutator(X_65,inverse(multiply(X_65,Y)))
    | commutator(X_65,inverse(Y)) = commutator(Y,X_65) ),
    inference(resolve,[$cnf( $equal(commutator(X_65,inverse(multiply(X_65,Y))),commutator(Y,X_65)) )],[refute_0_580,refute_0_581]) ).

cnf(refute_0_583,plain,
    ( commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65) != commutator(X_65,inverse(multiply(X_65,Y)))
    | commutator(X_65,inverse(Y)) = commutator(Y,X_65) ),
    inference(resolve,[$cnf( $equal(commutator(X_65,inverse(Y)),commutator(X_65,inverse(multiply(X_65,Y)))) )],[refute_0_501,refute_0_582]) ).

cnf(refute_0_584,plain,
    commutator(X_65,inverse(Y)) = commutator(Y,X_65),
    inference(resolve,[$cnf( $equal(commutator(inverse(multiply(Y,multiply(X_65,Y))),X_65),commutator(X_65,inverse(multiply(X_65,Y)))) )],[refute_0_372,refute_0_583]) ).

cnf(refute_0_585,plain,
    commutator(X_68,inverse(commutator(Y,X))) = commutator(commutator(Y,X),X_68),
    inference(subst,[],[refute_0_584:[bind(Y,$fot(commutator(Y,X))),bind(X_65,$fot(X_68))]]) ).

cnf(refute_0_586,plain,
    ( commutator(X_68,inverse(commutator(Y,X))) != commutator(commutator(Y,X),X_68)
    | inverse(commutator(Y,X)) != commutator(X,Y)
    | commutator(X_68,commutator(X,Y)) = commutator(commutator(Y,X),X_68) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X_68,inverse(commutator(Y,X))),commutator(commutator(Y,X),X_68)) ),[0,1],$fot(commutator(X,Y))]]) ).

cnf(refute_0_587,plain,
    ( commutator(X_68,inverse(commutator(Y,X))) != commutator(commutator(Y,X),X_68)
    | commutator(X_68,commutator(X,Y)) = commutator(commutator(Y,X),X_68) ),
    inference(resolve,[$cnf( $equal(inverse(commutator(Y,X)),commutator(X,Y)) )],[refute_0_236,refute_0_586]) ).

cnf(refute_0_588,plain,
    commutator(X_68,commutator(X,Y)) = commutator(commutator(Y,X),X_68),
    inference(resolve,[$cnf( $equal(commutator(X_68,inverse(commutator(Y,X))),commutator(commutator(Y,X),X_68)) )],[refute_0_585,refute_0_587]) ).

cnf(refute_0_589,plain,
    ( commutator(X_68,commutator(X,Y)) != commutator(commutator(Y,X),X_68)
    | commutator(commutator(Y,X),X_68) = commutator(X_68,commutator(X,Y)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(X_68,commutator(X,Y)))),bind(Y0,$fot(commutator(commutator(Y,X),X_68)))]]) ).

cnf(refute_0_590,plain,
    commutator(commutator(Y,X),X_68) = commutator(X_68,commutator(X,Y)),
    inference(resolve,[$cnf( $equal(commutator(X_68,commutator(X,Y)),commutator(commutator(Y,X),X_68)) )],[refute_0_588,refute_0_589]) ).

cnf(refute_0_591,plain,
    commutator(commutator(a,b),b) = commutator(b,commutator(b,a)),
    inference(subst,[],[refute_0_590:[bind(X,$fot(b)),bind(Y,$fot(a)),bind(X_68,$fot(b))]]) ).

cnf(refute_0_592,plain,
    ( commutator(b,commutator(b,a)) != identity
    | commutator(commutator(a,b),b) != commutator(b,commutator(b,a))
    | commutator(commutator(a,b),b) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(commutator(a,b),b),commutator(b,commutator(b,a))) ),[1],$fot(identity)]]) ).

cnf(refute_0_593,plain,
    ( commutator(b,commutator(b,a)) != identity
    | commutator(commutator(a,b),b) = identity ),
    inference(resolve,[$cnf( $equal(commutator(commutator(a,b),b),commutator(b,commutator(b,a))) )],[refute_0_591,refute_0_592]) ).

cnf(refute_0_594,plain,
    commutator(b,commutator(b,a)) != identity,
    inference(resolve,[$cnf( $equal(commutator(commutator(a,b),b),identity) )],[refute_0_593,prove_commutator]) ).

cnf(refute_0_595,plain,
    commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = multiply(X_11,multiply(inverse(X_11),commutator(inverse(X_11),commutator(inverse(X_11),X_72)))),
    inference(subst,[],[refute_0_9:[bind(X_13,$fot(commutator(inverse(X_11),commutator(inverse(X_11),X_72))))]]) ).

cnf(refute_0_596,plain,
    multiply(commutator(X_31,multiply(X_70,multiply(X_31,X_70))),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) = X_31,
    inference(subst,[],[refute_0_195:[bind(X_30,$fot(multiply(X_70,multiply(X_31,X_70))))]]) ).

cnf(refute_0_597,plain,
    commutator(X_60,inverse(X_62)) = commutator(X_62,X_60),
    inference(subst,[],[refute_0_584:[bind(Y,$fot(X_62)),bind(X_65,$fot(X_60))]]) ).

cnf(refute_0_598,plain,
    ( commutator(X_60,multiply(X_62,multiply(X_60,X_62))) != commutator(X_60,inverse(X_62))
    | commutator(X_60,inverse(X_62)) != commutator(X_62,X_60)
    | commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = commutator(X_62,X_60) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(commutator(X_60,multiply(X_62,multiply(X_60,X_62))),commutator(X_62,X_60)) ),[0],$fot(commutator(X_60,inverse(X_62)))]]) ).

cnf(refute_0_599,plain,
    ( commutator(X_60,multiply(X_62,multiply(X_60,X_62))) != commutator(X_60,inverse(X_62))
    | commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = commutator(X_62,X_60) ),
    inference(resolve,[$cnf( $equal(commutator(X_60,inverse(X_62)),commutator(X_62,X_60)) )],[refute_0_597,refute_0_598]) ).

cnf(refute_0_600,plain,
    commutator(X_60,multiply(X_62,multiply(X_60,X_62))) = commutator(X_62,X_60),
    inference(resolve,[$cnf( $equal(commutator(X_60,multiply(X_62,multiply(X_60,X_62))),commutator(X_60,inverse(X_62))) )],[refute_0_423,refute_0_599]) ).

cnf(refute_0_601,plain,
    commutator(X_31,multiply(X_70,multiply(X_31,X_70))) = commutator(X_70,X_31),
    inference(subst,[],[refute_0_600:[bind(X_60,$fot(X_31)),bind(X_62,$fot(X_70))]]) ).

cnf(refute_0_602,plain,
    ( multiply(commutator(X_31,multiply(X_70,multiply(X_31,X_70))),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) != X_31
    | commutator(X_31,multiply(X_70,multiply(X_31,X_70))) != commutator(X_70,X_31)
    | multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) = X_31 ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(X_31,multiply(X_70,multiply(X_31,X_70))),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))),X_31) ),[0,0],$fot(commutator(X_70,X_31))]]) ).

cnf(refute_0_603,plain,
    ( multiply(commutator(X_31,multiply(X_70,multiply(X_31,X_70))),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) != X_31
    | multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) = X_31 ),
    inference(resolve,[$cnf( $equal(commutator(X_31,multiply(X_70,multiply(X_31,X_70))),commutator(X_70,X_31)) )],[refute_0_601,refute_0_602]) ).

cnf(refute_0_604,plain,
    multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) = X_31,
    inference(resolve,[$cnf( $equal(multiply(commutator(X_31,multiply(X_70,multiply(X_31,X_70))),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))),X_31) )],[refute_0_596,refute_0_603]) ).

cnf(refute_0_605,plain,
    commutator(commutator(X_70,X_31),X_31) = commutator(X_31,commutator(X_31,X_70)),
    inference(subst,[],[refute_0_590:[bind(X,$fot(X_31)),bind(Y,$fot(X_70)),bind(X_68,$fot(X_31))]]) ).

cnf(refute_0_606,plain,
    multiply(X_31,commutator(commutator(X_70,X_31),X_31)) = multiply(X_31,commutator(commutator(X_70,X_31),X_31)),
    introduced(tautology,[refl,[$fot(multiply(X_31,commutator(commutator(X_70,X_31),X_31)))]]) ).

cnf(refute_0_607,plain,
    ( multiply(X_31,commutator(commutator(X_70,X_31),X_31)) != multiply(X_31,commutator(commutator(X_70,X_31),X_31))
    | commutator(commutator(X_70,X_31),X_31) != commutator(X_31,commutator(X_31,X_70))
    | multiply(X_31,commutator(commutator(X_70,X_31),X_31)) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_31,commutator(commutator(X_70,X_31),X_31)),multiply(X_31,commutator(commutator(X_70,X_31),X_31))) ),[1,1],$fot(commutator(X_31,commutator(X_31,X_70)))]]) ).

cnf(refute_0_608,plain,
    ( commutator(commutator(X_70,X_31),X_31) != commutator(X_31,commutator(X_31,X_70))
    | multiply(X_31,commutator(commutator(X_70,X_31),X_31)) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))) ),
    inference(resolve,[$cnf( $equal(multiply(X_31,commutator(commutator(X_70,X_31),X_31)),multiply(X_31,commutator(commutator(X_70,X_31),X_31))) )],[refute_0_606,refute_0_607]) ).

cnf(refute_0_609,plain,
    multiply(X_31,commutator(commutator(X_70,X_31),X_31)) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))),
    inference(resolve,[$cnf( $equal(commutator(commutator(X_70,X_31),X_31),commutator(X_31,commutator(X_31,X_70))) )],[refute_0_605,refute_0_608]) ).

cnf(refute_0_610,plain,
    inverse(multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50))) = multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14),
    inference(subst,[],[refute_0_295:[bind(X_38,$fot(commutator(inverse(inverse(X_14)),X_50)))]]) ).

cnf(refute_0_611,plain,
    multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) = multiply(X_14,multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))))),
    inference(subst,[],[refute_0_9:[bind(X_11,$fot(X_14)),bind(X_13,$fot(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))))]]) ).

cnf(refute_0_612,plain,
    commutator(inverse(X_14),Y) = multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))),
    inference(subst,[],[commutator:[bind(X,$fot(inverse(X_14)))]]) ).

cnf(refute_0_613,plain,
    ( commutator(inverse(X_14),Y) != multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))))
    | multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))) = commutator(inverse(X_14),Y) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(inverse(X_14),Y))),bind(Y0,$fot(multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))))))]]) ).

cnf(refute_0_614,plain,
    multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))) = commutator(inverse(X_14),Y),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_14),Y),multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))))) )],[refute_0_612,refute_0_613]) ).

cnf(refute_0_615,plain,
    ( multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) != multiply(X_14,multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))))
    | multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))) != commutator(inverse(X_14),Y)
    | multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) = multiply(X_14,commutator(inverse(X_14),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))),multiply(X_14,multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))))) ),[1,1],$fot(commutator(inverse(X_14),Y))]]) ).

cnf(refute_0_616,plain,
    ( multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) != multiply(X_14,multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))))
    | multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) = multiply(X_14,commutator(inverse(X_14),Y)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))),commutator(inverse(X_14),Y)) )],[refute_0_614,refute_0_615]) ).

cnf(refute_0_617,plain,
    multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) = multiply(X_14,commutator(inverse(X_14),Y)),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))),multiply(X_14,multiply(inverse(X_14),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))))) )],[refute_0_611,refute_0_616]) ).

cnf(refute_0_618,plain,
    multiply(inverse(inverse(X_11)),X_15) = multiply(X_11,multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15))),
    inference(subst,[],[refute_0_9:[bind(X_13,$fot(multiply(inverse(inverse(X_11)),X_15)))]]) ).

cnf(refute_0_619,plain,
    X_15 = multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)),
    inference(subst,[],[refute_0_9:[bind(X_11,$fot(inverse(X_11))),bind(X_13,$fot(X_15))]]) ).

cnf(refute_0_620,plain,
    ( X_15 != multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15))
    | multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)) = X_15 ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(X_15)),bind(Y0,$fot(multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15))))]]) ).

cnf(refute_0_621,plain,
    multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)) = X_15,
    inference(resolve,[$cnf( $equal(X_15,multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15))) )],[refute_0_619,refute_0_620]) ).

cnf(refute_0_622,plain,
    ( multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)) != X_15
    | multiply(inverse(inverse(X_11)),X_15) != multiply(X_11,multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)))
    | multiply(inverse(inverse(X_11)),X_15) = multiply(X_11,X_15) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_11)),X_15),multiply(X_11,multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)))) ),[1,1],$fot(X_15)]]) ).

cnf(refute_0_623,plain,
    ( multiply(inverse(inverse(X_11)),X_15) != multiply(X_11,multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)))
    | multiply(inverse(inverse(X_11)),X_15) = multiply(X_11,X_15) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)),X_15) )],[refute_0_621,refute_0_622]) ).

cnf(refute_0_624,plain,
    multiply(inverse(inverse(X_11)),X_15) = multiply(X_11,X_15),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_11)),X_15),multiply(X_11,multiply(inverse(X_11),multiply(inverse(inverse(X_11)),X_15)))) )],[refute_0_618,refute_0_623]) ).

cnf(refute_0_625,plain,
    multiply(inverse(inverse(X_14)),inverse(Y)) = multiply(X_14,inverse(Y)),
    inference(subst,[],[refute_0_624:[bind(X_11,$fot(X_14)),bind(X_15,$fot(inverse(Y)))]]) ).

cnf(refute_0_626,plain,
    multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) = multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))),
    introduced(tautology,[refl,[$fot(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))))]]) ).

cnf(refute_0_627,plain,
    ( multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) != multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))
    | multiply(inverse(inverse(X_14)),inverse(Y)) != multiply(X_14,inverse(Y))
    | multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) = multiply(Y,multiply(X_14,inverse(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))) ),[1,1],$fot(multiply(X_14,inverse(Y)))]]) ).

cnf(refute_0_628,plain,
    ( multiply(inverse(inverse(X_14)),inverse(Y)) != multiply(X_14,inverse(Y))
    | multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) = multiply(Y,multiply(X_14,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))),multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y)))) )],[refute_0_626,refute_0_627]) ).

cnf(refute_0_629,plain,
    multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) = multiply(Y,multiply(X_14,inverse(Y))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_14)),inverse(Y)),multiply(X_14,inverse(Y))) )],[refute_0_625,refute_0_628]) ).

cnf(refute_0_630,plain,
    ( multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) != multiply(Y,multiply(X_14,inverse(Y)))
    | multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) != multiply(X_14,commutator(inverse(X_14),Y))
    | multiply(Y,multiply(X_14,inverse(Y))) = multiply(X_14,commutator(inverse(X_14),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))),multiply(X_14,commutator(inverse(X_14),Y))) ),[0],$fot(multiply(Y,multiply(X_14,inverse(Y))))]]) ).

cnf(refute_0_631,plain,
    ( multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))) != multiply(X_14,commutator(inverse(X_14),Y))
    | multiply(Y,multiply(X_14,inverse(Y))) = multiply(X_14,commutator(inverse(X_14),Y)) ),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))),multiply(Y,multiply(X_14,inverse(Y)))) )],[refute_0_629,refute_0_630]) ).

cnf(refute_0_632,plain,
    multiply(Y,multiply(X_14,inverse(Y))) = multiply(X_14,commutator(inverse(X_14),Y)),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(inverse(X_14)),inverse(Y))),multiply(X_14,commutator(inverse(X_14),Y))) )],[refute_0_617,refute_0_631]) ).

cnf(refute_0_633,plain,
    multiply(X_50,multiply(inverse(X_14),inverse(X_50))) = multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50)),
    inference(subst,[],[refute_0_632:[bind(Y,$fot(X_50)),bind(X_14,$fot(inverse(X_14)))]]) ).

cnf(refute_0_634,plain,
    ( multiply(X_50,multiply(inverse(X_14),inverse(X_50))) != multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50))
    | multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50)) = multiply(X_50,multiply(inverse(X_14),inverse(X_50))) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(X_50,multiply(inverse(X_14),inverse(X_50))))),bind(Y0,$fot(multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50))))]]) ).

cnf(refute_0_635,plain,
    multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50)) = multiply(X_50,multiply(inverse(X_14),inverse(X_50))),
    inference(resolve,[$cnf( $equal(multiply(X_50,multiply(inverse(X_14),inverse(X_50))),multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50))) )],[refute_0_633,refute_0_634]) ).

cnf(refute_0_636,plain,
    ( multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50)) != multiply(X_50,multiply(inverse(X_14),inverse(X_50)))
    | inverse(multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50))) != multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)
    | inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) = multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50))),multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)) ),[0,0],$fot(multiply(X_50,multiply(inverse(X_14),inverse(X_50))))]]) ).

cnf(refute_0_637,plain,
    ( inverse(multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50))) != multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)
    | inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) = multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50)),multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) )],[refute_0_635,refute_0_636]) ).

cnf(refute_0_638,plain,
    inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) = multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_14),commutator(inverse(inverse(X_14)),X_50))),multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)) )],[refute_0_610,refute_0_637]) ).

cnf(refute_0_639,plain,
    inverse(multiply(X_50,inverse(X_14))) = multiply(X_14,inverse(X_50)),
    inference(subst,[],[refute_0_345:[bind(X_11,$fot(X_14)),bind(X_34,$fot(X_50))]]) ).

cnf(refute_0_640,plain,
    multiply(X_50,inverse(multiply(X_50,inverse(X_14)))) = multiply(X_50,inverse(multiply(X_50,inverse(X_14)))),
    introduced(tautology,[refl,[$fot(multiply(X_50,inverse(multiply(X_50,inverse(X_14)))))]]) ).

cnf(refute_0_641,plain,
    ( multiply(X_50,inverse(multiply(X_50,inverse(X_14)))) != multiply(X_50,inverse(multiply(X_50,inverse(X_14))))
    | inverse(multiply(X_50,inverse(X_14))) != multiply(X_14,inverse(X_50))
    | multiply(X_50,inverse(multiply(X_50,inverse(X_14)))) = multiply(X_50,multiply(X_14,inverse(X_50))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_50,inverse(multiply(X_50,inverse(X_14)))),multiply(X_50,inverse(multiply(X_50,inverse(X_14))))) ),[1,1],$fot(multiply(X_14,inverse(X_50)))]]) ).

cnf(refute_0_642,plain,
    ( inverse(multiply(X_50,inverse(X_14))) != multiply(X_14,inverse(X_50))
    | multiply(X_50,inverse(multiply(X_50,inverse(X_14)))) = multiply(X_50,multiply(X_14,inverse(X_50))) ),
    inference(resolve,[$cnf( $equal(multiply(X_50,inverse(multiply(X_50,inverse(X_14)))),multiply(X_50,inverse(multiply(X_50,inverse(X_14))))) )],[refute_0_640,refute_0_641]) ).

cnf(refute_0_643,plain,
    multiply(X_50,inverse(multiply(X_50,inverse(X_14)))) = multiply(X_50,multiply(X_14,inverse(X_50))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_50,inverse(X_14))),multiply(X_14,inverse(X_50))) )],[refute_0_639,refute_0_642]) ).

cnf(refute_0_644,plain,
    inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) = multiply(X_50,inverse(multiply(X_50,inverse(X_14)))),
    inference(subst,[],[refute_0_540:[bind(X_34,$fot(X_50)),bind(X_36,$fot(inverse(X_14))),bind(X_37,$fot(X_50))]]) ).

cnf(refute_0_645,plain,
    ( multiply(X_50,inverse(multiply(X_50,inverse(X_14)))) != multiply(X_50,multiply(X_14,inverse(X_50)))
    | inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) != multiply(X_50,inverse(multiply(X_50,inverse(X_14))))
    | inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) = multiply(X_50,multiply(X_14,inverse(X_50))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))))),bind(Y0,$fot(multiply(X_50,inverse(multiply(X_50,inverse(X_14)))))),bind(Z0,$fot(multiply(X_50,multiply(X_14,inverse(X_50)))))]]) ).

cnf(refute_0_646,plain,
    ( multiply(X_50,inverse(multiply(X_50,inverse(X_14)))) != multiply(X_50,multiply(X_14,inverse(X_50)))
    | inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) = multiply(X_50,multiply(X_14,inverse(X_50))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))),multiply(X_50,inverse(multiply(X_50,inverse(X_14))))) )],[refute_0_644,refute_0_645]) ).

cnf(refute_0_647,plain,
    inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) = multiply(X_50,multiply(X_14,inverse(X_50))),
    inference(resolve,[$cnf( $equal(multiply(X_50,inverse(multiply(X_50,inverse(X_14)))),multiply(X_50,multiply(X_14,inverse(X_50)))) )],[refute_0_643,refute_0_646]) ).

cnf(refute_0_648,plain,
    ( inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) != multiply(X_50,multiply(X_14,inverse(X_50)))
    | inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) != multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)
    | multiply(X_50,multiply(X_14,inverse(X_50))) = multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))),multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)) ),[0],$fot(multiply(X_50,multiply(X_14,inverse(X_50))))]]) ).

cnf(refute_0_649,plain,
    ( inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) != multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)
    | multiply(X_50,multiply(X_14,inverse(X_50))) = multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))),multiply(X_50,multiply(X_14,inverse(X_50)))) )],[refute_0_647,refute_0_648]) ).

cnf(refute_0_650,plain,
    commutator(X_50,inverse(inverse(X_14))) = commutator(X_50,inverse(inverse(X_14))),
    introduced(tautology,[refl,[$fot(commutator(X_50,inverse(inverse(X_14))))]]) ).

cnf(refute_0_651,plain,
    ( commutator(X_50,inverse(inverse(X_14))) != commutator(X_50,inverse(inverse(X_14)))
    | inverse(inverse(X_14)) != X_14
    | commutator(X_50,inverse(inverse(X_14))) = commutator(X_50,X_14) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X_50,inverse(inverse(X_14))),commutator(X_50,inverse(inverse(X_14)))) ),[1,1],$fot(X_14)]]) ).

cnf(refute_0_652,plain,
    ( inverse(inverse(X_14)) != X_14
    | commutator(X_50,inverse(inverse(X_14))) = commutator(X_50,X_14) ),
    inference(resolve,[$cnf( $equal(commutator(X_50,inverse(inverse(X_14))),commutator(X_50,inverse(inverse(X_14)))) )],[refute_0_650,refute_0_651]) ).

cnf(refute_0_653,plain,
    commutator(X_50,inverse(inverse(X_14))) = commutator(X_50,X_14),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_14)),X_14) )],[refute_0_134,refute_0_652]) ).

cnf(refute_0_654,plain,
    inverse(commutator(inverse(inverse(X_14)),X_50)) = commutator(X_50,inverse(inverse(X_14))),
    inference(subst,[],[refute_0_236:[bind(X,$fot(X_50)),bind(Y,$fot(inverse(inverse(X_14))))]]) ).

cnf(refute_0_655,plain,
    ( commutator(X_50,inverse(inverse(X_14))) != commutator(X_50,X_14)
    | inverse(commutator(inverse(inverse(X_14)),X_50)) != commutator(X_50,inverse(inverse(X_14)))
    | inverse(commutator(inverse(inverse(X_14)),X_50)) = commutator(X_50,X_14) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(inverse(commutator(inverse(inverse(X_14)),X_50)))),bind(Y0,$fot(commutator(X_50,inverse(inverse(X_14))))),bind(Z0,$fot(commutator(X_50,X_14)))]]) ).

cnf(refute_0_656,plain,
    ( commutator(X_50,inverse(inverse(X_14))) != commutator(X_50,X_14)
    | inverse(commutator(inverse(inverse(X_14)),X_50)) = commutator(X_50,X_14) ),
    inference(resolve,[$cnf( $equal(inverse(commutator(inverse(inverse(X_14)),X_50)),commutator(X_50,inverse(inverse(X_14)))) )],[refute_0_654,refute_0_655]) ).

cnf(refute_0_657,plain,
    inverse(commutator(inverse(inverse(X_14)),X_50)) = commutator(X_50,X_14),
    inference(resolve,[$cnf( $equal(commutator(X_50,inverse(inverse(X_14))),commutator(X_50,X_14)) )],[refute_0_653,refute_0_656]) ).

cnf(refute_0_658,plain,
    multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) = multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14),
    introduced(tautology,[refl,[$fot(multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14))]]) ).

cnf(refute_0_659,plain,
    ( multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) != multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)
    | inverse(commutator(inverse(inverse(X_14)),X_50)) != commutator(X_50,X_14)
    | multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) = multiply(commutator(X_50,X_14),X_14) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14),multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)) ),[1,0],$fot(commutator(X_50,X_14))]]) ).

cnf(refute_0_660,plain,
    ( inverse(commutator(inverse(inverse(X_14)),X_50)) != commutator(X_50,X_14)
    | multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) = multiply(commutator(X_50,X_14),X_14) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14),multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)) )],[refute_0_658,refute_0_659]) ).

cnf(refute_0_661,plain,
    multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) = multiply(commutator(X_50,X_14),X_14),
    inference(resolve,[$cnf( $equal(inverse(commutator(inverse(inverse(X_14)),X_50)),commutator(X_50,X_14)) )],[refute_0_657,refute_0_660]) ).

cnf(refute_0_662,plain,
    ( multiply(X_50,multiply(X_14,inverse(X_50))) != multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)
    | multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14) != multiply(commutator(X_50,X_14),X_14)
    | multiply(X_50,multiply(X_14,inverse(X_50))) = multiply(commutator(X_50,X_14),X_14) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_50,multiply(X_14,inverse(X_50))),multiply(commutator(X_50,X_14),X_14)) ),[0],$fot(multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14))]]) ).

cnf(refute_0_663,plain,
    ( multiply(X_50,multiply(X_14,inverse(X_50))) != multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)
    | multiply(X_50,multiply(X_14,inverse(X_50))) = multiply(commutator(X_50,X_14),X_14) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14),multiply(commutator(X_50,X_14),X_14)) )],[refute_0_661,refute_0_662]) ).

cnf(refute_0_664,plain,
    ( inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))) != multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)
    | multiply(X_50,multiply(X_14,inverse(X_50))) = multiply(commutator(X_50,X_14),X_14) ),
    inference(resolve,[$cnf( $equal(multiply(X_50,multiply(X_14,inverse(X_50))),multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)) )],[refute_0_649,refute_0_663]) ).

cnf(refute_0_665,plain,
    multiply(X_50,multiply(X_14,inverse(X_50))) = multiply(commutator(X_50,X_14),X_14),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_50,multiply(inverse(X_14),inverse(X_50)))),multiply(inverse(commutator(inverse(inverse(X_14)),X_50)),X_14)) )],[refute_0_638,refute_0_664]) ).

cnf(refute_0_666,plain,
    multiply(commutator(Y,X),multiply(X_52,inverse(commutator(Y,X)))) = multiply(commutator(commutator(Y,X),X_52),X_52),
    inference(subst,[],[refute_0_665:[bind(X_14,$fot(X_52)),bind(X_50,$fot(commutator(Y,X)))]]) ).

cnf(refute_0_667,plain,
    ( multiply(commutator(Y,X),multiply(X_52,inverse(commutator(Y,X)))) != multiply(commutator(commutator(Y,X),X_52),X_52)
    | inverse(commutator(Y,X)) != commutator(X,Y)
    | multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))) = multiply(commutator(commutator(Y,X),X_52),X_52) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(Y,X),multiply(X_52,inverse(commutator(Y,X)))),multiply(commutator(commutator(Y,X),X_52),X_52)) ),[0,1,1],$fot(commutator(X,Y))]]) ).

cnf(refute_0_668,plain,
    ( multiply(commutator(Y,X),multiply(X_52,inverse(commutator(Y,X)))) != multiply(commutator(commutator(Y,X),X_52),X_52)
    | multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))) = multiply(commutator(commutator(Y,X),X_52),X_52) ),
    inference(resolve,[$cnf( $equal(inverse(commutator(Y,X)),commutator(X,Y)) )],[refute_0_236,refute_0_667]) ).

cnf(refute_0_669,plain,
    multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))) = multiply(commutator(commutator(Y,X),X_52),X_52),
    inference(resolve,[$cnf( $equal(multiply(commutator(Y,X),multiply(X_52,inverse(commutator(Y,X)))),multiply(commutator(commutator(Y,X),X_52),X_52)) )],[refute_0_666,refute_0_668]) ).

cnf(refute_0_670,plain,
    multiply(Y,multiply(X_14,inverse(Y))) = multiply(commutator(Y,X_14),X_14),
    inference(subst,[],[refute_0_665:[bind(X_50,$fot(Y))]]) ).

cnf(refute_0_671,plain,
    ( multiply(Y,multiply(X_14,inverse(Y))) != multiply(X_14,commutator(inverse(X_14),Y))
    | multiply(Y,multiply(X_14,inverse(Y))) != multiply(commutator(Y,X_14),X_14)
    | multiply(commutator(Y,X_14),X_14) = multiply(X_14,commutator(inverse(X_14),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(Y,multiply(X_14,inverse(Y))),multiply(X_14,commutator(inverse(X_14),Y))) ),[0],$fot(multiply(commutator(Y,X_14),X_14))]]) ).

cnf(refute_0_672,plain,
    ( multiply(Y,multiply(X_14,inverse(Y))) != multiply(X_14,commutator(inverse(X_14),Y))
    | multiply(commutator(Y,X_14),X_14) = multiply(X_14,commutator(inverse(X_14),Y)) ),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(X_14,inverse(Y))),multiply(commutator(Y,X_14),X_14)) )],[refute_0_670,refute_0_671]) ).

cnf(refute_0_673,plain,
    multiply(commutator(Y,X_14),X_14) = multiply(X_14,commutator(inverse(X_14),Y)),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(X_14,inverse(Y))),multiply(X_14,commutator(inverse(X_14),Y))) )],[refute_0_632,refute_0_672]) ).

cnf(refute_0_674,plain,
    commutator(inverse(X_14),Y) = commutator(Y,X_14),
    inference(subst,[],[refute_0_495:[bind(X_13,$fot(X_14)),bind(X_65,$fot(Y))]]) ).

cnf(refute_0_675,plain,
    multiply(X_14,commutator(inverse(X_14),Y)) = multiply(X_14,commutator(inverse(X_14),Y)),
    introduced(tautology,[refl,[$fot(multiply(X_14,commutator(inverse(X_14),Y)))]]) ).

cnf(refute_0_676,plain,
    ( multiply(X_14,commutator(inverse(X_14),Y)) != multiply(X_14,commutator(inverse(X_14),Y))
    | commutator(inverse(X_14),Y) != commutator(Y,X_14)
    | multiply(X_14,commutator(inverse(X_14),Y)) = multiply(X_14,commutator(Y,X_14)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_14,commutator(inverse(X_14),Y)),multiply(X_14,commutator(inverse(X_14),Y))) ),[1,1],$fot(commutator(Y,X_14))]]) ).

cnf(refute_0_677,plain,
    ( commutator(inverse(X_14),Y) != commutator(Y,X_14)
    | multiply(X_14,commutator(inverse(X_14),Y)) = multiply(X_14,commutator(Y,X_14)) ),
    inference(resolve,[$cnf( $equal(multiply(X_14,commutator(inverse(X_14),Y)),multiply(X_14,commutator(inverse(X_14),Y))) )],[refute_0_675,refute_0_676]) ).

cnf(refute_0_678,plain,
    multiply(X_14,commutator(inverse(X_14),Y)) = multiply(X_14,commutator(Y,X_14)),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_14),Y),commutator(Y,X_14)) )],[refute_0_674,refute_0_677]) ).

cnf(refute_0_679,plain,
    ( multiply(X_14,commutator(inverse(X_14),Y)) != multiply(X_14,commutator(Y,X_14))
    | multiply(commutator(Y,X_14),X_14) != multiply(X_14,commutator(inverse(X_14),Y))
    | multiply(commutator(Y,X_14),X_14) = multiply(X_14,commutator(Y,X_14)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(Y,X_14),X_14),multiply(X_14,commutator(inverse(X_14),Y))) ),[1],$fot(multiply(X_14,commutator(Y,X_14)))]]) ).

cnf(refute_0_680,plain,
    ( multiply(commutator(Y,X_14),X_14) != multiply(X_14,commutator(inverse(X_14),Y))
    | multiply(commutator(Y,X_14),X_14) = multiply(X_14,commutator(Y,X_14)) ),
    inference(resolve,[$cnf( $equal(multiply(X_14,commutator(inverse(X_14),Y)),multiply(X_14,commutator(Y,X_14))) )],[refute_0_678,refute_0_679]) ).

cnf(refute_0_681,plain,
    multiply(commutator(Y,X_14),X_14) = multiply(X_14,commutator(Y,X_14)),
    inference(resolve,[$cnf( $equal(multiply(commutator(Y,X_14),X_14),multiply(X_14,commutator(inverse(X_14),Y))) )],[refute_0_673,refute_0_680]) ).

cnf(refute_0_682,plain,
    multiply(commutator(commutator(Y,X),X_52),X_52) = multiply(X_52,commutator(commutator(Y,X),X_52)),
    inference(subst,[],[refute_0_681:[bind(Y,$fot(commutator(Y,X))),bind(X_14,$fot(X_52))]]) ).

cnf(refute_0_683,plain,
    ( multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))) != multiply(commutator(commutator(Y,X),X_52),X_52)
    | multiply(commutator(commutator(Y,X),X_52),X_52) != multiply(X_52,commutator(commutator(Y,X),X_52))
    | multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))) = multiply(X_52,commutator(commutator(Y,X),X_52)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))),multiply(X_52,commutator(commutator(Y,X),X_52))) ),[0],$fot(multiply(commutator(commutator(Y,X),X_52),X_52))]]) ).

cnf(refute_0_684,plain,
    ( multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))) != multiply(commutator(commutator(Y,X),X_52),X_52)
    | multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))) = multiply(X_52,commutator(commutator(Y,X),X_52)) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(commutator(Y,X),X_52),X_52),multiply(X_52,commutator(commutator(Y,X),X_52))) )],[refute_0_682,refute_0_683]) ).

cnf(refute_0_685,plain,
    multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))) = multiply(X_52,commutator(commutator(Y,X),X_52)),
    inference(resolve,[$cnf( $equal(multiply(commutator(Y,X),multiply(X_52,commutator(X,Y))),multiply(commutator(commutator(Y,X),X_52),X_52)) )],[refute_0_669,refute_0_684]) ).

cnf(refute_0_686,plain,
    multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) = multiply(X_31,commutator(commutator(X_70,X_31),X_31)),
    inference(subst,[],[refute_0_685:[bind(X,$fot(X_31)),bind(Y,$fot(X_70)),bind(X_52,$fot(X_31))]]) ).

cnf(refute_0_687,plain,
    ( multiply(X_31,commutator(commutator(X_70,X_31),X_31)) != multiply(X_31,commutator(X_31,commutator(X_31,X_70)))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) != multiply(X_31,commutator(commutator(X_70,X_31),X_31))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))))),bind(Y0,$fot(multiply(X_31,commutator(commutator(X_70,X_31),X_31)))),bind(Z0,$fot(multiply(X_31,commutator(X_31,commutator(X_31,X_70)))))]]) ).

cnf(refute_0_688,plain,
    ( multiply(X_31,commutator(commutator(X_70,X_31),X_31)) != multiply(X_31,commutator(X_31,commutator(X_31,X_70)))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))),multiply(X_31,commutator(commutator(X_70,X_31),X_31))) )],[refute_0_686,refute_0_687]) ).

cnf(refute_0_689,plain,
    multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))),
    inference(resolve,[$cnf( $equal(multiply(X_31,commutator(commutator(X_70,X_31),X_31)),multiply(X_31,commutator(X_31,commutator(X_31,X_70)))) )],[refute_0_609,refute_0_688]) ).

cnf(refute_0_690,plain,
    commutator(multiply(Y,multiply(X_63,Y)),X_63) = commutator(inverse(X_63),multiply(X_63,multiply(Y,multiply(X_63,Y)))),
    inference(subst,[],[refute_0_551:[bind(X_12,$fot(X_63)),bind(X_62,$fot(multiply(Y,multiply(X_63,Y))))]]) ).

cnf(refute_0_691,plain,
    inverse(multiply(X_63,Y)) = multiply(X_63,multiply(Y,multiply(X_63,Y))),
    inference(subst,[],[refute_0_121:[bind(X,$fot(X_63))]]) ).

cnf(refute_0_692,plain,
    ( inverse(multiply(X_63,Y)) != multiply(X_63,multiply(Y,multiply(X_63,Y)))
    | multiply(X_63,multiply(Y,multiply(X_63,Y))) = inverse(multiply(X_63,Y)) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X_63,Y)))),bind(Y0,$fot(multiply(X_63,multiply(Y,multiply(X_63,Y)))))]]) ).

cnf(refute_0_693,plain,
    multiply(X_63,multiply(Y,multiply(X_63,Y))) = inverse(multiply(X_63,Y)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_63,Y)),multiply(X_63,multiply(Y,multiply(X_63,Y)))) )],[refute_0_691,refute_0_692]) ).

cnf(refute_0_694,plain,
    ( multiply(X_63,multiply(Y,multiply(X_63,Y))) != inverse(multiply(X_63,Y))
    | commutator(multiply(Y,multiply(X_63,Y)),X_63) != commutator(inverse(X_63),multiply(X_63,multiply(Y,multiply(X_63,Y))))
    | commutator(multiply(Y,multiply(X_63,Y)),X_63) = commutator(inverse(X_63),inverse(multiply(X_63,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(multiply(Y,multiply(X_63,Y)),X_63),commutator(inverse(X_63),multiply(X_63,multiply(Y,multiply(X_63,Y))))) ),[1,1],$fot(inverse(multiply(X_63,Y)))]]) ).

cnf(refute_0_695,plain,
    ( commutator(multiply(Y,multiply(X_63,Y)),X_63) != commutator(inverse(X_63),multiply(X_63,multiply(Y,multiply(X_63,Y))))
    | commutator(multiply(Y,multiply(X_63,Y)),X_63) = commutator(inverse(X_63),inverse(multiply(X_63,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(X_63,multiply(Y,multiply(X_63,Y))),inverse(multiply(X_63,Y))) )],[refute_0_693,refute_0_694]) ).

cnf(refute_0_696,plain,
    commutator(multiply(Y,multiply(X_63,Y)),X_63) = commutator(inverse(X_63),inverse(multiply(X_63,Y))),
    inference(resolve,[$cnf( $equal(commutator(multiply(Y,multiply(X_63,Y)),X_63),commutator(inverse(X_63),multiply(X_63,multiply(Y,multiply(X_63,Y))))) )],[refute_0_690,refute_0_695]) ).

cnf(refute_0_697,plain,
    commutator(inverse(X_62),Y) = commutator(Y,X_62),
    inference(subst,[],[refute_0_495:[bind(X_13,$fot(X_62)),bind(X_65,$fot(Y))]]) ).

cnf(refute_0_698,plain,
    ( commutator(inverse(X_62),Y) != commutator(Y,X_62)
    | commutator(inverse(X_62),Y) != commutator(Y,multiply(Y,X_62))
    | commutator(Y,X_62) = commutator(Y,multiply(Y,X_62)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(X_62),Y),commutator(Y,multiply(Y,X_62))) ),[0],$fot(commutator(Y,X_62))]]) ).

cnf(refute_0_699,plain,
    ( commutator(inverse(X_62),Y) != commutator(Y,multiply(Y,X_62))
    | commutator(Y,X_62) = commutator(Y,multiply(Y,X_62)) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_62),Y),commutator(Y,X_62)) )],[refute_0_697,refute_0_698]) ).

cnf(refute_0_700,plain,
    commutator(Y,X_62) = commutator(Y,multiply(Y,X_62)),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_62),Y),commutator(Y,multiply(Y,X_62))) )],[refute_0_365,refute_0_699]) ).

cnf(refute_0_701,plain,
    ( commutator(Y,X_62) != commutator(Y,multiply(Y,X_62))
    | commutator(Y,multiply(Y,X_62)) = commutator(Y,X_62) ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(commutator(Y,X_62))),bind(Y0,$fot(commutator(Y,multiply(Y,X_62))))]]) ).

cnf(refute_0_702,plain,
    commutator(Y,multiply(Y,X_62)) = commutator(Y,X_62),
    inference(resolve,[$cnf( $equal(commutator(Y,X_62),commutator(Y,multiply(Y,X_62))) )],[refute_0_700,refute_0_701]) ).

cnf(refute_0_703,plain,
    commutator(X_63,multiply(X_63,Y)) = commutator(X_63,Y),
    inference(subst,[],[refute_0_702:[bind(Y,$fot(X_63)),bind(X_62,$fot(Y))]]) ).

cnf(refute_0_704,plain,
    commutator(multiply(X_63,Y),inverse(X_63)) = commutator(X_63,multiply(X_63,Y)),
    inference(subst,[],[refute_0_584:[bind(Y,$fot(X_63)),bind(X_65,$fot(multiply(X_63,Y)))]]) ).

cnf(refute_0_705,plain,
    ( commutator(X_63,multiply(X_63,Y)) != commutator(X_63,Y)
    | commutator(multiply(X_63,Y),inverse(X_63)) != commutator(X_63,multiply(X_63,Y))
    | commutator(multiply(X_63,Y),inverse(X_63)) = commutator(X_63,Y) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(commutator(multiply(X_63,Y),inverse(X_63)))),bind(Y0,$fot(commutator(X_63,multiply(X_63,Y)))),bind(Z0,$fot(commutator(X_63,Y)))]]) ).

cnf(refute_0_706,plain,
    ( commutator(X_63,multiply(X_63,Y)) != commutator(X_63,Y)
    | commutator(multiply(X_63,Y),inverse(X_63)) = commutator(X_63,Y) ),
    inference(resolve,[$cnf( $equal(commutator(multiply(X_63,Y),inverse(X_63)),commutator(X_63,multiply(X_63,Y))) )],[refute_0_704,refute_0_705]) ).

cnf(refute_0_707,plain,
    commutator(multiply(X_63,Y),inverse(X_63)) = commutator(X_63,Y),
    inference(resolve,[$cnf( $equal(commutator(X_63,multiply(X_63,Y)),commutator(X_63,Y)) )],[refute_0_703,refute_0_706]) ).

cnf(refute_0_708,plain,
    commutator(inverse(X_63),inverse(multiply(X_63,Y))) = commutator(multiply(X_63,Y),inverse(X_63)),
    inference(subst,[],[refute_0_584:[bind(Y,$fot(multiply(X_63,Y))),bind(X_65,$fot(inverse(X_63)))]]) ).

cnf(refute_0_709,plain,
    ( commutator(multiply(X_63,Y),inverse(X_63)) != commutator(X_63,Y)
    | commutator(inverse(X_63),inverse(multiply(X_63,Y))) != commutator(multiply(X_63,Y),inverse(X_63))
    | commutator(inverse(X_63),inverse(multiply(X_63,Y))) = commutator(X_63,Y) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(commutator(inverse(X_63),inverse(multiply(X_63,Y))))),bind(Y0,$fot(commutator(multiply(X_63,Y),inverse(X_63)))),bind(Z0,$fot(commutator(X_63,Y)))]]) ).

cnf(refute_0_710,plain,
    ( commutator(multiply(X_63,Y),inverse(X_63)) != commutator(X_63,Y)
    | commutator(inverse(X_63),inverse(multiply(X_63,Y))) = commutator(X_63,Y) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_63),inverse(multiply(X_63,Y))),commutator(multiply(X_63,Y),inverse(X_63))) )],[refute_0_708,refute_0_709]) ).

cnf(refute_0_711,plain,
    commutator(inverse(X_63),inverse(multiply(X_63,Y))) = commutator(X_63,Y),
    inference(resolve,[$cnf( $equal(commutator(multiply(X_63,Y),inverse(X_63)),commutator(X_63,Y)) )],[refute_0_707,refute_0_710]) ).

cnf(refute_0_712,plain,
    ( commutator(multiply(Y,multiply(X_63,Y)),X_63) != commutator(inverse(X_63),inverse(multiply(X_63,Y)))
    | commutator(inverse(X_63),inverse(multiply(X_63,Y))) != commutator(X_63,Y)
    | commutator(multiply(Y,multiply(X_63,Y)),X_63) = commutator(X_63,Y) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(commutator(multiply(Y,multiply(X_63,Y)),X_63),commutator(X_63,Y)) ),[0],$fot(commutator(inverse(X_63),inverse(multiply(X_63,Y))))]]) ).

cnf(refute_0_713,plain,
    ( commutator(multiply(Y,multiply(X_63,Y)),X_63) != commutator(inverse(X_63),inverse(multiply(X_63,Y)))
    | commutator(multiply(Y,multiply(X_63,Y)),X_63) = commutator(X_63,Y) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_63),inverse(multiply(X_63,Y))),commutator(X_63,Y)) )],[refute_0_711,refute_0_712]) ).

cnf(refute_0_714,plain,
    commutator(multiply(Y,multiply(X_63,Y)),X_63) = commutator(X_63,Y),
    inference(resolve,[$cnf( $equal(commutator(multiply(Y,multiply(X_63,Y)),X_63),commutator(inverse(X_63),inverse(multiply(X_63,Y)))) )],[refute_0_696,refute_0_713]) ).

cnf(refute_0_715,plain,
    commutator(multiply(X_70,multiply(X_31,X_70)),X_31) = commutator(X_31,X_70),
    inference(subst,[],[refute_0_714:[bind(Y,$fot(X_70)),bind(X_63,$fot(X_31))]]) ).

cnf(refute_0_716,plain,
    multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)) = multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)),
    introduced(tautology,[refl,[$fot(multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)))]]) ).

cnf(refute_0_717,plain,
    ( multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)) != multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))
    | commutator(multiply(X_70,multiply(X_31,X_70)),X_31) != commutator(X_31,X_70)
    | multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)) = multiply(X_31,commutator(X_31,X_70)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) ),[1,1],$fot(commutator(X_31,X_70))]]) ).

cnf(refute_0_718,plain,
    ( commutator(multiply(X_70,multiply(X_31,X_70)),X_31) != commutator(X_31,X_70)
    | multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)) = multiply(X_31,commutator(X_31,X_70)) ),
    inference(resolve,[$cnf( $equal(multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) )],[refute_0_716,refute_0_717]) ).

cnf(refute_0_719,plain,
    multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)) = multiply(X_31,commutator(X_31,X_70)),
    inference(resolve,[$cnf( $equal(commutator(multiply(X_70,multiply(X_31,X_70)),X_31),commutator(X_31,X_70)) )],[refute_0_715,refute_0_718]) ).

cnf(refute_0_720,plain,
    multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) = multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))),
    introduced(tautology,[refl,[$fot(multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))))]]) ).

cnf(refute_0_721,plain,
    ( multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)) != multiply(X_31,commutator(X_31,X_70))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) != multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) = multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))),multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)))) ),[1,1],$fot(multiply(X_31,commutator(X_31,X_70)))]]) ).

cnf(refute_0_722,plain,
    ( multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)) != multiply(X_31,commutator(X_31,X_70))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) = multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))),multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)))) )],[refute_0_720,refute_0_721]) ).

cnf(refute_0_723,plain,
    multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) = multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))),
    inference(resolve,[$cnf( $equal(multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)),multiply(X_31,commutator(X_31,X_70))) )],[refute_0_719,refute_0_722]) ).

cnf(refute_0_724,plain,
    ( multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) != multiply(X_31,commutator(X_31,commutator(X_31,X_70)))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) != multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70)))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))))),bind(Y0,$fot(multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))))),bind(Z0,$fot(multiply(X_31,commutator(X_31,commutator(X_31,X_70)))))]]) ).

cnf(refute_0_725,plain,
    ( multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))) != multiply(X_31,commutator(X_31,commutator(X_31,X_70)))
    | multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))),multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70)))) )],[refute_0_723,refute_0_724]) ).

cnf(refute_0_726,plain,
    multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(X_31,commutator(X_31,X_70))),multiply(X_31,commutator(X_31,commutator(X_31,X_70)))) )],[refute_0_689,refute_0_725]) ).

cnf(refute_0_727,plain,
    multiply(multiply(X,Y),multiply(X_52,inverse(Y))) = multiply(X,multiply(Y,multiply(X_52,inverse(Y)))),
    inference(subst,[],[associativity:[bind(Z,$fot(multiply(X_52,inverse(Y))))]]) ).

cnf(refute_0_728,plain,
    multiply(Y,multiply(X_52,inverse(Y))) = multiply(commutator(Y,X_52),X_52),
    inference(subst,[],[refute_0_665:[bind(X_14,$fot(X_52)),bind(X_50,$fot(Y))]]) ).

cnf(refute_0_729,plain,
    ( multiply(Y,multiply(X_52,inverse(Y))) != multiply(commutator(Y,X_52),X_52)
    | multiply(multiply(X,Y),multiply(X_52,inverse(Y))) != multiply(X,multiply(Y,multiply(X_52,inverse(Y))))
    | multiply(multiply(X,Y),multiply(X_52,inverse(Y))) = multiply(X,multiply(commutator(Y,X_52),X_52)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),multiply(X_52,inverse(Y))),multiply(X,multiply(Y,multiply(X_52,inverse(Y))))) ),[1,1],$fot(multiply(commutator(Y,X_52),X_52))]]) ).

cnf(refute_0_730,plain,
    ( multiply(multiply(X,Y),multiply(X_52,inverse(Y))) != multiply(X,multiply(Y,multiply(X_52,inverse(Y))))
    | multiply(multiply(X,Y),multiply(X_52,inverse(Y))) = multiply(X,multiply(commutator(Y,X_52),X_52)) ),
    inference(resolve,[$cnf( $equal(multiply(Y,multiply(X_52,inverse(Y))),multiply(commutator(Y,X_52),X_52)) )],[refute_0_728,refute_0_729]) ).

cnf(refute_0_731,plain,
    multiply(multiply(X,Y),multiply(X_52,inverse(Y))) = multiply(X,multiply(commutator(Y,X_52),X_52)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),multiply(X_52,inverse(Y))),multiply(X,multiply(Y,multiply(X_52,inverse(Y))))) )],[refute_0_727,refute_0_730]) ).

cnf(refute_0_732,plain,
    ( multiply(multiply(X,Y),multiply(X_52,inverse(Y))) != multiply(X,multiply(Y,multiply(X_52,inverse(Y))))
    | multiply(multiply(X,Y),multiply(X_52,inverse(Y))) != multiply(X,multiply(commutator(Y,X_52),X_52))
    | multiply(X,multiply(Y,multiply(X_52,inverse(Y)))) = multiply(X,multiply(commutator(Y,X_52),X_52)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),multiply(X_52,inverse(Y))),multiply(X,multiply(commutator(Y,X_52),X_52))) ),[0],$fot(multiply(X,multiply(Y,multiply(X_52,inverse(Y)))))]]) ).

cnf(refute_0_733,plain,
    ( multiply(multiply(X,Y),multiply(X_52,inverse(Y))) != multiply(X,multiply(commutator(Y,X_52),X_52))
    | multiply(X,multiply(Y,multiply(X_52,inverse(Y)))) = multiply(X,multiply(commutator(Y,X_52),X_52)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),multiply(X_52,inverse(Y))),multiply(X,multiply(Y,multiply(X_52,inverse(Y))))) )],[refute_0_727,refute_0_732]) ).

cnf(refute_0_734,plain,
    multiply(X,multiply(Y,multiply(X_52,inverse(Y)))) = multiply(X,multiply(commutator(Y,X_52),X_52)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),multiply(X_52,inverse(Y))),multiply(X,multiply(commutator(Y,X_52),X_52))) )],[refute_0_731,refute_0_733]) ).

cnf(refute_0_735,plain,
    multiply(commutator(Y,X_52),X_52) = multiply(X_52,commutator(Y,X_52)),
    inference(subst,[],[refute_0_681:[bind(X_14,$fot(X_52))]]) ).

cnf(refute_0_736,plain,
    multiply(X,multiply(commutator(Y,X_52),X_52)) = multiply(X,multiply(commutator(Y,X_52),X_52)),
    introduced(tautology,[refl,[$fot(multiply(X,multiply(commutator(Y,X_52),X_52)))]]) ).

cnf(refute_0_737,plain,
    ( multiply(X,multiply(commutator(Y,X_52),X_52)) != multiply(X,multiply(commutator(Y,X_52),X_52))
    | multiply(commutator(Y,X_52),X_52) != multiply(X_52,commutator(Y,X_52))
    | multiply(X,multiply(commutator(Y,X_52),X_52)) = multiply(X,multiply(X_52,commutator(Y,X_52))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(commutator(Y,X_52),X_52)),multiply(X,multiply(commutator(Y,X_52),X_52))) ),[1,1],$fot(multiply(X_52,commutator(Y,X_52)))]]) ).

cnf(refute_0_738,plain,
    ( multiply(commutator(Y,X_52),X_52) != multiply(X_52,commutator(Y,X_52))
    | multiply(X,multiply(commutator(Y,X_52),X_52)) = multiply(X,multiply(X_52,commutator(Y,X_52))) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(commutator(Y,X_52),X_52)),multiply(X,multiply(commutator(Y,X_52),X_52))) )],[refute_0_736,refute_0_737]) ).

cnf(refute_0_739,plain,
    multiply(X,multiply(commutator(Y,X_52),X_52)) = multiply(X,multiply(X_52,commutator(Y,X_52))),
    inference(resolve,[$cnf( $equal(multiply(commutator(Y,X_52),X_52),multiply(X_52,commutator(Y,X_52))) )],[refute_0_735,refute_0_738]) ).

cnf(refute_0_740,plain,
    ( multiply(X,multiply(Y,multiply(X_52,inverse(Y)))) != multiply(X,multiply(commutator(Y,X_52),X_52))
    | multiply(X,multiply(commutator(Y,X_52),X_52)) != multiply(X,multiply(X_52,commutator(Y,X_52)))
    | multiply(X,multiply(Y,multiply(X_52,inverse(Y)))) = multiply(X,multiply(X_52,commutator(Y,X_52))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,multiply(Y,multiply(X_52,inverse(Y)))),multiply(X,multiply(X_52,commutator(Y,X_52)))) ),[0],$fot(multiply(X,multiply(commutator(Y,X_52),X_52)))]]) ).

cnf(refute_0_741,plain,
    ( multiply(X,multiply(Y,multiply(X_52,inverse(Y)))) != multiply(X,multiply(commutator(Y,X_52),X_52))
    | multiply(X,multiply(Y,multiply(X_52,inverse(Y)))) = multiply(X,multiply(X_52,commutator(Y,X_52))) ),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(commutator(Y,X_52),X_52)),multiply(X,multiply(X_52,commutator(Y,X_52)))) )],[refute_0_739,refute_0_740]) ).

cnf(refute_0_742,plain,
    multiply(X,multiply(Y,multiply(X_52,inverse(Y)))) = multiply(X,multiply(X_52,commutator(Y,X_52))),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,multiply(X_52,inverse(Y)))),multiply(X,multiply(commutator(Y,X_52),X_52))) )],[refute_0_734,refute_0_741]) ).

cnf(refute_0_743,plain,
    multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) = multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))),
    inference(subst,[],[refute_0_742:[bind(X,$fot(commutator(X_70,X_31))),bind(Y,$fot(multiply(X_70,multiply(X_31,X_70)))),bind(X_52,$fot(X_31))]]) ).

cnf(refute_0_744,plain,
    ( multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) != multiply(X_31,commutator(X_31,commutator(X_31,X_70)))
    | multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) != multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)))
    | multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))))),bind(Y0,$fot(multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))))),bind(Z0,$fot(multiply(X_31,commutator(X_31,commutator(X_31,X_70)))))]]) ).

cnf(refute_0_745,plain,
    ( multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))) != multiply(X_31,commutator(X_31,commutator(X_31,X_70)))
    | multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))) ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))),multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31)))) )],[refute_0_743,refute_0_744]) ).

cnf(refute_0_746,plain,
    multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) = multiply(X_31,commutator(X_31,commutator(X_31,X_70))),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(X_31,commutator(multiply(X_70,multiply(X_31,X_70)),X_31))),multiply(X_31,commutator(X_31,commutator(X_31,X_70)))) )],[refute_0_726,refute_0_745]) ).

cnf(refute_0_747,plain,
    ( multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) != X_31
    | multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) != multiply(X_31,commutator(X_31,commutator(X_31,X_70)))
    | multiply(X_31,commutator(X_31,commutator(X_31,X_70))) = X_31 ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))),X_31) ),[0],$fot(multiply(X_31,commutator(X_31,commutator(X_31,X_70))))]]) ).

cnf(refute_0_748,plain,
    ( multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))) != X_31
    | multiply(X_31,commutator(X_31,commutator(X_31,X_70))) = X_31 ),
    inference(resolve,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))),multiply(X_31,commutator(X_31,commutator(X_31,X_70)))) )],[refute_0_746,refute_0_747]) ).

cnf(refute_0_749,plain,
    multiply(X_31,commutator(X_31,commutator(X_31,X_70))) = X_31,
    inference(resolve,[$cnf( $equal(multiply(commutator(X_70,X_31),multiply(multiply(X_70,multiply(X_31,X_70)),multiply(X_31,inverse(multiply(X_70,multiply(X_31,X_70)))))),X_31) )],[refute_0_604,refute_0_748]) ).

cnf(refute_0_750,plain,
    multiply(inverse(X_11),commutator(inverse(X_11),commutator(inverse(X_11),X_72))) = inverse(X_11),
    inference(subst,[],[refute_0_749:[bind(X_31,$fot(inverse(X_11))),bind(X_70,$fot(X_72))]]) ).

cnf(refute_0_751,plain,
    ( multiply(inverse(X_11),commutator(inverse(X_11),commutator(inverse(X_11),X_72))) != inverse(X_11)
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) != multiply(X_11,multiply(inverse(X_11),commutator(inverse(X_11),commutator(inverse(X_11),X_72))))
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = multiply(X_11,inverse(X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(X_11),commutator(inverse(X_11),X_72)),multiply(X_11,multiply(inverse(X_11),commutator(inverse(X_11),commutator(inverse(X_11),X_72))))) ),[1,1],$fot(inverse(X_11))]]) ).

cnf(refute_0_752,plain,
    ( commutator(inverse(X_11),commutator(inverse(X_11),X_72)) != multiply(X_11,multiply(inverse(X_11),commutator(inverse(X_11),commutator(inverse(X_11),X_72))))
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = multiply(X_11,inverse(X_11)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_11),commutator(inverse(X_11),commutator(inverse(X_11),X_72))),inverse(X_11)) )],[refute_0_750,refute_0_751]) ).

cnf(refute_0_753,plain,
    commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = multiply(X_11,inverse(X_11)),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_11),commutator(inverse(X_11),X_72)),multiply(X_11,multiply(inverse(X_11),commutator(inverse(X_11),commutator(inverse(X_11),X_72))))) )],[refute_0_595,refute_0_752]) ).

cnf(refute_0_754,plain,
    commutator(X_72,inverse(X_11)) = commutator(X_11,X_72),
    inference(subst,[],[refute_0_584:[bind(Y,$fot(X_11)),bind(X_65,$fot(X_72))]]) ).

cnf(refute_0_755,plain,
    commutator(X_11,commutator(X_72,inverse(X_11))) = commutator(X_11,commutator(X_72,inverse(X_11))),
    introduced(tautology,[refl,[$fot(commutator(X_11,commutator(X_72,inverse(X_11))))]]) ).

cnf(refute_0_756,plain,
    ( commutator(X_11,commutator(X_72,inverse(X_11))) != commutator(X_11,commutator(X_72,inverse(X_11)))
    | commutator(X_72,inverse(X_11)) != commutator(X_11,X_72)
    | commutator(X_11,commutator(X_72,inverse(X_11))) = commutator(X_11,commutator(X_11,X_72)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X_11,commutator(X_72,inverse(X_11))),commutator(X_11,commutator(X_72,inverse(X_11)))) ),[1,1],$fot(commutator(X_11,X_72))]]) ).

cnf(refute_0_757,plain,
    ( commutator(X_72,inverse(X_11)) != commutator(X_11,X_72)
    | commutator(X_11,commutator(X_72,inverse(X_11))) = commutator(X_11,commutator(X_11,X_72)) ),
    inference(resolve,[$cnf( $equal(commutator(X_11,commutator(X_72,inverse(X_11))),commutator(X_11,commutator(X_72,inverse(X_11)))) )],[refute_0_755,refute_0_756]) ).

cnf(refute_0_758,plain,
    commutator(X_11,commutator(X_72,inverse(X_11))) = commutator(X_11,commutator(X_11,X_72)),
    inference(resolve,[$cnf( $equal(commutator(X_72,inverse(X_11)),commutator(X_11,X_72)) )],[refute_0_754,refute_0_757]) ).

cnf(refute_0_759,plain,
    commutator(commutator(inverse(X_11),X_72),X_11) = commutator(X_11,commutator(X_72,inverse(X_11))),
    inference(subst,[],[refute_0_590:[bind(X,$fot(X_72)),bind(Y,$fot(inverse(X_11))),bind(X_68,$fot(X_11))]]) ).

cnf(refute_0_760,plain,
    commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = commutator(commutator(inverse(X_11),X_72),X_11),
    inference(subst,[],[refute_0_495:[bind(X_13,$fot(X_11)),bind(X_65,$fot(commutator(inverse(X_11),X_72)))]]) ).

cnf(refute_0_761,plain,
    ( commutator(commutator(inverse(X_11),X_72),X_11) != commutator(X_11,commutator(X_72,inverse(X_11)))
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) != commutator(commutator(inverse(X_11),X_72),X_11)
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = commutator(X_11,commutator(X_72,inverse(X_11))) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(commutator(inverse(X_11),commutator(inverse(X_11),X_72)))),bind(Y0,$fot(commutator(commutator(inverse(X_11),X_72),X_11))),bind(Z0,$fot(commutator(X_11,commutator(X_72,inverse(X_11)))))]]) ).

cnf(refute_0_762,plain,
    ( commutator(commutator(inverse(X_11),X_72),X_11) != commutator(X_11,commutator(X_72,inverse(X_11)))
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = commutator(X_11,commutator(X_72,inverse(X_11))) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_11),commutator(inverse(X_11),X_72)),commutator(commutator(inverse(X_11),X_72),X_11)) )],[refute_0_760,refute_0_761]) ).

cnf(refute_0_763,plain,
    commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = commutator(X_11,commutator(X_72,inverse(X_11))),
    inference(resolve,[$cnf( $equal(commutator(commutator(inverse(X_11),X_72),X_11),commutator(X_11,commutator(X_72,inverse(X_11)))) )],[refute_0_759,refute_0_762]) ).

cnf(refute_0_764,plain,
    ( commutator(X_11,commutator(X_72,inverse(X_11))) != commutator(X_11,commutator(X_11,X_72))
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) != commutator(X_11,commutator(X_72,inverse(X_11)))
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = commutator(X_11,commutator(X_11,X_72)) ),
    inference(subst,[],[refute_0_75:[bind(X0,$fot(commutator(inverse(X_11),commutator(inverse(X_11),X_72)))),bind(Y0,$fot(commutator(X_11,commutator(X_72,inverse(X_11))))),bind(Z0,$fot(commutator(X_11,commutator(X_11,X_72))))]]) ).

cnf(refute_0_765,plain,
    ( commutator(X_11,commutator(X_72,inverse(X_11))) != commutator(X_11,commutator(X_11,X_72))
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = commutator(X_11,commutator(X_11,X_72)) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_11),commutator(inverse(X_11),X_72)),commutator(X_11,commutator(X_72,inverse(X_11)))) )],[refute_0_763,refute_0_764]) ).

cnf(refute_0_766,plain,
    commutator(inverse(X_11),commutator(inverse(X_11),X_72)) = commutator(X_11,commutator(X_11,X_72)),
    inference(resolve,[$cnf( $equal(commutator(X_11,commutator(X_72,inverse(X_11))),commutator(X_11,commutator(X_11,X_72))) )],[refute_0_758,refute_0_765]) ).

cnf(refute_0_767,plain,
    ( commutator(inverse(X_11),commutator(inverse(X_11),X_72)) != multiply(X_11,inverse(X_11))
    | commutator(inverse(X_11),commutator(inverse(X_11),X_72)) != commutator(X_11,commutator(X_11,X_72))
    | commutator(X_11,commutator(X_11,X_72)) = multiply(X_11,inverse(X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(inverse(X_11),commutator(inverse(X_11),X_72)),multiply(X_11,inverse(X_11))) ),[0],$fot(commutator(X_11,commutator(X_11,X_72)))]]) ).

cnf(refute_0_768,plain,
    ( commutator(inverse(X_11),commutator(inverse(X_11),X_72)) != multiply(X_11,inverse(X_11))
    | commutator(X_11,commutator(X_11,X_72)) = multiply(X_11,inverse(X_11)) ),
    inference(resolve,[$cnf( $equal(commutator(inverse(X_11),commutator(inverse(X_11),X_72)),commutator(X_11,commutator(X_11,X_72))) )],[refute_0_766,refute_0_767]) ).

cnf(refute_0_769,plain,
    ( multiply(X_11,inverse(X_11)) != identity
    | commutator(X_11,commutator(X_11,X_72)) != multiply(X_11,inverse(X_11))
    | commutator(X_11,commutator(X_11,X_72)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(commutator(X_11,commutator(X_11,X_72)),multiply(X_11,inverse(X_11))) ),[1],$fot(identity)]]) ).

cnf(refute_0_770,plain,
    ( commutator(X_11,commutator(X_11,X_72)) != multiply(X_11,inverse(X_11))
    | commutator(X_11,commutator(X_11,X_72)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(X_11,inverse(X_11)),identity) )],[refute_0_2,refute_0_769]) ).

cnf(refute_0_771,plain,
    ( commutator(inverse(X_11),commutator(inverse(X_11),X_72)) != multiply(X_11,inverse(X_11))
    | commutator(X_11,commutator(X_11,X_72)) = identity ),
    inference(resolve,[$cnf( $equal(commutator(X_11,commutator(X_11,X_72)),multiply(X_11,inverse(X_11))) )],[refute_0_768,refute_0_770]) ).

cnf(refute_0_772,plain,
    commutator(X_11,commutator(X_11,X_72)) = identity,
    inference(resolve,[$cnf( $equal(commutator(inverse(X_11),commutator(inverse(X_11),X_72)),multiply(X_11,inverse(X_11))) )],[refute_0_753,refute_0_771]) ).

cnf(refute_0_773,plain,
    commutator(b,commutator(b,a)) = identity,
    inference(subst,[],[refute_0_772:[bind(X_11,$fot(b)),bind(X_72,$fot(a))]]) ).

cnf(refute_0_774,plain,
    ( commutator(b,commutator(b,a)) != identity
    | identity != identity
    | commutator(b,commutator(b,a)) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(commutator(b,commutator(b,a)),identity) ),[0],$fot(identity)]]) ).

cnf(refute_0_775,plain,
    ( identity != identity
    | commutator(b,commutator(b,a)) = identity ),
    inference(resolve,[$cnf( $equal(commutator(b,commutator(b,a)),identity) )],[refute_0_773,refute_0_774]) ).

cnf(refute_0_776,plain,
    identity != identity,
    inference(resolve,[$cnf( $equal(commutator(b,commutator(b,a)),identity) )],[refute_0_775,refute_0_594]) ).

cnf(refute_0_777,plain,
    identity = identity,
    introduced(tautology,[refl,[$fot(identity)]]) ).

cnf(refute_0_778,plain,
    $false,
    inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_777,refute_0_776]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP002-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n008.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  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 16:29:07 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.62  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.62  
% 0.41/0.62  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.57/0.74  
%------------------------------------------------------------------------------