TSTP Solution File: GRP002-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 10:32:09 EDT 2022
% Result : Unsatisfiable 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 101
% Syntax : Number of clauses : 392 ( 199 unt; 0 nHn; 297 RR)
% Number of literals : 670 ( 669 equ; 279 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 231 ( 0 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(x_cubed_is_identity,hypothesis,
multiply(X,multiply(X,X)) = identity ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
multiply(c,inverse(a)) = d ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
multiply(d,inverse(b)) = h ).
cnf(h_times_b_is_j,negated_conjecture,
multiply(h,b) = j ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
multiply(j,inverse(h)) = k ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
multiply(k,inverse(b)) != identity ).
cnf(refute_0_0,plain,
multiply(inverse(multiply(c,a)),multiply(c,a)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(multiply(c,a)))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_6),X_6),X_7) = multiply(inverse(X_6),multiply(X_6,X_7)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_6))),bind(Y,$fot(X_6)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_6),X_6) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_6),X_6),X_7) != multiply(inverse(X_6),multiply(X_6,X_7))
| multiply(inverse(X_6),X_6) != identity
| multiply(identity,X_7) = multiply(inverse(X_6),multiply(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_6),X_6),X_7),multiply(inverse(X_6),multiply(X_6,X_7))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_6),X_6),X_7) != multiply(inverse(X_6),multiply(X_6,X_7))
| multiply(identity,X_7) = multiply(inverse(X_6),multiply(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_6),X_6),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_7) = multiply(inverse(X_6),multiply(X_6,X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),X_6),X_7),multiply(inverse(X_6),multiply(X_6,X_7))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_7) = X_7,
inference(subst,[],[left_identity:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_7) != X_7
| multiply(identity,X_7) != multiply(inverse(X_6),multiply(X_6,X_7))
| X_7 = multiply(inverse(X_6),multiply(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_7),multiply(inverse(X_6),multiply(X_6,X_7))) ),[0],$fot(X_7)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_7) != multiply(inverse(X_6),multiply(X_6,X_7))
| X_7 = multiply(inverse(X_6),multiply(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_7),X_7) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_7 = multiply(inverse(X_6),multiply(X_6,X_7)),
inference(resolve,[$cnf( $equal(multiply(identity,X_7),multiply(inverse(X_6),multiply(X_6,X_7))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(k,c) = multiply(inverse(inverse(c)),multiply(inverse(c),multiply(k,c))),
inference(subst,[],[refute_0_9:[bind(X_6,$fot(inverse(c))),bind(X_7,$fot(multiply(k,c)))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(X_5,multiply(X_5,X_5)),X_7) = multiply(X_5,multiply(multiply(X_5,X_5),X_7)),
inference(subst,[],[associativity:[bind(X,$fot(X_5)),bind(Y,$fot(multiply(X_5,X_5))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_12,plain,
multiply(X_5,multiply(X_5,X_5)) = identity,
inference(subst,[],[x_cubed_is_identity:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_13,plain,
( multiply(X_5,multiply(X_5,X_5)) != identity
| multiply(multiply(X_5,multiply(X_5,X_5)),X_7) != multiply(X_5,multiply(multiply(X_5,X_5),X_7))
| multiply(identity,X_7) = multiply(X_5,multiply(multiply(X_5,X_5),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_5,multiply(X_5,X_5)),X_7),multiply(X_5,multiply(multiply(X_5,X_5),X_7))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_14,plain,
( multiply(multiply(X_5,multiply(X_5,X_5)),X_7) != multiply(X_5,multiply(multiply(X_5,X_5),X_7))
| multiply(identity,X_7) = multiply(X_5,multiply(multiply(X_5,X_5),X_7)) ),
inference(resolve,[$cnf( $equal(multiply(X_5,multiply(X_5,X_5)),identity) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(identity,X_7) = multiply(X_5,multiply(multiply(X_5,X_5),X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_5,multiply(X_5,X_5)),X_7),multiply(X_5,multiply(multiply(X_5,X_5),X_7))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( multiply(identity,X_7) != X_7
| multiply(identity,X_7) != multiply(X_5,multiply(multiply(X_5,X_5),X_7))
| X_7 = multiply(X_5,multiply(multiply(X_5,X_5),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_7),multiply(X_5,multiply(multiply(X_5,X_5),X_7))) ),[0],$fot(X_7)]]) ).
cnf(refute_0_17,plain,
( multiply(identity,X_7) != multiply(X_5,multiply(multiply(X_5,X_5),X_7))
| X_7 = multiply(X_5,multiply(multiply(X_5,X_5),X_7)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_7),X_7) )],[refute_0_6,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(multiply(X_5,X_5),X_7) = multiply(X_5,multiply(X_5,X_7)),
inference(subst,[],[associativity:[bind(X,$fot(X_5)),bind(Y,$fot(X_5)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_19,plain,
multiply(X_5,multiply(multiply(X_5,X_5),X_7)) = multiply(X_5,multiply(multiply(X_5,X_5),X_7)),
introduced(tautology,[refl,[$fot(multiply(X_5,multiply(multiply(X_5,X_5),X_7)))]]) ).
cnf(refute_0_20,plain,
( multiply(X_5,multiply(multiply(X_5,X_5),X_7)) != multiply(X_5,multiply(multiply(X_5,X_5),X_7))
| multiply(multiply(X_5,X_5),X_7) != multiply(X_5,multiply(X_5,X_7))
| multiply(X_5,multiply(multiply(X_5,X_5),X_7)) = multiply(X_5,multiply(X_5,multiply(X_5,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_5,multiply(multiply(X_5,X_5),X_7)),multiply(X_5,multiply(multiply(X_5,X_5),X_7))) ),[1,1],$fot(multiply(X_5,multiply(X_5,X_7)))]]) ).
cnf(refute_0_21,plain,
( multiply(multiply(X_5,X_5),X_7) != multiply(X_5,multiply(X_5,X_7))
| multiply(X_5,multiply(multiply(X_5,X_5),X_7)) = multiply(X_5,multiply(X_5,multiply(X_5,X_7))) ),
inference(resolve,[$cnf( $equal(multiply(X_5,multiply(multiply(X_5,X_5),X_7)),multiply(X_5,multiply(multiply(X_5,X_5),X_7))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_5,multiply(multiply(X_5,X_5),X_7)) = multiply(X_5,multiply(X_5,multiply(X_5,X_7))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_5,X_5),X_7),multiply(X_5,multiply(X_5,X_7))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( X_7 != multiply(X_5,multiply(multiply(X_5,X_5),X_7))
| multiply(X_5,multiply(multiply(X_5,X_5),X_7)) != multiply(X_5,multiply(X_5,multiply(X_5,X_7)))
| X_7 = multiply(X_5,multiply(X_5,multiply(X_5,X_7))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_7,multiply(X_5,multiply(X_5,multiply(X_5,X_7)))) ),[0],$fot(multiply(X_5,multiply(multiply(X_5,X_5),X_7)))]]) ).
cnf(refute_0_24,plain,
( X_7 != multiply(X_5,multiply(multiply(X_5,X_5),X_7))
| X_7 = multiply(X_5,multiply(X_5,multiply(X_5,X_7))) ),
inference(resolve,[$cnf( $equal(multiply(X_5,multiply(multiply(X_5,X_5),X_7)),multiply(X_5,multiply(X_5,multiply(X_5,X_7)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(identity,X_7) != multiply(X_5,multiply(multiply(X_5,X_5),X_7))
| X_7 = multiply(X_5,multiply(X_5,multiply(X_5,X_7))) ),
inference(resolve,[$cnf( $equal(X_7,multiply(X_5,multiply(multiply(X_5,X_5),X_7))) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
X_7 = multiply(X_5,multiply(X_5,multiply(X_5,X_7))),
inference(resolve,[$cnf( $equal(multiply(identity,X_7),multiply(X_5,multiply(multiply(X_5,X_5),X_7))) )],[refute_0_15,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(inverse(a),X_7) = multiply(c,multiply(c,multiply(c,multiply(inverse(a),X_7)))),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(c)),bind(X_7,$fot(multiply(inverse(a),X_7)))]]) ).
cnf(refute_0_28,plain,
multiply(multiply(c,inverse(a)),X_7) = multiply(c,multiply(inverse(a),X_7)),
inference(subst,[],[associativity:[bind(X,$fot(c)),bind(Y,$fot(inverse(a))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_29,plain,
( multiply(multiply(c,inverse(a)),X_7) != multiply(c,multiply(inverse(a),X_7))
| multiply(c,inverse(a)) != d
| multiply(d,X_7) = multiply(c,multiply(inverse(a),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(c,inverse(a)),X_7),multiply(c,multiply(inverse(a),X_7))) ),[0,0],$fot(d)]]) ).
cnf(refute_0_30,plain,
( multiply(multiply(c,inverse(a)),X_7) != multiply(c,multiply(inverse(a),X_7))
| multiply(d,X_7) = multiply(c,multiply(inverse(a),X_7)) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(a)),d) )],[c_times_inverse_a_is_d,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(d,X_7) = multiply(c,multiply(inverse(a),X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(c,inverse(a)),X_7),multiply(c,multiply(inverse(a),X_7))) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_33,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_34,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(d,X_7) != multiply(c,multiply(inverse(a),X_7))
| multiply(c,multiply(inverse(a),X_7)) = multiply(d,X_7) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(d,X_7))),bind(Y0,$fot(multiply(c,multiply(inverse(a),X_7))))]]) ).
cnf(refute_0_36,plain,
multiply(c,multiply(inverse(a),X_7)) = multiply(d,X_7),
inference(resolve,[$cnf( $equal(multiply(d,X_7),multiply(c,multiply(inverse(a),X_7))) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
( multiply(c,multiply(inverse(a),X_7)) != multiply(d,X_7)
| multiply(inverse(a),X_7) != multiply(c,multiply(c,multiply(c,multiply(inverse(a),X_7))))
| multiply(inverse(a),X_7) = multiply(c,multiply(c,multiply(d,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),X_7),multiply(c,multiply(c,multiply(c,multiply(inverse(a),X_7))))) ),[1,1,1],$fot(multiply(d,X_7))]]) ).
cnf(refute_0_38,plain,
( multiply(inverse(a),X_7) != multiply(c,multiply(c,multiply(c,multiply(inverse(a),X_7))))
| multiply(inverse(a),X_7) = multiply(c,multiply(c,multiply(d,X_7))) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(inverse(a),X_7)),multiply(d,X_7)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(inverse(a),X_7) = multiply(c,multiply(c,multiply(d,X_7))),
inference(resolve,[$cnf( $equal(multiply(inverse(a),X_7),multiply(c,multiply(c,multiply(c,multiply(inverse(a),X_7))))) )],[refute_0_27,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(multiply(Y,Y),Z) = multiply(Y,multiply(Y,Z)),
inference(subst,[],[associativity:[bind(X,$fot(Y))]]) ).
cnf(refute_0_41,plain,
inverse(X_11) = multiply(X_11,multiply(X_11,multiply(X_11,inverse(X_11)))),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(X_11)),bind(X_7,$fot(inverse(X_11)))]]) ).
cnf(refute_0_42,plain,
multiply(X_11,inverse(X_11)) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_43,plain,
( multiply(X_11,inverse(X_11)) != identity
| inverse(X_11) != multiply(X_11,multiply(X_11,multiply(X_11,inverse(X_11))))
| inverse(X_11) = multiply(X_11,multiply(X_11,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_11),multiply(X_11,multiply(X_11,multiply(X_11,inverse(X_11))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_44,plain,
( inverse(X_11) != multiply(X_11,multiply(X_11,multiply(X_11,inverse(X_11))))
| inverse(X_11) = multiply(X_11,multiply(X_11,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_11,inverse(X_11)),identity) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
inverse(X_11) = multiply(X_11,multiply(X_11,identity)),
inference(resolve,[$cnf( $equal(inverse(X_11),multiply(X_11,multiply(X_11,multiply(X_11,inverse(X_11))))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(X_11,identity) = X_11,
inference(subst,[],[right_identity:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_47,plain,
multiply(X_11,multiply(X_11,identity)) = multiply(X_11,multiply(X_11,identity)),
introduced(tautology,[refl,[$fot(multiply(X_11,multiply(X_11,identity)))]]) ).
cnf(refute_0_48,plain,
( multiply(X_11,multiply(X_11,identity)) != multiply(X_11,multiply(X_11,identity))
| multiply(X_11,identity) != X_11
| multiply(X_11,multiply(X_11,identity)) = multiply(X_11,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,multiply(X_11,identity)),multiply(X_11,multiply(X_11,identity))) ),[1,1],$fot(X_11)]]) ).
cnf(refute_0_49,plain,
( multiply(X_11,identity) != X_11
| multiply(X_11,multiply(X_11,identity)) = multiply(X_11,X_11) ),
inference(resolve,[$cnf( $equal(multiply(X_11,multiply(X_11,identity)),multiply(X_11,multiply(X_11,identity))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(X_11,multiply(X_11,identity)) = multiply(X_11,X_11),
inference(resolve,[$cnf( $equal(multiply(X_11,identity),X_11) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
( multiply(X_11,multiply(X_11,identity)) != multiply(X_11,X_11)
| inverse(X_11) != multiply(X_11,multiply(X_11,identity))
| inverse(X_11) = multiply(X_11,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_11),multiply(X_11,multiply(X_11,identity))) ),[1],$fot(multiply(X_11,X_11))]]) ).
cnf(refute_0_52,plain,
( inverse(X_11) != multiply(X_11,multiply(X_11,identity))
| inverse(X_11) = multiply(X_11,X_11) ),
inference(resolve,[$cnf( $equal(multiply(X_11,multiply(X_11,identity)),multiply(X_11,X_11)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
inverse(X_11) = multiply(X_11,X_11),
inference(resolve,[$cnf( $equal(inverse(X_11),multiply(X_11,multiply(X_11,identity))) )],[refute_0_45,refute_0_52]) ).
cnf(refute_0_54,plain,
inverse(Y) = multiply(Y,Y),
inference(subst,[],[refute_0_53:[bind(X_11,$fot(Y))]]) ).
cnf(refute_0_55,plain,
( inverse(Y) != multiply(Y,Y)
| multiply(Y,Y) = inverse(Y) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(inverse(Y))),bind(Y0,$fot(multiply(Y,Y)))]]) ).
cnf(refute_0_56,plain,
multiply(Y,Y) = inverse(Y),
inference(resolve,[$cnf( $equal(inverse(Y),multiply(Y,Y)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( multiply(Y,Y) != inverse(Y)
| multiply(multiply(Y,Y),Z) != multiply(Y,multiply(Y,Z))
| multiply(inverse(Y),Z) = multiply(Y,multiply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(Y,Y),Z),multiply(Y,multiply(Y,Z))) ),[0,0],$fot(inverse(Y))]]) ).
cnf(refute_0_58,plain,
( multiply(multiply(Y,Y),Z) != multiply(Y,multiply(Y,Z))
| multiply(inverse(Y),Z) = multiply(Y,multiply(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(Y,Y),inverse(Y)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(inverse(Y),Z) = multiply(Y,multiply(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(Y,Y),Z),multiply(Y,multiply(Y,Z))) )],[refute_0_40,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiply(inverse(Y),Z) != multiply(Y,multiply(Y,Z))
| multiply(Y,multiply(Y,Z)) = multiply(inverse(Y),Z) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(inverse(Y),Z))),bind(Y0,$fot(multiply(Y,multiply(Y,Z))))]]) ).
cnf(refute_0_61,plain,
multiply(Y,multiply(Y,Z)) = multiply(inverse(Y),Z),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),Z),multiply(Y,multiply(Y,Z))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(c,multiply(c,multiply(d,X_7))) = multiply(inverse(c),multiply(d,X_7)),
inference(subst,[],[refute_0_61:[bind(Y,$fot(c)),bind(Z,$fot(multiply(d,X_7)))]]) ).
cnf(refute_0_63,plain,
( multiply(c,multiply(c,multiply(d,X_7))) != multiply(inverse(c),multiply(d,X_7))
| multiply(inverse(a),X_7) != multiply(c,multiply(c,multiply(d,X_7)))
| multiply(inverse(a),X_7) = multiply(inverse(c),multiply(d,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),X_7),multiply(c,multiply(c,multiply(d,X_7)))) ),[1],$fot(multiply(inverse(c),multiply(d,X_7)))]]) ).
cnf(refute_0_64,plain,
( multiply(inverse(a),X_7) != multiply(c,multiply(c,multiply(d,X_7)))
| multiply(inverse(a),X_7) = multiply(inverse(c),multiply(d,X_7)) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,multiply(d,X_7))),multiply(inverse(c),multiply(d,X_7))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(inverse(a),X_7) = multiply(inverse(c),multiply(d,X_7)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),X_7),multiply(c,multiply(c,multiply(d,X_7)))) )],[refute_0_39,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(inverse(a),multiply(b,a)) = multiply(inverse(c),multiply(d,multiply(b,a))),
inference(subst,[],[refute_0_65:[bind(X_7,$fot(multiply(b,a)))]]) ).
cnf(refute_0_67,plain,
multiply(multiply(j,inverse(h)),X_7) = multiply(j,multiply(inverse(h),X_7)),
inference(subst,[],[associativity:[bind(X,$fot(j)),bind(Y,$fot(inverse(h))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_68,plain,
( multiply(multiply(j,inverse(h)),X_7) != multiply(j,multiply(inverse(h),X_7))
| multiply(j,inverse(h)) != k
| multiply(k,X_7) = multiply(j,multiply(inverse(h),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(j,inverse(h)),X_7),multiply(j,multiply(inverse(h),X_7))) ),[0,0],$fot(k)]]) ).
cnf(refute_0_69,plain,
( multiply(multiply(j,inverse(h)),X_7) != multiply(j,multiply(inverse(h),X_7))
| multiply(k,X_7) = multiply(j,multiply(inverse(h),X_7)) ),
inference(resolve,[$cnf( $equal(multiply(j,inverse(h)),k) )],[j_times_inverse_h_is_k,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(k,X_7) = multiply(j,multiply(inverse(h),X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(j,inverse(h)),X_7),multiply(j,multiply(inverse(h),X_7))) )],[refute_0_67,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(multiply(d,inverse(b)),X_7) = multiply(d,multiply(inverse(b),X_7)),
inference(subst,[],[associativity:[bind(X,$fot(d)),bind(Y,$fot(inverse(b))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_72,plain,
( multiply(multiply(d,inverse(b)),X_7) != multiply(d,multiply(inverse(b),X_7))
| multiply(d,inverse(b)) != h
| multiply(h,X_7) = multiply(d,multiply(inverse(b),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(d,inverse(b)),X_7),multiply(d,multiply(inverse(b),X_7))) ),[0,0],$fot(h)]]) ).
cnf(refute_0_73,plain,
( multiply(multiply(d,inverse(b)),X_7) != multiply(d,multiply(inverse(b),X_7))
| multiply(h,X_7) = multiply(d,multiply(inverse(b),X_7)) ),
inference(resolve,[$cnf( $equal(multiply(d,inverse(b)),h) )],[d_times_inverse_b_is_h,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(h,X_7) = multiply(d,multiply(inverse(b),X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(d,inverse(b)),X_7),multiply(d,multiply(inverse(b),X_7))) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(h,b) = multiply(d,multiply(inverse(b),b)),
inference(subst,[],[refute_0_74:[bind(X_7,$fot(b))]]) ).
cnf(refute_0_76,plain,
multiply(inverse(b),b) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(b))]]) ).
cnf(refute_0_77,plain,
( multiply(h,b) != multiply(d,multiply(inverse(b),b))
| multiply(inverse(b),b) != identity
| multiply(h,b) = multiply(d,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(h,b),multiply(d,multiply(inverse(b),b))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_78,plain,
( multiply(h,b) != multiply(d,multiply(inverse(b),b))
| multiply(h,b) = multiply(d,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),b),identity) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(h,b) = multiply(d,identity),
inference(resolve,[$cnf( $equal(multiply(h,b),multiply(d,multiply(inverse(b),b))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( multiply(h,b) != multiply(d,identity)
| multiply(h,b) != j
| j = multiply(d,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(h,b),multiply(d,identity)) ),[0],$fot(j)]]) ).
cnf(refute_0_81,plain,
( multiply(h,b) != multiply(d,identity)
| j = multiply(d,identity) ),
inference(resolve,[$cnf( $equal(multiply(h,b),j) )],[h_times_b_is_j,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(d,identity) = d,
inference(subst,[],[right_identity:[bind(X,$fot(d))]]) ).
cnf(refute_0_83,plain,
( multiply(d,identity) != d
| j != multiply(d,identity)
| j = d ),
introduced(tautology,[equality,[$cnf( $equal(j,multiply(d,identity)) ),[1],$fot(d)]]) ).
cnf(refute_0_84,plain,
( j != multiply(d,identity)
| j = d ),
inference(resolve,[$cnf( $equal(multiply(d,identity),d) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( multiply(h,b) != multiply(d,identity)
| j = d ),
inference(resolve,[$cnf( $equal(j,multiply(d,identity)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
j = d,
inference(resolve,[$cnf( $equal(multiply(h,b),multiply(d,identity)) )],[refute_0_79,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(j,multiply(inverse(h),X_7)) = multiply(j,multiply(inverse(h),X_7)),
introduced(tautology,[refl,[$fot(multiply(j,multiply(inverse(h),X_7)))]]) ).
cnf(refute_0_88,plain,
( multiply(j,multiply(inverse(h),X_7)) != multiply(j,multiply(inverse(h),X_7))
| j != d
| multiply(j,multiply(inverse(h),X_7)) = multiply(d,multiply(inverse(h),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(j,multiply(inverse(h),X_7)),multiply(j,multiply(inverse(h),X_7))) ),[1,0],$fot(d)]]) ).
cnf(refute_0_89,plain,
( j != d
| multiply(j,multiply(inverse(h),X_7)) = multiply(d,multiply(inverse(h),X_7)) ),
inference(resolve,[$cnf( $equal(multiply(j,multiply(inverse(h),X_7)),multiply(j,multiply(inverse(h),X_7))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
multiply(j,multiply(inverse(h),X_7)) = multiply(d,multiply(inverse(h),X_7)),
inference(resolve,[$cnf( $equal(j,d) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( multiply(j,multiply(inverse(h),X_7)) != multiply(d,multiply(inverse(h),X_7))
| multiply(k,X_7) != multiply(j,multiply(inverse(h),X_7))
| multiply(k,X_7) = multiply(d,multiply(inverse(h),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(k,X_7),multiply(j,multiply(inverse(h),X_7))) ),[1],$fot(multiply(d,multiply(inverse(h),X_7)))]]) ).
cnf(refute_0_92,plain,
( multiply(k,X_7) != multiply(j,multiply(inverse(h),X_7))
| multiply(k,X_7) = multiply(d,multiply(inverse(h),X_7)) ),
inference(resolve,[$cnf( $equal(multiply(j,multiply(inverse(h),X_7)),multiply(d,multiply(inverse(h),X_7))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(k,X_7) = multiply(d,multiply(inverse(h),X_7)),
inference(resolve,[$cnf( $equal(multiply(k,X_7),multiply(j,multiply(inverse(h),X_7))) )],[refute_0_70,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(k,c) = multiply(d,multiply(inverse(h),c)),
inference(subst,[],[refute_0_93:[bind(X_7,$fot(c))]]) ).
cnf(refute_0_95,plain,
inverse(multiply(inverse(a),inverse(b))) = multiply(inverse(h),multiply(h,inverse(multiply(inverse(a),inverse(b))))),
inference(subst,[],[refute_0_9:[bind(X_6,$fot(h)),bind(X_7,$fot(inverse(multiply(inverse(a),inverse(b)))))]]) ).
cnf(refute_0_96,plain,
multiply(h,inverse(multiply(inverse(a),inverse(b)))) = multiply(d,multiply(inverse(b),inverse(multiply(inverse(a),inverse(b))))),
inference(subst,[],[refute_0_74:[bind(X_7,$fot(inverse(multiply(inverse(a),inverse(b)))))]]) ).
cnf(refute_0_97,plain,
multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) = multiply(c,multiply(inverse(a),multiply(X_16,inverse(multiply(inverse(a),X_16))))),
inference(subst,[],[refute_0_31:[bind(X_7,$fot(multiply(X_16,inverse(multiply(inverse(a),X_16)))))]]) ).
cnf(refute_0_98,plain,
multiply(multiply(X_5,X_6),inverse(multiply(X_5,X_6))) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(multiply(X_5,X_6)))]]) ).
cnf(refute_0_99,plain,
multiply(multiply(X_5,X_6),inverse(multiply(X_5,X_6))) = multiply(X_5,multiply(X_6,inverse(multiply(X_5,X_6)))),
inference(subst,[],[associativity:[bind(X,$fot(X_5)),bind(Y,$fot(X_6)),bind(Z,$fot(inverse(multiply(X_5,X_6))))]]) ).
cnf(refute_0_100,plain,
( multiply(multiply(X_5,X_6),inverse(multiply(X_5,X_6))) != multiply(X_5,multiply(X_6,inverse(multiply(X_5,X_6))))
| multiply(multiply(X_5,X_6),inverse(multiply(X_5,X_6))) != identity
| multiply(X_5,multiply(X_6,inverse(multiply(X_5,X_6)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_5,X_6),inverse(multiply(X_5,X_6))),identity) ),[0],$fot(multiply(X_5,multiply(X_6,inverse(multiply(X_5,X_6)))))]]) ).
cnf(refute_0_101,plain,
( multiply(multiply(X_5,X_6),inverse(multiply(X_5,X_6))) != identity
| multiply(X_5,multiply(X_6,inverse(multiply(X_5,X_6)))) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_5,X_6),inverse(multiply(X_5,X_6))),multiply(X_5,multiply(X_6,inverse(multiply(X_5,X_6))))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(X_5,multiply(X_6,inverse(multiply(X_5,X_6)))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(X_5,X_6),inverse(multiply(X_5,X_6))),identity) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(inverse(a),multiply(X_16,inverse(multiply(inverse(a),X_16)))) = identity,
inference(subst,[],[refute_0_102:[bind(X_5,$fot(inverse(a))),bind(X_6,$fot(X_16))]]) ).
cnf(refute_0_104,plain,
( multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) != multiply(c,multiply(inverse(a),multiply(X_16,inverse(multiply(inverse(a),X_16)))))
| multiply(inverse(a),multiply(X_16,inverse(multiply(inverse(a),X_16)))) != identity
| multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) = multiply(c,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))),multiply(c,multiply(inverse(a),multiply(X_16,inverse(multiply(inverse(a),X_16)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_105,plain,
( multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) != multiply(c,multiply(inverse(a),multiply(X_16,inverse(multiply(inverse(a),X_16)))))
| multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) = multiply(c,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(X_16,inverse(multiply(inverse(a),X_16)))),identity) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) = multiply(c,identity),
inference(resolve,[$cnf( $equal(multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))),multiply(c,multiply(inverse(a),multiply(X_16,inverse(multiply(inverse(a),X_16)))))) )],[refute_0_97,refute_0_105]) ).
cnf(refute_0_107,plain,
multiply(c,identity) = c,
inference(subst,[],[right_identity:[bind(X,$fot(c))]]) ).
cnf(refute_0_108,plain,
( multiply(c,identity) != c
| multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) != multiply(c,identity)
| multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) = c ),
introduced(tautology,[equality,[$cnf( $equal(multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))),multiply(c,identity)) ),[1],$fot(c)]]) ).
cnf(refute_0_109,plain,
( multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) != multiply(c,identity)
| multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) = c ),
inference(resolve,[$cnf( $equal(multiply(c,identity),c) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))) = c,
inference(resolve,[$cnf( $equal(multiply(d,multiply(X_16,inverse(multiply(inverse(a),X_16)))),multiply(c,identity)) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(d,multiply(inverse(b),inverse(multiply(inverse(a),inverse(b))))) = c,
inference(subst,[],[refute_0_110:[bind(X_16,$fot(inverse(b)))]]) ).
cnf(refute_0_112,plain,
( multiply(d,multiply(inverse(b),inverse(multiply(inverse(a),inverse(b))))) != c
| multiply(h,inverse(multiply(inverse(a),inverse(b)))) != multiply(d,multiply(inverse(b),inverse(multiply(inverse(a),inverse(b)))))
| multiply(h,inverse(multiply(inverse(a),inverse(b)))) = c ),
introduced(tautology,[equality,[$cnf( $equal(multiply(h,inverse(multiply(inverse(a),inverse(b)))),multiply(d,multiply(inverse(b),inverse(multiply(inverse(a),inverse(b)))))) ),[1],$fot(c)]]) ).
cnf(refute_0_113,plain,
( multiply(h,inverse(multiply(inverse(a),inverse(b)))) != multiply(d,multiply(inverse(b),inverse(multiply(inverse(a),inverse(b)))))
| multiply(h,inverse(multiply(inverse(a),inverse(b)))) = c ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(inverse(b),inverse(multiply(inverse(a),inverse(b))))),c) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(h,inverse(multiply(inverse(a),inverse(b)))) = c,
inference(resolve,[$cnf( $equal(multiply(h,inverse(multiply(inverse(a),inverse(b)))),multiply(d,multiply(inverse(b),inverse(multiply(inverse(a),inverse(b)))))) )],[refute_0_96,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiply(h,inverse(multiply(inverse(a),inverse(b)))) != c
| inverse(multiply(inverse(a),inverse(b))) != multiply(inverse(h),multiply(h,inverse(multiply(inverse(a),inverse(b)))))
| inverse(multiply(inverse(a),inverse(b))) = multiply(inverse(h),c) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(a),inverse(b))),multiply(inverse(h),multiply(h,inverse(multiply(inverse(a),inverse(b)))))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_116,plain,
( inverse(multiply(inverse(a),inverse(b))) != multiply(inverse(h),multiply(h,inverse(multiply(inverse(a),inverse(b)))))
| inverse(multiply(inverse(a),inverse(b))) = multiply(inverse(h),c) ),
inference(resolve,[$cnf( $equal(multiply(h,inverse(multiply(inverse(a),inverse(b)))),c) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
inverse(multiply(inverse(a),inverse(b))) = multiply(inverse(h),c),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(a),inverse(b))),multiply(inverse(h),multiply(h,inverse(multiply(inverse(a),inverse(b)))))) )],[refute_0_95,refute_0_116]) ).
cnf(refute_0_118,plain,
X_12 = multiply(inverse(X_12),multiply(inverse(X_12),multiply(inverse(X_12),X_12))),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(inverse(X_12))),bind(X_7,$fot(X_12))]]) ).
cnf(refute_0_119,plain,
multiply(inverse(X_12),X_12) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_120,plain,
( X_12 != multiply(inverse(X_12),multiply(inverse(X_12),multiply(inverse(X_12),X_12)))
| multiply(inverse(X_12),X_12) != identity
| X_12 = multiply(inverse(X_12),multiply(inverse(X_12),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(X_12,multiply(inverse(X_12),multiply(inverse(X_12),multiply(inverse(X_12),X_12)))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_121,plain,
( X_12 != multiply(inverse(X_12),multiply(inverse(X_12),multiply(inverse(X_12),X_12)))
| X_12 = multiply(inverse(X_12),multiply(inverse(X_12),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),X_12),identity) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
X_12 = multiply(inverse(X_12),multiply(inverse(X_12),identity)),
inference(resolve,[$cnf( $equal(X_12,multiply(inverse(X_12),multiply(inverse(X_12),multiply(inverse(X_12),X_12)))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(inverse(X_12),identity) = inverse(X_12),
inference(subst,[],[right_identity:[bind(X,$fot(inverse(X_12)))]]) ).
cnf(refute_0_124,plain,
multiply(inverse(X_12),multiply(inverse(X_12),identity)) = multiply(inverse(X_12),multiply(inverse(X_12),identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(X_12),multiply(inverse(X_12),identity)))]]) ).
cnf(refute_0_125,plain,
( multiply(inverse(X_12),multiply(inverse(X_12),identity)) != multiply(inverse(X_12),multiply(inverse(X_12),identity))
| multiply(inverse(X_12),identity) != inverse(X_12)
| multiply(inverse(X_12),multiply(inverse(X_12),identity)) = multiply(inverse(X_12),inverse(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_12),multiply(inverse(X_12),identity)),multiply(inverse(X_12),multiply(inverse(X_12),identity))) ),[1,1],$fot(inverse(X_12))]]) ).
cnf(refute_0_126,plain,
( multiply(inverse(X_12),identity) != inverse(X_12)
| multiply(inverse(X_12),multiply(inverse(X_12),identity)) = multiply(inverse(X_12),inverse(X_12)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(inverse(X_12),identity)),multiply(inverse(X_12),multiply(inverse(X_12),identity))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(inverse(X_12),multiply(inverse(X_12),identity)) = multiply(inverse(X_12),inverse(X_12)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),identity),inverse(X_12)) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
( X_12 != multiply(inverse(X_12),multiply(inverse(X_12),identity))
| multiply(inverse(X_12),multiply(inverse(X_12),identity)) != multiply(inverse(X_12),inverse(X_12))
| X_12 = multiply(inverse(X_12),inverse(X_12)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_12,multiply(inverse(X_12),inverse(X_12))) ),[0],$fot(multiply(inverse(X_12),multiply(inverse(X_12),identity)))]]) ).
cnf(refute_0_129,plain,
( X_12 != multiply(inverse(X_12),multiply(inverse(X_12),identity))
| X_12 = multiply(inverse(X_12),inverse(X_12)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(inverse(X_12),identity)),multiply(inverse(X_12),inverse(X_12))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
X_12 = multiply(inverse(X_12),inverse(X_12)),
inference(resolve,[$cnf( $equal(X_12,multiply(inverse(X_12),multiply(inverse(X_12),identity))) )],[refute_0_122,refute_0_129]) ).
cnf(refute_0_131,plain,
( inverse(X_11) != multiply(X_11,X_11)
| multiply(X_11,X_11) = inverse(X_11) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(inverse(X_11))),bind(Y0,$fot(multiply(X_11,X_11)))]]) ).
cnf(refute_0_132,plain,
multiply(X_11,X_11) = inverse(X_11),
inference(resolve,[$cnf( $equal(inverse(X_11),multiply(X_11,X_11)) )],[refute_0_53,refute_0_131]) ).
cnf(refute_0_133,plain,
multiply(inverse(X_12),inverse(X_12)) = inverse(inverse(X_12)),
inference(subst,[],[refute_0_132:[bind(X_11,$fot(inverse(X_12)))]]) ).
cnf(refute_0_134,plain,
( X_12 != multiply(inverse(X_12),inverse(X_12))
| multiply(inverse(X_12),inverse(X_12)) != inverse(inverse(X_12))
| X_12 = inverse(inverse(X_12)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_12,inverse(inverse(X_12))) ),[0],$fot(multiply(inverse(X_12),inverse(X_12)))]]) ).
cnf(refute_0_135,plain,
( X_12 != multiply(inverse(X_12),inverse(X_12))
| X_12 = inverse(inverse(X_12)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),inverse(X_12)),inverse(inverse(X_12))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
X_12 = inverse(inverse(X_12)),
inference(resolve,[$cnf( $equal(X_12,multiply(inverse(X_12),inverse(X_12))) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
( X_12 != inverse(inverse(X_12))
| inverse(inverse(X_12)) = X_12 ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(X_12)),bind(Y0,$fot(inverse(inverse(X_12))))]]) ).
cnf(refute_0_138,plain,
inverse(inverse(X_12)) = X_12,
inference(resolve,[$cnf( $equal(X_12,inverse(inverse(X_12))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
inverse(inverse(multiply(b,a))) = multiply(b,a),
inference(subst,[],[refute_0_138:[bind(X_12,$fot(multiply(b,a)))]]) ).
cnf(refute_0_140,plain,
inverse(multiply(b,a)) = multiply(inverse(a),multiply(a,inverse(multiply(b,a)))),
inference(subst,[],[refute_0_9:[bind(X_6,$fot(a)),bind(X_7,$fot(inverse(multiply(b,a))))]]) ).
cnf(refute_0_141,plain,
multiply(multiply(d,c),Z) = multiply(d,multiply(c,Z)),
inference(subst,[],[associativity:[bind(X,$fot(d)),bind(Y,$fot(c))]]) ).
cnf(refute_0_142,plain,
multiply(multiply(d,a),Z) = multiply(d,multiply(a,Z)),
inference(subst,[],[associativity:[bind(X,$fot(d)),bind(Y,$fot(a))]]) ).
cnf(refute_0_143,plain,
multiply(d,a) = multiply(c,multiply(inverse(a),a)),
inference(subst,[],[refute_0_31:[bind(X_7,$fot(a))]]) ).
cnf(refute_0_144,plain,
multiply(inverse(a),a) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_145,plain,
( multiply(d,a) != multiply(c,multiply(inverse(a),a))
| multiply(inverse(a),a) != identity
| multiply(d,a) = multiply(c,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(d,a),multiply(c,multiply(inverse(a),a))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_146,plain,
( multiply(d,a) != multiply(c,multiply(inverse(a),a))
| multiply(d,a) = multiply(c,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(d,a) = multiply(c,identity),
inference(resolve,[$cnf( $equal(multiply(d,a),multiply(c,multiply(inverse(a),a))) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
( multiply(c,identity) != c
| multiply(d,a) != multiply(c,identity)
| multiply(d,a) = c ),
introduced(tautology,[equality,[$cnf( $equal(multiply(d,a),multiply(c,identity)) ),[1],$fot(c)]]) ).
cnf(refute_0_149,plain,
( multiply(d,a) != multiply(c,identity)
| multiply(d,a) = c ),
inference(resolve,[$cnf( $equal(multiply(c,identity),c) )],[refute_0_107,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(d,a) = c,
inference(resolve,[$cnf( $equal(multiply(d,a),multiply(c,identity)) )],[refute_0_147,refute_0_149]) ).
cnf(refute_0_151,plain,
( multiply(multiply(d,a),Z) != multiply(d,multiply(a,Z))
| multiply(d,a) != c
| multiply(c,Z) = multiply(d,multiply(a,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(d,a),Z),multiply(d,multiply(a,Z))) ),[0,0],$fot(c)]]) ).
cnf(refute_0_152,plain,
( multiply(multiply(d,a),Z) != multiply(d,multiply(a,Z))
| multiply(c,Z) = multiply(d,multiply(a,Z)) ),
inference(resolve,[$cnf( $equal(multiply(d,a),c) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(c,Z) = multiply(d,multiply(a,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(d,a),Z),multiply(d,multiply(a,Z))) )],[refute_0_142,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(c,b) = multiply(d,multiply(a,b)),
inference(subst,[],[refute_0_153:[bind(Z,$fot(b))]]) ).
cnf(refute_0_155,plain,
( multiply(a,b) != c
| multiply(c,b) != multiply(d,multiply(a,b))
| multiply(c,b) = multiply(d,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,b),multiply(d,multiply(a,b))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_156,plain,
( multiply(c,b) != multiply(d,multiply(a,b))
| multiply(c,b) = multiply(d,c) ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[a_times_b_is_c,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(c,b) = multiply(d,c),
inference(resolve,[$cnf( $equal(multiply(c,b),multiply(d,multiply(a,b))) )],[refute_0_154,refute_0_156]) ).
cnf(refute_0_158,plain,
( multiply(c,b) != multiply(d,c)
| multiply(d,c) = multiply(c,b) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(c,b))),bind(Y0,$fot(multiply(d,c)))]]) ).
cnf(refute_0_159,plain,
multiply(d,c) = multiply(c,b),
inference(resolve,[$cnf( $equal(multiply(c,b),multiply(d,c)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( multiply(multiply(d,c),Z) != multiply(d,multiply(c,Z))
| multiply(d,c) != multiply(c,b)
| multiply(multiply(c,b),Z) = multiply(d,multiply(c,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(d,c),Z),multiply(d,multiply(c,Z))) ),[0,0],$fot(multiply(c,b))]]) ).
cnf(refute_0_161,plain,
( multiply(multiply(d,c),Z) != multiply(d,multiply(c,Z))
| multiply(multiply(c,b),Z) = multiply(d,multiply(c,Z)) ),
inference(resolve,[$cnf( $equal(multiply(d,c),multiply(c,b)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
multiply(multiply(c,b),Z) = multiply(d,multiply(c,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(d,c),Z),multiply(d,multiply(c,Z))) )],[refute_0_141,refute_0_161]) ).
cnf(refute_0_163,plain,
multiply(multiply(c,b),Z) = multiply(c,multiply(b,Z)),
inference(subst,[],[associativity:[bind(X,$fot(c)),bind(Y,$fot(b))]]) ).
cnf(refute_0_164,plain,
( multiply(multiply(c,b),Z) != multiply(c,multiply(b,Z))
| multiply(multiply(c,b),Z) != multiply(d,multiply(c,Z))
| multiply(c,multiply(b,Z)) = multiply(d,multiply(c,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(c,b),Z),multiply(d,multiply(c,Z))) ),[0],$fot(multiply(c,multiply(b,Z)))]]) ).
cnf(refute_0_165,plain,
( multiply(multiply(c,b),Z) != multiply(d,multiply(c,Z))
| multiply(c,multiply(b,Z)) = multiply(d,multiply(c,Z)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(c,b),Z),multiply(c,multiply(b,Z))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
multiply(c,multiply(b,Z)) = multiply(d,multiply(c,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(c,b),Z),multiply(d,multiply(c,Z))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(d,multiply(c,multiply(b,inverse(multiply(b,a))))),
inference(subst,[],[refute_0_166:[bind(Z,$fot(multiply(b,inverse(multiply(b,a)))))]]) ).
cnf(refute_0_168,plain,
multiply(c,multiply(b,inverse(multiply(b,a)))) = multiply(d,multiply(c,inverse(multiply(b,a)))),
inference(subst,[],[refute_0_166:[bind(Z,$fot(inverse(multiply(b,a))))]]) ).
cnf(refute_0_169,plain,
multiply(c,inverse(multiply(b,a))) = multiply(d,multiply(a,inverse(multiply(b,a)))),
inference(subst,[],[refute_0_153:[bind(Z,$fot(inverse(multiply(b,a))))]]) ).
cnf(refute_0_170,plain,
multiply(multiply(h,b),X_7) = multiply(h,multiply(b,X_7)),
inference(subst,[],[associativity:[bind(X,$fot(h)),bind(Y,$fot(b)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_171,plain,
( multiply(multiply(h,b),X_7) != multiply(h,multiply(b,X_7))
| multiply(h,b) != j
| multiply(j,X_7) = multiply(h,multiply(b,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(h,b),X_7),multiply(h,multiply(b,X_7))) ),[0,0],$fot(j)]]) ).
cnf(refute_0_172,plain,
( multiply(multiply(h,b),X_7) != multiply(h,multiply(b,X_7))
| multiply(j,X_7) = multiply(h,multiply(b,X_7)) ),
inference(resolve,[$cnf( $equal(multiply(h,b),j) )],[h_times_b_is_j,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(j,X_7) = multiply(h,multiply(b,X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(h,b),X_7),multiply(h,multiply(b,X_7))) )],[refute_0_170,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(j,X_7) = multiply(j,X_7),
introduced(tautology,[refl,[$fot(multiply(j,X_7))]]) ).
cnf(refute_0_175,plain,
( multiply(j,X_7) != multiply(j,X_7)
| j != d
| multiply(j,X_7) = multiply(d,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(j,X_7),multiply(j,X_7)) ),[1,0],$fot(d)]]) ).
cnf(refute_0_176,plain,
( j != d
| multiply(j,X_7) = multiply(d,X_7) ),
inference(resolve,[$cnf( $equal(multiply(j,X_7),multiply(j,X_7)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(j,X_7) = multiply(d,X_7),
inference(resolve,[$cnf( $equal(j,d) )],[refute_0_86,refute_0_176]) ).
cnf(refute_0_178,plain,
( multiply(j,X_7) != multiply(d,X_7)
| multiply(j,X_7) != multiply(h,multiply(b,X_7))
| multiply(d,X_7) = multiply(h,multiply(b,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(j,X_7),multiply(h,multiply(b,X_7))) ),[0],$fot(multiply(d,X_7))]]) ).
cnf(refute_0_179,plain,
( multiply(j,X_7) != multiply(h,multiply(b,X_7))
| multiply(d,X_7) = multiply(h,multiply(b,X_7)) ),
inference(resolve,[$cnf( $equal(multiply(j,X_7),multiply(d,X_7)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
multiply(d,X_7) = multiply(h,multiply(b,X_7)),
inference(resolve,[$cnf( $equal(multiply(j,X_7),multiply(h,multiply(b,X_7))) )],[refute_0_173,refute_0_179]) ).
cnf(refute_0_181,plain,
multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) = multiply(h,multiply(b,multiply(X_6,inverse(multiply(b,X_6))))),
inference(subst,[],[refute_0_180:[bind(X_7,$fot(multiply(X_6,inverse(multiply(b,X_6)))))]]) ).
cnf(refute_0_182,plain,
multiply(b,multiply(X_6,inverse(multiply(b,X_6)))) = identity,
inference(subst,[],[refute_0_102:[bind(X_5,$fot(b))]]) ).
cnf(refute_0_183,plain,
( multiply(b,multiply(X_6,inverse(multiply(b,X_6)))) != identity
| multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) != multiply(h,multiply(b,multiply(X_6,inverse(multiply(b,X_6)))))
| multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) = multiply(h,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(d,multiply(X_6,inverse(multiply(b,X_6)))),multiply(h,multiply(b,multiply(X_6,inverse(multiply(b,X_6)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_184,plain,
( multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) != multiply(h,multiply(b,multiply(X_6,inverse(multiply(b,X_6)))))
| multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) = multiply(h,identity) ),
inference(resolve,[$cnf( $equal(multiply(b,multiply(X_6,inverse(multiply(b,X_6)))),identity) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) = multiply(h,identity),
inference(resolve,[$cnf( $equal(multiply(d,multiply(X_6,inverse(multiply(b,X_6)))),multiply(h,multiply(b,multiply(X_6,inverse(multiply(b,X_6)))))) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(h,identity) = h,
inference(subst,[],[right_identity:[bind(X,$fot(h))]]) ).
cnf(refute_0_187,plain,
( multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) != multiply(h,identity)
| multiply(h,identity) != h
| multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) = h ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(d,multiply(X_6,inverse(multiply(b,X_6)))),h) ),[0],$fot(multiply(h,identity))]]) ).
cnf(refute_0_188,plain,
( multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) != multiply(h,identity)
| multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) = h ),
inference(resolve,[$cnf( $equal(multiply(h,identity),h) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(d,multiply(X_6,inverse(multiply(b,X_6)))) = h,
inference(resolve,[$cnf( $equal(multiply(d,multiply(X_6,inverse(multiply(b,X_6)))),multiply(h,identity)) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
multiply(d,multiply(a,inverse(multiply(b,a)))) = h,
inference(subst,[],[refute_0_189:[bind(X_6,$fot(a))]]) ).
cnf(refute_0_191,plain,
( multiply(c,inverse(multiply(b,a))) != multiply(d,multiply(a,inverse(multiply(b,a))))
| multiply(d,multiply(a,inverse(multiply(b,a)))) != h
| multiply(c,inverse(multiply(b,a))) = h ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(c,inverse(multiply(b,a))),h) ),[0],$fot(multiply(d,multiply(a,inverse(multiply(b,a)))))]]) ).
cnf(refute_0_192,plain,
( multiply(c,inverse(multiply(b,a))) != multiply(d,multiply(a,inverse(multiply(b,a))))
| multiply(c,inverse(multiply(b,a))) = h ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(a,inverse(multiply(b,a)))),h) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
multiply(c,inverse(multiply(b,a))) = h,
inference(resolve,[$cnf( $equal(multiply(c,inverse(multiply(b,a))),multiply(d,multiply(a,inverse(multiply(b,a))))) )],[refute_0_169,refute_0_192]) ).
cnf(refute_0_194,plain,
( multiply(c,multiply(b,inverse(multiply(b,a)))) != multiply(d,multiply(c,inverse(multiply(b,a))))
| multiply(c,inverse(multiply(b,a))) != h
| multiply(c,multiply(b,inverse(multiply(b,a)))) = multiply(d,h) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(b,inverse(multiply(b,a)))),multiply(d,multiply(c,inverse(multiply(b,a))))) ),[1,1],$fot(h)]]) ).
cnf(refute_0_195,plain,
( multiply(c,multiply(b,inverse(multiply(b,a)))) != multiply(d,multiply(c,inverse(multiply(b,a))))
| multiply(c,multiply(b,inverse(multiply(b,a)))) = multiply(d,h) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(multiply(b,a))),h) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
multiply(c,multiply(b,inverse(multiply(b,a)))) = multiply(d,h),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,inverse(multiply(b,a)))),multiply(d,multiply(c,inverse(multiply(b,a))))) )],[refute_0_168,refute_0_195]) ).
cnf(refute_0_197,plain,
( multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) != multiply(d,multiply(c,multiply(b,inverse(multiply(b,a)))))
| multiply(c,multiply(b,inverse(multiply(b,a)))) != multiply(d,h)
| multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(d,multiply(d,h)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),multiply(d,multiply(c,multiply(b,inverse(multiply(b,a)))))) ),[1,1],$fot(multiply(d,h))]]) ).
cnf(refute_0_198,plain,
( multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) != multiply(d,multiply(c,multiply(b,inverse(multiply(b,a)))))
| multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(d,multiply(d,h)) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,inverse(multiply(b,a)))),multiply(d,h)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(d,multiply(d,h)),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),multiply(d,multiply(c,multiply(b,inverse(multiply(b,a)))))) )],[refute_0_167,refute_0_198]) ).
cnf(refute_0_200,plain,
multiply(multiply(c,inverse(b)),Z) = multiply(c,multiply(inverse(b),Z)),
inference(subst,[],[associativity:[bind(X,$fot(c)),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_201,plain,
a = multiply(d,multiply(d,multiply(d,a))),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(d)),bind(X_7,$fot(a))]]) ).
cnf(refute_0_202,plain,
( multiply(d,a) != c
| a != multiply(d,multiply(d,multiply(d,a)))
| a = multiply(d,multiply(d,c)) ),
introduced(tautology,[equality,[$cnf( $equal(a,multiply(d,multiply(d,multiply(d,a)))) ),[1,1,1],$fot(c)]]) ).
cnf(refute_0_203,plain,
( a != multiply(d,multiply(d,multiply(d,a)))
| a = multiply(d,multiply(d,c)) ),
inference(resolve,[$cnf( $equal(multiply(d,a),c) )],[refute_0_150,refute_0_202]) ).
cnf(refute_0_204,plain,
a = multiply(d,multiply(d,c)),
inference(resolve,[$cnf( $equal(a,multiply(d,multiply(d,multiply(d,a)))) )],[refute_0_201,refute_0_203]) ).
cnf(refute_0_205,plain,
( multiply(c,multiply(b,Z)) != multiply(d,multiply(c,Z))
| multiply(d,multiply(c,Z)) = multiply(c,multiply(b,Z)) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(c,multiply(b,Z)))),bind(Y0,$fot(multiply(d,multiply(c,Z))))]]) ).
cnf(refute_0_206,plain,
multiply(d,multiply(c,Z)) = multiply(c,multiply(b,Z)),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,Z)),multiply(d,multiply(c,Z))) )],[refute_0_166,refute_0_205]) ).
cnf(refute_0_207,plain,
multiply(d,multiply(c,b)) = multiply(c,multiply(b,b)),
inference(subst,[],[refute_0_206:[bind(Z,$fot(b))]]) ).
cnf(refute_0_208,plain,
multiply(d,multiply(d,c)) = multiply(d,multiply(d,c)),
introduced(tautology,[refl,[$fot(multiply(d,multiply(d,c)))]]) ).
cnf(refute_0_209,plain,
( multiply(d,multiply(d,c)) != multiply(d,multiply(d,c))
| multiply(d,c) != multiply(c,b)
| multiply(d,multiply(d,c)) = multiply(d,multiply(c,b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(d,multiply(d,c)),multiply(d,multiply(d,c))) ),[1,1],$fot(multiply(c,b))]]) ).
cnf(refute_0_210,plain,
( multiply(d,c) != multiply(c,b)
| multiply(d,multiply(d,c)) = multiply(d,multiply(c,b)) ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(d,c)),multiply(d,multiply(d,c))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
multiply(d,multiply(d,c)) = multiply(d,multiply(c,b)),
inference(resolve,[$cnf( $equal(multiply(d,c),multiply(c,b)) )],[refute_0_159,refute_0_210]) ).
cnf(refute_0_212,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_213,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_34,refute_0_212]) ).
cnf(refute_0_214,plain,
( multiply(d,multiply(c,b)) != multiply(c,multiply(b,b))
| multiply(d,multiply(d,c)) != multiply(d,multiply(c,b))
| multiply(d,multiply(d,c)) = multiply(c,multiply(b,b)) ),
inference(subst,[],[refute_0_213:[bind(X0,$fot(multiply(d,multiply(d,c)))),bind(Y0,$fot(multiply(d,multiply(c,b)))),bind(Z0,$fot(multiply(c,multiply(b,b))))]]) ).
cnf(refute_0_215,plain,
( multiply(d,multiply(c,b)) != multiply(c,multiply(b,b))
| multiply(d,multiply(d,c)) = multiply(c,multiply(b,b)) ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(d,c)),multiply(d,multiply(c,b))) )],[refute_0_211,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(d,multiply(d,c)) = multiply(c,multiply(b,b)),
inference(resolve,[$cnf( $equal(multiply(d,multiply(c,b)),multiply(c,multiply(b,b))) )],[refute_0_207,refute_0_215]) ).
cnf(refute_0_217,plain,
( multiply(d,multiply(d,c)) != multiply(c,multiply(b,b))
| a != multiply(d,multiply(d,c))
| a = multiply(c,multiply(b,b)) ),
introduced(tautology,[equality,[$cnf( $equal(a,multiply(d,multiply(d,c))) ),[1],$fot(multiply(c,multiply(b,b)))]]) ).
cnf(refute_0_218,plain,
( a != multiply(d,multiply(d,c))
| a = multiply(c,multiply(b,b)) ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(d,c)),multiply(c,multiply(b,b))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
a = multiply(c,multiply(b,b)),
inference(resolve,[$cnf( $equal(a,multiply(d,multiply(d,c))) )],[refute_0_204,refute_0_218]) ).
cnf(refute_0_220,plain,
multiply(b,b) = inverse(b),
inference(subst,[],[refute_0_132:[bind(X_11,$fot(b))]]) ).
cnf(refute_0_221,plain,
multiply(c,multiply(b,b)) = multiply(c,multiply(b,b)),
introduced(tautology,[refl,[$fot(multiply(c,multiply(b,b)))]]) ).
cnf(refute_0_222,plain,
( multiply(b,b) != inverse(b)
| multiply(c,multiply(b,b)) != multiply(c,multiply(b,b))
| multiply(c,multiply(b,b)) = multiply(c,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(b,b)),multiply(c,multiply(b,b))) ),[1,1],$fot(inverse(b))]]) ).
cnf(refute_0_223,plain,
( multiply(b,b) != inverse(b)
| multiply(c,multiply(b,b)) = multiply(c,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,b)),multiply(c,multiply(b,b))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
multiply(c,multiply(b,b)) = multiply(c,inverse(b)),
inference(resolve,[$cnf( $equal(multiply(b,b),inverse(b)) )],[refute_0_220,refute_0_223]) ).
cnf(refute_0_225,plain,
( multiply(c,multiply(b,b)) != multiply(c,inverse(b))
| a != multiply(c,multiply(b,b))
| a = multiply(c,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(a,multiply(c,multiply(b,b))) ),[1],$fot(multiply(c,inverse(b)))]]) ).
cnf(refute_0_226,plain,
( a != multiply(c,multiply(b,b))
| a = multiply(c,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,b)),multiply(c,inverse(b))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
a = multiply(c,inverse(b)),
inference(resolve,[$cnf( $equal(a,multiply(c,multiply(b,b))) )],[refute_0_219,refute_0_226]) ).
cnf(refute_0_228,plain,
( a != multiply(c,inverse(b))
| multiply(c,inverse(b)) = a ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(a)),bind(Y0,$fot(multiply(c,inverse(b))))]]) ).
cnf(refute_0_229,plain,
multiply(c,inverse(b)) = a,
inference(resolve,[$cnf( $equal(a,multiply(c,inverse(b))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
( multiply(multiply(c,inverse(b)),Z) != multiply(c,multiply(inverse(b),Z))
| multiply(c,inverse(b)) != a
| multiply(a,Z) = multiply(c,multiply(inverse(b),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(c,inverse(b)),Z),multiply(c,multiply(inverse(b),Z))) ),[0,0],$fot(a)]]) ).
cnf(refute_0_231,plain,
( multiply(multiply(c,inverse(b)),Z) != multiply(c,multiply(inverse(b),Z))
| multiply(a,Z) = multiply(c,multiply(inverse(b),Z)) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(b)),a) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
multiply(a,Z) = multiply(c,multiply(inverse(b),Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(c,inverse(b)),Z),multiply(c,multiply(inverse(b),Z))) )],[refute_0_200,refute_0_231]) ).
cnf(refute_0_233,plain,
( multiply(a,Z) != multiply(c,multiply(inverse(b),Z))
| multiply(c,multiply(inverse(b),Z)) = multiply(a,Z) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(a,Z))),bind(Y0,$fot(multiply(c,multiply(inverse(b),Z))))]]) ).
cnf(refute_0_234,plain,
multiply(c,multiply(inverse(b),Z)) = multiply(a,Z),
inference(resolve,[$cnf( $equal(multiply(a,Z),multiply(c,multiply(inverse(b),Z))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
multiply(c,multiply(inverse(b),inverse(multiply(b,a)))) = multiply(a,inverse(multiply(b,a))),
inference(subst,[],[refute_0_234:[bind(Z,$fot(inverse(multiply(b,a))))]]) ).
cnf(refute_0_236,plain,
multiply(b,multiply(b,inverse(multiply(b,a)))) = multiply(inverse(b),inverse(multiply(b,a))),
inference(subst,[],[refute_0_61:[bind(Y,$fot(b)),bind(Z,$fot(inverse(multiply(b,a))))]]) ).
cnf(refute_0_237,plain,
multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),
introduced(tautology,[refl,[$fot(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))))]]) ).
cnf(refute_0_238,plain,
( multiply(b,multiply(b,inverse(multiply(b,a)))) != multiply(inverse(b),inverse(multiply(b,a)))
| multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) != multiply(c,multiply(b,multiply(b,inverse(multiply(b,a)))))
| multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(c,multiply(inverse(b),inverse(multiply(b,a)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),multiply(c,multiply(b,multiply(b,inverse(multiply(b,a)))))) ),[1,1],$fot(multiply(inverse(b),inverse(multiply(b,a))))]]) ).
cnf(refute_0_239,plain,
( multiply(b,multiply(b,inverse(multiply(b,a)))) != multiply(inverse(b),inverse(multiply(b,a)))
| multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(c,multiply(inverse(b),inverse(multiply(b,a)))) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),multiply(c,multiply(b,multiply(b,inverse(multiply(b,a)))))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(c,multiply(inverse(b),inverse(multiply(b,a)))),
inference(resolve,[$cnf( $equal(multiply(b,multiply(b,inverse(multiply(b,a)))),multiply(inverse(b),inverse(multiply(b,a)))) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
( multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) != multiply(c,multiply(inverse(b),inverse(multiply(b,a))))
| multiply(c,multiply(inverse(b),inverse(multiply(b,a)))) != multiply(a,inverse(multiply(b,a)))
| multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(a,inverse(multiply(b,a))) ),
inference(subst,[],[refute_0_213:[bind(X0,$fot(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))))),bind(Y0,$fot(multiply(c,multiply(inverse(b),inverse(multiply(b,a)))))),bind(Z0,$fot(multiply(a,inverse(multiply(b,a)))))]]) ).
cnf(refute_0_242,plain,
( multiply(c,multiply(inverse(b),inverse(multiply(b,a)))) != multiply(a,inverse(multiply(b,a)))
| multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(a,inverse(multiply(b,a))) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),multiply(c,multiply(inverse(b),inverse(multiply(b,a))))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) = multiply(a,inverse(multiply(b,a))),
inference(resolve,[$cnf( $equal(multiply(c,multiply(inverse(b),inverse(multiply(b,a)))),multiply(a,inverse(multiply(b,a)))) )],[refute_0_235,refute_0_242]) ).
cnf(refute_0_244,plain,
( multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) != multiply(a,inverse(multiply(b,a)))
| multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) != multiply(d,multiply(d,h))
| multiply(a,inverse(multiply(b,a))) = multiply(d,multiply(d,h)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),multiply(d,multiply(d,h))) ),[0],$fot(multiply(a,inverse(multiply(b,a))))]]) ).
cnf(refute_0_245,plain,
( multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) != multiply(d,multiply(d,h))
| multiply(a,inverse(multiply(b,a))) = multiply(d,multiply(d,h)) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),multiply(a,inverse(multiply(b,a)))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
inverse(b) = multiply(d,multiply(d,multiply(d,inverse(b)))),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(d)),bind(X_7,$fot(inverse(b)))]]) ).
cnf(refute_0_247,plain,
( multiply(d,inverse(b)) != h
| inverse(b) != multiply(d,multiply(d,multiply(d,inverse(b))))
| inverse(b) = multiply(d,multiply(d,h)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(d,multiply(d,multiply(d,inverse(b))))) ),[1,1,1],$fot(h)]]) ).
cnf(refute_0_248,plain,
( inverse(b) != multiply(d,multiply(d,multiply(d,inverse(b))))
| inverse(b) = multiply(d,multiply(d,h)) ),
inference(resolve,[$cnf( $equal(multiply(d,inverse(b)),h) )],[d_times_inverse_b_is_h,refute_0_247]) ).
cnf(refute_0_249,plain,
inverse(b) = multiply(d,multiply(d,h)),
inference(resolve,[$cnf( $equal(inverse(b),multiply(d,multiply(d,multiply(d,inverse(b))))) )],[refute_0_246,refute_0_248]) ).
cnf(refute_0_250,plain,
multiply(d,multiply(d,h)) = multiply(inverse(d),h),
inference(subst,[],[refute_0_61:[bind(Y,$fot(d)),bind(Z,$fot(h))]]) ).
cnf(refute_0_251,plain,
( multiply(d,multiply(d,h)) != multiply(inverse(d),h)
| inverse(b) != multiply(d,multiply(d,h))
| inverse(b) = multiply(inverse(d),h) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(d,multiply(d,h))) ),[1],$fot(multiply(inverse(d),h))]]) ).
cnf(refute_0_252,plain,
( inverse(b) != multiply(d,multiply(d,h))
| inverse(b) = multiply(inverse(d),h) ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(d,h)),multiply(inverse(d),h)) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
inverse(b) = multiply(inverse(d),h),
inference(resolve,[$cnf( $equal(inverse(b),multiply(d,multiply(d,h))) )],[refute_0_249,refute_0_252]) ).
cnf(refute_0_254,plain,
( inverse(b) != multiply(inverse(d),h)
| multiply(inverse(d),h) = inverse(b) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(inverse(b))),bind(Y0,$fot(multiply(inverse(d),h)))]]) ).
cnf(refute_0_255,plain,
multiply(inverse(d),h) = inverse(b),
inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(d),h)) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
( multiply(d,multiply(d,h)) != multiply(inverse(d),h)
| multiply(inverse(d),h) != inverse(b)
| multiply(d,multiply(d,h)) = inverse(b) ),
inference(subst,[],[refute_0_213:[bind(X0,$fot(multiply(d,multiply(d,h)))),bind(Y0,$fot(multiply(inverse(d),h))),bind(Z0,$fot(inverse(b)))]]) ).
cnf(refute_0_257,plain,
( multiply(inverse(d),h) != inverse(b)
| multiply(d,multiply(d,h)) = inverse(b) ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(d,h)),multiply(inverse(d),h)) )],[refute_0_250,refute_0_256]) ).
cnf(refute_0_258,plain,
multiply(d,multiply(d,h)) = inverse(b),
inference(resolve,[$cnf( $equal(multiply(inverse(d),h),inverse(b)) )],[refute_0_255,refute_0_257]) ).
cnf(refute_0_259,plain,
( multiply(a,inverse(multiply(b,a))) != multiply(d,multiply(d,h))
| multiply(d,multiply(d,h)) != inverse(b)
| multiply(a,inverse(multiply(b,a))) = inverse(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,inverse(multiply(b,a))),inverse(b)) ),[0],$fot(multiply(d,multiply(d,h)))]]) ).
cnf(refute_0_260,plain,
( multiply(a,inverse(multiply(b,a))) != multiply(d,multiply(d,h))
| multiply(a,inverse(multiply(b,a))) = inverse(b) ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(d,h)),inverse(b)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
( multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))) != multiply(d,multiply(d,h))
| multiply(a,inverse(multiply(b,a))) = inverse(b) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(multiply(b,a))),multiply(d,multiply(d,h))) )],[refute_0_245,refute_0_260]) ).
cnf(refute_0_262,plain,
multiply(a,inverse(multiply(b,a))) = inverse(b),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,multiply(b,inverse(multiply(b,a))))),multiply(d,multiply(d,h))) )],[refute_0_199,refute_0_261]) ).
cnf(refute_0_263,plain,
( multiply(a,inverse(multiply(b,a))) != inverse(b)
| inverse(multiply(b,a)) != multiply(inverse(a),multiply(a,inverse(multiply(b,a))))
| inverse(multiply(b,a)) = multiply(inverse(a),inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(b,a)),multiply(inverse(a),multiply(a,inverse(multiply(b,a))))) ),[1,1],$fot(inverse(b))]]) ).
cnf(refute_0_264,plain,
( inverse(multiply(b,a)) != multiply(inverse(a),multiply(a,inverse(multiply(b,a))))
| inverse(multiply(b,a)) = multiply(inverse(a),inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(multiply(b,a))),inverse(b)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
inverse(multiply(b,a)) = multiply(inverse(a),inverse(b)),
inference(resolve,[$cnf( $equal(inverse(multiply(b,a)),multiply(inverse(a),multiply(a,inverse(multiply(b,a))))) )],[refute_0_140,refute_0_264]) ).
cnf(refute_0_266,plain,
( inverse(multiply(b,a)) != multiply(inverse(a),inverse(b))
| multiply(inverse(a),inverse(b)) = inverse(multiply(b,a)) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(inverse(multiply(b,a)))),bind(Y0,$fot(multiply(inverse(a),inverse(b))))]]) ).
cnf(refute_0_267,plain,
multiply(inverse(a),inverse(b)) = inverse(multiply(b,a)),
inference(resolve,[$cnf( $equal(inverse(multiply(b,a)),multiply(inverse(a),inverse(b))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
inverse(multiply(inverse(a),inverse(b))) = inverse(multiply(inverse(a),inverse(b))),
introduced(tautology,[refl,[$fot(inverse(multiply(inverse(a),inverse(b))))]]) ).
cnf(refute_0_269,plain,
( multiply(inverse(a),inverse(b)) != inverse(multiply(b,a))
| inverse(multiply(inverse(a),inverse(b))) != inverse(multiply(inverse(a),inverse(b)))
| inverse(multiply(inverse(a),inverse(b))) = inverse(inverse(multiply(b,a))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(a),inverse(b))),inverse(multiply(inverse(a),inverse(b)))) ),[1,0],$fot(inverse(multiply(b,a)))]]) ).
cnf(refute_0_270,plain,
( multiply(inverse(a),inverse(b)) != inverse(multiply(b,a))
| inverse(multiply(inverse(a),inverse(b))) = inverse(inverse(multiply(b,a))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(a),inverse(b))),inverse(multiply(inverse(a),inverse(b)))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
inverse(multiply(inverse(a),inverse(b))) = inverse(inverse(multiply(b,a))),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(b)),inverse(multiply(b,a))) )],[refute_0_267,refute_0_270]) ).
cnf(refute_0_272,plain,
( inverse(multiply(inverse(a),inverse(b))) != inverse(inverse(multiply(b,a)))
| inverse(inverse(multiply(b,a))) != multiply(b,a)
| inverse(multiply(inverse(a),inverse(b))) = multiply(b,a) ),
inference(subst,[],[refute_0_213:[bind(X0,$fot(inverse(multiply(inverse(a),inverse(b))))),bind(Y0,$fot(inverse(inverse(multiply(b,a))))),bind(Z0,$fot(multiply(b,a)))]]) ).
cnf(refute_0_273,plain,
( inverse(inverse(multiply(b,a))) != multiply(b,a)
| inverse(multiply(inverse(a),inverse(b))) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(a),inverse(b))),inverse(inverse(multiply(b,a)))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
inverse(multiply(inverse(a),inverse(b))) = multiply(b,a),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(b,a))),multiply(b,a)) )],[refute_0_139,refute_0_273]) ).
cnf(refute_0_275,plain,
( inverse(multiply(inverse(a),inverse(b))) != multiply(b,a)
| inverse(multiply(inverse(a),inverse(b))) != multiply(inverse(h),c)
| multiply(b,a) = multiply(inverse(h),c) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(a),inverse(b))),multiply(inverse(h),c)) ),[0],$fot(multiply(b,a))]]) ).
cnf(refute_0_276,plain,
( inverse(multiply(inverse(a),inverse(b))) != multiply(inverse(h),c)
| multiply(b,a) = multiply(inverse(h),c) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(a),inverse(b))),multiply(b,a)) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
multiply(b,a) = multiply(inverse(h),c),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(a),inverse(b))),multiply(inverse(h),c)) )],[refute_0_117,refute_0_276]) ).
cnf(refute_0_278,plain,
( multiply(b,a) != multiply(inverse(h),c)
| multiply(inverse(h),c) = multiply(b,a) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(b,a))),bind(Y0,$fot(multiply(inverse(h),c)))]]) ).
cnf(refute_0_279,plain,
multiply(inverse(h),c) = multiply(b,a),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(inverse(h),c)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
( multiply(inverse(h),c) != multiply(b,a)
| multiply(k,c) != multiply(d,multiply(inverse(h),c))
| multiply(k,c) = multiply(d,multiply(b,a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(k,c),multiply(d,multiply(inverse(h),c))) ),[1,1],$fot(multiply(b,a))]]) ).
cnf(refute_0_281,plain,
( multiply(k,c) != multiply(d,multiply(inverse(h),c))
| multiply(k,c) = multiply(d,multiply(b,a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(h),c),multiply(b,a)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
multiply(k,c) = multiply(d,multiply(b,a)),
inference(resolve,[$cnf( $equal(multiply(k,c),multiply(d,multiply(inverse(h),c))) )],[refute_0_94,refute_0_281]) ).
cnf(refute_0_283,plain,
( multiply(k,c) != multiply(d,multiply(b,a))
| multiply(d,multiply(b,a)) = multiply(k,c) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(k,c))),bind(Y0,$fot(multiply(d,multiply(b,a))))]]) ).
cnf(refute_0_284,plain,
multiply(d,multiply(b,a)) = multiply(k,c),
inference(resolve,[$cnf( $equal(multiply(k,c),multiply(d,multiply(b,a))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( multiply(d,multiply(b,a)) != multiply(k,c)
| multiply(inverse(a),multiply(b,a)) != multiply(inverse(c),multiply(d,multiply(b,a)))
| multiply(inverse(a),multiply(b,a)) = multiply(inverse(c),multiply(k,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),multiply(b,a)),multiply(inverse(c),multiply(d,multiply(b,a)))) ),[1,1],$fot(multiply(k,c))]]) ).
cnf(refute_0_286,plain,
( multiply(inverse(a),multiply(b,a)) != multiply(inverse(c),multiply(d,multiply(b,a)))
| multiply(inverse(a),multiply(b,a)) = multiply(inverse(c),multiply(k,c)) ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(b,a)),multiply(k,c)) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
multiply(inverse(a),multiply(b,a)) = multiply(inverse(c),multiply(k,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(b,a)),multiply(inverse(c),multiply(d,multiply(b,a)))) )],[refute_0_66,refute_0_286]) ).
cnf(refute_0_288,plain,
multiply(multiply(inverse(a),b),Z) = multiply(inverse(a),multiply(b,Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(a))),bind(Y,$fot(b))]]) ).
cnf(refute_0_289,plain,
multiply(a,c) = multiply(c,multiply(c,multiply(c,multiply(a,c)))),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(c)),bind(X_7,$fot(multiply(a,c)))]]) ).
cnf(refute_0_290,plain,
multiply(c,multiply(a,c)) = multiply(d,multiply(a,multiply(a,c))),
inference(subst,[],[refute_0_153:[bind(Z,$fot(multiply(a,c)))]]) ).
cnf(refute_0_291,plain,
b = multiply(a,multiply(a,multiply(a,b))),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(a)),bind(X_7,$fot(b))]]) ).
cnf(refute_0_292,plain,
( multiply(a,b) != c
| b != multiply(a,multiply(a,multiply(a,b)))
| b = multiply(a,multiply(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(a,multiply(a,multiply(a,b)))) ),[1,1,1],$fot(c)]]) ).
cnf(refute_0_293,plain,
( b != multiply(a,multiply(a,multiply(a,b)))
| b = multiply(a,multiply(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[a_times_b_is_c,refute_0_292]) ).
cnf(refute_0_294,plain,
b = multiply(a,multiply(a,c)),
inference(resolve,[$cnf( $equal(b,multiply(a,multiply(a,multiply(a,b)))) )],[refute_0_291,refute_0_293]) ).
cnf(refute_0_295,plain,
( b != multiply(a,multiply(a,c))
| multiply(a,multiply(a,c)) = b ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(a,multiply(a,c))))]]) ).
cnf(refute_0_296,plain,
multiply(a,multiply(a,c)) = b,
inference(resolve,[$cnf( $equal(b,multiply(a,multiply(a,c))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
( multiply(a,multiply(a,c)) != b
| multiply(c,multiply(a,c)) != multiply(d,multiply(a,multiply(a,c)))
| multiply(c,multiply(a,c)) = multiply(d,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(a,c)),multiply(d,multiply(a,multiply(a,c)))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_298,plain,
( multiply(c,multiply(a,c)) != multiply(d,multiply(a,multiply(a,c)))
| multiply(c,multiply(a,c)) = multiply(d,b) ),
inference(resolve,[$cnf( $equal(multiply(a,multiply(a,c)),b) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
multiply(c,multiply(a,c)) = multiply(d,b),
inference(resolve,[$cnf( $equal(multiply(c,multiply(a,c)),multiply(d,multiply(a,multiply(a,c)))) )],[refute_0_290,refute_0_298]) ).
cnf(refute_0_300,plain,
( multiply(a,c) != multiply(c,multiply(c,multiply(c,multiply(a,c))))
| multiply(c,multiply(a,c)) != multiply(d,b)
| multiply(a,c) = multiply(c,multiply(c,multiply(d,b))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,c),multiply(c,multiply(c,multiply(c,multiply(a,c))))) ),[1,1,1],$fot(multiply(d,b))]]) ).
cnf(refute_0_301,plain,
( multiply(a,c) != multiply(c,multiply(c,multiply(c,multiply(a,c))))
| multiply(a,c) = multiply(c,multiply(c,multiply(d,b))) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(a,c)),multiply(d,b)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
multiply(a,c) = multiply(c,multiply(c,multiply(d,b))),
inference(resolve,[$cnf( $equal(multiply(a,c),multiply(c,multiply(c,multiply(c,multiply(a,c))))) )],[refute_0_289,refute_0_301]) ).
cnf(refute_0_303,plain,
( multiply(inverse(a),X_7) != multiply(c,multiply(c,multiply(d,X_7)))
| multiply(c,multiply(c,multiply(d,X_7))) = multiply(inverse(a),X_7) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(inverse(a),X_7))),bind(Y0,$fot(multiply(c,multiply(c,multiply(d,X_7)))))]]) ).
cnf(refute_0_304,plain,
multiply(c,multiply(c,multiply(d,X_7))) = multiply(inverse(a),X_7),
inference(resolve,[$cnf( $equal(multiply(inverse(a),X_7),multiply(c,multiply(c,multiply(d,X_7)))) )],[refute_0_39,refute_0_303]) ).
cnf(refute_0_305,plain,
multiply(c,multiply(c,multiply(d,b))) = multiply(inverse(a),b),
inference(subst,[],[refute_0_304:[bind(X_7,$fot(b))]]) ).
cnf(refute_0_306,plain,
( multiply(a,c) != multiply(c,multiply(c,multiply(d,b)))
| multiply(c,multiply(c,multiply(d,b))) != multiply(inverse(a),b)
| multiply(a,c) = multiply(inverse(a),b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,c),multiply(inverse(a),b)) ),[0],$fot(multiply(c,multiply(c,multiply(d,b))))]]) ).
cnf(refute_0_307,plain,
( multiply(a,c) != multiply(c,multiply(c,multiply(d,b)))
| multiply(a,c) = multiply(inverse(a),b) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,multiply(d,b))),multiply(inverse(a),b)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
multiply(a,c) = multiply(inverse(a),b),
inference(resolve,[$cnf( $equal(multiply(a,c),multiply(c,multiply(c,multiply(d,b)))) )],[refute_0_302,refute_0_307]) ).
cnf(refute_0_309,plain,
( multiply(a,c) != multiply(inverse(a),b)
| multiply(inverse(a),b) = multiply(a,c) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(a,c))),bind(Y0,$fot(multiply(inverse(a),b)))]]) ).
cnf(refute_0_310,plain,
multiply(inverse(a),b) = multiply(a,c),
inference(resolve,[$cnf( $equal(multiply(a,c),multiply(inverse(a),b)) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
( multiply(multiply(inverse(a),b),Z) != multiply(inverse(a),multiply(b,Z))
| multiply(inverse(a),b) != multiply(a,c)
| multiply(multiply(a,c),Z) = multiply(inverse(a),multiply(b,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(a),b),Z),multiply(inverse(a),multiply(b,Z))) ),[0,0],$fot(multiply(a,c))]]) ).
cnf(refute_0_312,plain,
( multiply(multiply(inverse(a),b),Z) != multiply(inverse(a),multiply(b,Z))
| multiply(multiply(a,c),Z) = multiply(inverse(a),multiply(b,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),b),multiply(a,c)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
multiply(multiply(a,c),Z) = multiply(inverse(a),multiply(b,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(a),b),Z),multiply(inverse(a),multiply(b,Z))) )],[refute_0_288,refute_0_312]) ).
cnf(refute_0_314,plain,
multiply(multiply(a,c),Z) = multiply(a,multiply(c,Z)),
inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).
cnf(refute_0_315,plain,
( multiply(multiply(a,c),Z) != multiply(a,multiply(c,Z))
| multiply(multiply(a,c),Z) != multiply(inverse(a),multiply(b,Z))
| multiply(a,multiply(c,Z)) = multiply(inverse(a),multiply(b,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,c),Z),multiply(inverse(a),multiply(b,Z))) ),[0],$fot(multiply(a,multiply(c,Z)))]]) ).
cnf(refute_0_316,plain,
( multiply(multiply(a,c),Z) != multiply(inverse(a),multiply(b,Z))
| multiply(a,multiply(c,Z)) = multiply(inverse(a),multiply(b,Z)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a,c),Z),multiply(a,multiply(c,Z))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
multiply(a,multiply(c,Z)) = multiply(inverse(a),multiply(b,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,c),Z),multiply(inverse(a),multiply(b,Z))) )],[refute_0_313,refute_0_316]) ).
cnf(refute_0_318,plain,
( multiply(a,multiply(c,Z)) != multiply(inverse(a),multiply(b,Z))
| multiply(inverse(a),multiply(b,Z)) = multiply(a,multiply(c,Z)) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(a,multiply(c,Z)))),bind(Y0,$fot(multiply(inverse(a),multiply(b,Z))))]]) ).
cnf(refute_0_319,plain,
multiply(inverse(a),multiply(b,Z)) = multiply(a,multiply(c,Z)),
inference(resolve,[$cnf( $equal(multiply(a,multiply(c,Z)),multiply(inverse(a),multiply(b,Z))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
multiply(inverse(a),multiply(b,a)) = multiply(a,multiply(c,a)),
inference(subst,[],[refute_0_319:[bind(Z,$fot(a))]]) ).
cnf(refute_0_321,plain,
( multiply(inverse(a),multiply(b,a)) != multiply(a,multiply(c,a))
| multiply(inverse(a),multiply(b,a)) != multiply(inverse(c),multiply(k,c))
| multiply(a,multiply(c,a)) = multiply(inverse(c),multiply(k,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),multiply(b,a)),multiply(inverse(c),multiply(k,c))) ),[0],$fot(multiply(a,multiply(c,a)))]]) ).
cnf(refute_0_322,plain,
( multiply(inverse(a),multiply(b,a)) != multiply(inverse(c),multiply(k,c))
| multiply(a,multiply(c,a)) = multiply(inverse(c),multiply(k,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(b,a)),multiply(a,multiply(c,a))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
multiply(a,multiply(c,a)) = multiply(inverse(c),multiply(k,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(b,a)),multiply(inverse(c),multiply(k,c))) )],[refute_0_287,refute_0_322]) ).
cnf(refute_0_324,plain,
( multiply(a,multiply(c,a)) != multiply(inverse(c),multiply(k,c))
| multiply(inverse(c),multiply(k,c)) = multiply(a,multiply(c,a)) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(a,multiply(c,a)))),bind(Y0,$fot(multiply(inverse(c),multiply(k,c))))]]) ).
cnf(refute_0_325,plain,
multiply(inverse(c),multiply(k,c)) = multiply(a,multiply(c,a)),
inference(resolve,[$cnf( $equal(multiply(a,multiply(c,a)),multiply(inverse(c),multiply(k,c))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
( multiply(inverse(c),multiply(k,c)) != multiply(a,multiply(c,a))
| multiply(k,c) != multiply(inverse(inverse(c)),multiply(inverse(c),multiply(k,c)))
| multiply(k,c) = multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(k,c),multiply(inverse(inverse(c)),multiply(inverse(c),multiply(k,c)))) ),[1,1],$fot(multiply(a,multiply(c,a)))]]) ).
cnf(refute_0_327,plain,
( multiply(k,c) != multiply(inverse(inverse(c)),multiply(inverse(c),multiply(k,c)))
| multiply(k,c) = multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),multiply(k,c)),multiply(a,multiply(c,a))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
multiply(k,c) = multiply(inverse(inverse(c)),multiply(a,multiply(c,a))),
inference(resolve,[$cnf( $equal(multiply(k,c),multiply(inverse(inverse(c)),multiply(inverse(c),multiply(k,c)))) )],[refute_0_10,refute_0_327]) ).
cnf(refute_0_329,plain,
multiply(multiply(X,Y),multiply(X,Y)) = multiply(X,multiply(Y,multiply(X,Y))),
inference(subst,[],[associativity:[bind(Z,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_330,plain,
inverse(multiply(X,Y)) = multiply(multiply(X,Y),multiply(X,Y)),
inference(subst,[],[refute_0_53:[bind(X_11,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_331,plain,
( inverse(multiply(X,Y)) != multiply(multiply(X,Y),multiply(X,Y))
| multiply(multiply(X,Y),multiply(X,Y)) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(multiply(X,Y),multiply(X,Y))))]]) ).
cnf(refute_0_332,plain,
multiply(multiply(X,Y),multiply(X,Y)) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(multiply(X,Y),multiply(X,Y))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
( multiply(multiply(X,Y),multiply(X,Y)) != multiply(X,multiply(Y,multiply(X,Y)))
| multiply(multiply(X,Y),multiply(X,Y)) != inverse(multiply(X,Y))
| inverse(multiply(X,Y)) = multiply(X,multiply(Y,multiply(X,Y))) ),
introduced(tautology,[equality,[$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_334,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( $equal(multiply(multiply(X,Y),multiply(X,Y)),inverse(multiply(X,Y))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
inverse(multiply(X,Y)) = multiply(X,multiply(Y,multiply(X,Y))),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),multiply(X,Y)),multiply(X,multiply(Y,multiply(X,Y)))) )],[refute_0_329,refute_0_334]) ).
cnf(refute_0_336,plain,
( inverse(multiply(X,Y)) != multiply(X,multiply(Y,multiply(X,Y)))
| multiply(X,multiply(Y,multiply(X,Y))) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(X,multiply(Y,multiply(X,Y)))))]]) ).
cnf(refute_0_337,plain,
multiply(X,multiply(Y,multiply(X,Y))) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(X,Y)))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
multiply(c,multiply(a,multiply(c,a))) = inverse(multiply(c,a)),
inference(subst,[],[refute_0_337:[bind(X,$fot(c)),bind(Y,$fot(a))]]) ).
cnf(refute_0_339,plain,
inverse(inverse(c)) = c,
inference(subst,[],[refute_0_138:[bind(X_12,$fot(c))]]) ).
cnf(refute_0_340,plain,
multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) = multiply(inverse(inverse(c)),multiply(a,multiply(c,a))),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(c)),multiply(a,multiply(c,a))))]]) ).
cnf(refute_0_341,plain,
( multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) != multiply(inverse(inverse(c)),multiply(a,multiply(c,a)))
| inverse(inverse(c)) != c
| multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) = multiply(c,multiply(a,multiply(c,a))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(c)),multiply(a,multiply(c,a))),multiply(inverse(inverse(c)),multiply(a,multiply(c,a)))) ),[1,0],$fot(c)]]) ).
cnf(refute_0_342,plain,
( inverse(inverse(c)) != c
| multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) = multiply(c,multiply(a,multiply(c,a))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(c)),multiply(a,multiply(c,a))),multiply(inverse(inverse(c)),multiply(a,multiply(c,a)))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) = multiply(c,multiply(a,multiply(c,a))),
inference(resolve,[$cnf( $equal(inverse(inverse(c)),c) )],[refute_0_339,refute_0_342]) ).
cnf(refute_0_344,plain,
( multiply(c,multiply(a,multiply(c,a))) != inverse(multiply(c,a))
| multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) != multiply(c,multiply(a,multiply(c,a)))
| multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) = inverse(multiply(c,a)) ),
inference(subst,[],[refute_0_213:[bind(X0,$fot(multiply(inverse(inverse(c)),multiply(a,multiply(c,a))))),bind(Y0,$fot(multiply(c,multiply(a,multiply(c,a))))),bind(Z0,$fot(inverse(multiply(c,a))))]]) ).
cnf(refute_0_345,plain,
( multiply(c,multiply(a,multiply(c,a))) != inverse(multiply(c,a))
| multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) = inverse(multiply(c,a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(c)),multiply(a,multiply(c,a))),multiply(c,multiply(a,multiply(c,a)))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) = inverse(multiply(c,a)),
inference(resolve,[$cnf( $equal(multiply(c,multiply(a,multiply(c,a))),inverse(multiply(c,a))) )],[refute_0_338,refute_0_345]) ).
cnf(refute_0_347,plain,
( multiply(inverse(inverse(c)),multiply(a,multiply(c,a))) != inverse(multiply(c,a))
| multiply(k,c) != multiply(inverse(inverse(c)),multiply(a,multiply(c,a)))
| multiply(k,c) = inverse(multiply(c,a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(k,c),multiply(inverse(inverse(c)),multiply(a,multiply(c,a)))) ),[1],$fot(inverse(multiply(c,a)))]]) ).
cnf(refute_0_348,plain,
( multiply(k,c) != multiply(inverse(inverse(c)),multiply(a,multiply(c,a)))
| multiply(k,c) = inverse(multiply(c,a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(c)),multiply(a,multiply(c,a))),inverse(multiply(c,a))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
multiply(k,c) = inverse(multiply(c,a)),
inference(resolve,[$cnf( $equal(multiply(k,c),multiply(inverse(inverse(c)),multiply(a,multiply(c,a)))) )],[refute_0_328,refute_0_348]) ).
cnf(refute_0_350,plain,
( multiply(k,c) != inverse(multiply(c,a))
| inverse(multiply(c,a)) = multiply(k,c) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(multiply(k,c))),bind(Y0,$fot(inverse(multiply(c,a))))]]) ).
cnf(refute_0_351,plain,
inverse(multiply(c,a)) = multiply(k,c),
inference(resolve,[$cnf( $equal(multiply(k,c),inverse(multiply(c,a))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
( multiply(inverse(multiply(c,a)),multiply(c,a)) != identity
| inverse(multiply(c,a)) != multiply(k,c)
| multiply(multiply(k,c),multiply(c,a)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(c,a)),multiply(c,a)),identity) ),[0,0],$fot(multiply(k,c))]]) ).
cnf(refute_0_353,plain,
( multiply(inverse(multiply(c,a)),multiply(c,a)) != identity
| multiply(multiply(k,c),multiply(c,a)) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(c,a)),multiply(k,c)) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
multiply(multiply(k,c),multiply(c,a)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(c,a)),multiply(c,a)),identity) )],[refute_0_0,refute_0_353]) ).
cnf(refute_0_355,plain,
inverse(b) = multiply(c,multiply(c,multiply(c,inverse(b)))),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(c)),bind(X_7,$fot(inverse(b)))]]) ).
cnf(refute_0_356,plain,
( multiply(c,inverse(b)) != a
| inverse(b) != multiply(c,multiply(c,multiply(c,inverse(b))))
| inverse(b) = multiply(c,multiply(c,a)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(c,multiply(c,multiply(c,inverse(b))))) ),[1,1,1],$fot(a)]]) ).
cnf(refute_0_357,plain,
( inverse(b) != multiply(c,multiply(c,multiply(c,inverse(b))))
| inverse(b) = multiply(c,multiply(c,a)) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(b)),a) )],[refute_0_229,refute_0_356]) ).
cnf(refute_0_358,plain,
inverse(b) = multiply(c,multiply(c,a)),
inference(resolve,[$cnf( $equal(inverse(b),multiply(c,multiply(c,multiply(c,inverse(b))))) )],[refute_0_355,refute_0_357]) ).
cnf(refute_0_359,plain,
multiply(c,multiply(c,a)) = multiply(inverse(c),a),
inference(subst,[],[refute_0_61:[bind(Y,$fot(c)),bind(Z,$fot(a))]]) ).
cnf(refute_0_360,plain,
( multiply(c,multiply(c,a)) != multiply(inverse(c),a)
| inverse(b) != multiply(c,multiply(c,a))
| inverse(b) = multiply(inverse(c),a) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(c,multiply(c,a))) ),[1],$fot(multiply(inverse(c),a))]]) ).
cnf(refute_0_361,plain,
( inverse(b) != multiply(c,multiply(c,a))
| inverse(b) = multiply(inverse(c),a) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,a)),multiply(inverse(c),a)) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
inverse(b) = multiply(inverse(c),a),
inference(resolve,[$cnf( $equal(inverse(b),multiply(c,multiply(c,a))) )],[refute_0_358,refute_0_361]) ).
cnf(refute_0_363,plain,
( inverse(b) != multiply(inverse(c),a)
| multiply(inverse(c),a) = inverse(b) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(inverse(b))),bind(Y0,$fot(multiply(inverse(c),a)))]]) ).
cnf(refute_0_364,plain,
multiply(inverse(c),a) = inverse(b),
inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(c),a)) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
( multiply(c,multiply(c,a)) != multiply(inverse(c),a)
| multiply(inverse(c),a) != inverse(b)
| multiply(c,multiply(c,a)) = inverse(b) ),
inference(subst,[],[refute_0_213:[bind(X0,$fot(multiply(c,multiply(c,a)))),bind(Y0,$fot(multiply(inverse(c),a))),bind(Z0,$fot(inverse(b)))]]) ).
cnf(refute_0_366,plain,
( multiply(inverse(c),a) != inverse(b)
| multiply(c,multiply(c,a)) = inverse(b) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,a)),multiply(inverse(c),a)) )],[refute_0_359,refute_0_365]) ).
cnf(refute_0_367,plain,
multiply(c,multiply(c,a)) = inverse(b),
inference(resolve,[$cnf( $equal(multiply(inverse(c),a),inverse(b)) )],[refute_0_364,refute_0_366]) ).
cnf(refute_0_368,plain,
multiply(k,multiply(c,multiply(c,a))) = multiply(k,multiply(c,multiply(c,a))),
introduced(tautology,[refl,[$fot(multiply(k,multiply(c,multiply(c,a))))]]) ).
cnf(refute_0_369,plain,
( multiply(c,multiply(c,a)) != inverse(b)
| multiply(k,multiply(c,multiply(c,a))) != multiply(k,multiply(c,multiply(c,a)))
| multiply(k,multiply(c,multiply(c,a))) = multiply(k,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(k,multiply(c,multiply(c,a))),multiply(k,multiply(c,multiply(c,a)))) ),[1,1],$fot(inverse(b))]]) ).
cnf(refute_0_370,plain,
( multiply(c,multiply(c,a)) != inverse(b)
| multiply(k,multiply(c,multiply(c,a))) = multiply(k,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(k,multiply(c,multiply(c,a))),multiply(k,multiply(c,multiply(c,a)))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
multiply(k,multiply(c,multiply(c,a))) = multiply(k,inverse(b)),
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,a)),inverse(b)) )],[refute_0_367,refute_0_370]) ).
cnf(refute_0_372,plain,
multiply(multiply(k,c),multiply(c,a)) = multiply(k,multiply(c,multiply(c,a))),
inference(subst,[],[associativity:[bind(X,$fot(k)),bind(Y,$fot(c)),bind(Z,$fot(multiply(c,a)))]]) ).
cnf(refute_0_373,plain,
( multiply(multiply(k,c),multiply(c,a)) != multiply(k,multiply(c,multiply(c,a)))
| multiply(k,multiply(c,multiply(c,a))) != multiply(k,inverse(b))
| multiply(multiply(k,c),multiply(c,a)) = multiply(k,inverse(b)) ),
inference(subst,[],[refute_0_213:[bind(X0,$fot(multiply(multiply(k,c),multiply(c,a)))),bind(Y0,$fot(multiply(k,multiply(c,multiply(c,a))))),bind(Z0,$fot(multiply(k,inverse(b))))]]) ).
cnf(refute_0_374,plain,
( multiply(k,multiply(c,multiply(c,a))) != multiply(k,inverse(b))
| multiply(multiply(k,c),multiply(c,a)) = multiply(k,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(k,c),multiply(c,a)),multiply(k,multiply(c,multiply(c,a)))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
multiply(multiply(k,c),multiply(c,a)) = multiply(k,inverse(b)),
inference(resolve,[$cnf( $equal(multiply(k,multiply(c,multiply(c,a))),multiply(k,inverse(b))) )],[refute_0_371,refute_0_374]) ).
cnf(refute_0_376,plain,
( multiply(multiply(k,c),multiply(c,a)) != multiply(k,inverse(b))
| multiply(multiply(k,c),multiply(c,a)) != identity
| multiply(k,inverse(b)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(k,c),multiply(c,a)),identity) ),[0],$fot(multiply(k,inverse(b)))]]) ).
cnf(refute_0_377,plain,
( multiply(multiply(k,c),multiply(c,a)) != identity
| multiply(k,inverse(b)) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(k,c),multiply(c,a)),multiply(k,inverse(b))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
multiply(k,inverse(b)) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(k,c),multiply(c,a)),identity) )],[refute_0_354,refute_0_377]) ).
cnf(refute_0_379,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(k,inverse(b)),identity) )],[refute_0_378,prove_k_times_inverse_b_is_e]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 07:04:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50
% 0.21/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.54
%------------------------------------------------------------------------------