TSTP Solution File: GRP606-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP606-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 10:43:54 EDT 2022
% Result : Unsatisfiable 0.41s 0.60s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 54
% Syntax : Number of clauses : 203 ( 109 unt; 0 nHn; 100 RR)
% Number of literals : 344 ( 343 equ; 143 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 440 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B ).
cnf(multiply,axiom,
multiply(A,B) = inverse(double_divide(B,A)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_4,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[multiply,refute_0_3]) ).
cnf(refute_0_5,plain,
inverse(double_divide(inverse(B),double_divide(A,C))) = multiply(double_divide(A,C),inverse(B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(A,C))),bind(B,$fot(inverse(B)))]]) ).
cnf(refute_0_6,plain,
multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A) = multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A),
introduced(tautology,[refl,[$fot(multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A))]]) ).
cnf(refute_0_7,plain,
( multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A) != multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A)
| inverse(double_divide(inverse(B),double_divide(A,C))) != multiply(double_divide(A,C),inverse(B))
| multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A) = multiply(multiply(double_divide(A,C),inverse(B)),A) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A),multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A)) ),[1,0],$fot(multiply(double_divide(A,C),inverse(B)))]]) ).
cnf(refute_0_8,plain,
( inverse(double_divide(inverse(B),double_divide(A,C))) != multiply(double_divide(A,C),inverse(B))
| multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A) = multiply(multiply(double_divide(A,C),inverse(B)),A) ),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A),multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A) = multiply(multiply(double_divide(A,C),inverse(B)),A),
inference(resolve,[$cnf( $equal(inverse(double_divide(inverse(B),double_divide(A,C))),multiply(double_divide(A,C),inverse(B))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))) = multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(double_divide(inverse(B),double_divide(A,C))))),bind(B,$fot(A))]]) ).
cnf(refute_0_11,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A) != multiply(multiply(double_divide(A,C),inverse(B)),A)
| inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))) != multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A)
| inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))) = multiply(multiply(double_divide(A,C),inverse(B)),A) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))))),bind(Y,$fot(multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A))),bind(Z,$fot(multiply(multiply(double_divide(A,C),inverse(B)),A)))]]) ).
cnf(refute_0_14,plain,
( multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A) != multiply(multiply(double_divide(A,C),inverse(B)),A)
| inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))) = multiply(multiply(double_divide(A,C),inverse(B)),A) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))) = multiply(multiply(double_divide(A,C),inverse(B)),A),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(inverse(B),double_divide(A,C))),A),multiply(multiply(double_divide(A,C),inverse(B)),A)) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C),
introduced(tautology,[refl,[$fot(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C))]]) ).
cnf(refute_0_17,plain,
( double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) != double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)
| inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))) != multiply(multiply(double_divide(A,C),inverse(B)),A)
| double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C),double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)) ),[1,0],$fot(multiply(multiply(double_divide(A,C),inverse(B)),A))]]) ).
cnf(refute_0_18,plain,
( inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))) != multiply(multiply(double_divide(A,C),inverse(B)),A)
| double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C),double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C),
inference(resolve,[$cnf( $equal(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),multiply(multiply(double_divide(A,C),inverse(B)),A)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) != B
| double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) != double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C)
| double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C),B) ),[0],$fot(double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C))]]) ).
cnf(refute_0_21,plain,
( double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) != B
| double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C) = B ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C),double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
double_divide(multiply(multiply(double_divide(A,C),inverse(B)),A),C) = B,
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C),B) )],[single_axiom,refute_0_21]) ).
cnf(refute_0_23,plain,
double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C) = B,
inference(subst,[],[refute_0_22:[bind(A,$fot(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)))]]) ).
cnf(refute_0_24,plain,
double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C) = X_3,
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_25,plain,
( double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C) != X_3
| double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C) != B
| double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C),B) ),[0,0,0,0],$fot(X_3)]]) ).
cnf(refute_0_26,plain,
( double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C) != B
| double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C) = B ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),X_3) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C) = B,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C),B) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,multiply(X_3,inverse(B))),inverse(X_3)),X_2)),multiply(X_3,inverse(B))) = B,
inference(subst,[],[refute_0_27:[bind(C,$fot(multiply(X_3,inverse(B))))]]) ).
cnf(refute_0_29,plain,
multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) = inverse(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A)),
inference(subst,[],[multiply:[bind(B,$fot(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)))]]) ).
cnf(refute_0_30,plain,
double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A) = X_3,
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2)),bind(B,$fot(X_3)),bind(C,$fot(A))]]) ).
cnf(refute_0_31,plain,
( multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) != inverse(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A))
| double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A) != X_3
| multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) = inverse(X_3) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)),inverse(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A))) ),[1,0],$fot(X_3)]]) ).
cnf(refute_0_32,plain,
( multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) != inverse(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A))
| multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) = inverse(X_3) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A),X_3) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) = inverse(X_3),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)),inverse(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,multiply(X_3,inverse(B))),inverse(X_3)),X_2)) = inverse(X_3),
inference(subst,[],[refute_0_33:[bind(A,$fot(multiply(X_3,inverse(B))))]]) ).
cnf(refute_0_35,plain,
( multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,multiply(X_3,inverse(B))),inverse(X_3)),X_2)) != inverse(X_3)
| double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,multiply(X_3,inverse(B))),inverse(X_3)),X_2)),multiply(X_3,inverse(B))) != B
| double_divide(inverse(X_3),multiply(X_3,inverse(B))) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,multiply(X_3,inverse(B))),inverse(X_3)),X_2)),multiply(X_3,inverse(B))),B) ),[0,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_36,plain,
( double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,multiply(X_3,inverse(B))),inverse(X_3)),X_2)),multiply(X_3,inverse(B))) != B
| double_divide(inverse(X_3),multiply(X_3,inverse(B))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,multiply(X_3,inverse(B))),inverse(X_3)),X_2)),inverse(X_3)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
double_divide(inverse(X_3),multiply(X_3,inverse(B))) = B,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,multiply(X_3,inverse(B))),inverse(X_3)),X_2)),multiply(X_3,inverse(B))),B) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(inverse(multiply(X_39,inverse(X_39))),multiply(multiply(X_39,inverse(X_39)),inverse(B))) = B,
inference(subst,[],[refute_0_37:[bind(X_3,$fot(multiply(X_39,inverse(X_39))))]]) ).
cnf(refute_0_39,plain,
multiply(multiply(X_37,inverse(X_37)),inverse(X_36)) = inverse(double_divide(inverse(X_36),multiply(X_37,inverse(X_37)))),
inference(subst,[],[multiply:[bind(A,$fot(multiply(X_37,inverse(X_37)))),bind(B,$fot(inverse(X_36)))]]) ).
cnf(refute_0_40,plain,
double_divide(multiply(multiply(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))),inverse(B)),inverse(X_17)),multiply(X_17,inverse(X_16))) = B,
inference(subst,[],[refute_0_22:[bind(A,$fot(inverse(X_17))),bind(C,$fot(multiply(X_17,inverse(X_16))))]]) ).
cnf(refute_0_41,plain,
double_divide(inverse(X_17),multiply(X_17,inverse(X_16))) = X_16,
inference(subst,[],[refute_0_37:[bind(B,$fot(X_16)),bind(X_3,$fot(X_17))]]) ).
cnf(refute_0_42,plain,
( double_divide(multiply(multiply(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))),inverse(B)),inverse(X_17)),multiply(X_17,inverse(X_16))) != B
| double_divide(inverse(X_17),multiply(X_17,inverse(X_16))) != X_16
| double_divide(multiply(multiply(X_16,inverse(B)),inverse(X_17)),multiply(X_17,inverse(X_16))) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))),inverse(B)),inverse(X_17)),multiply(X_17,inverse(X_16))),B) ),[0,0,0,0],$fot(X_16)]]) ).
cnf(refute_0_43,plain,
( double_divide(multiply(multiply(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))),inverse(B)),inverse(X_17)),multiply(X_17,inverse(X_16))) != B
| double_divide(multiply(multiply(X_16,inverse(B)),inverse(X_17)),multiply(X_17,inverse(X_16))) = B ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))),X_16) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
double_divide(multiply(multiply(X_16,inverse(B)),inverse(X_17)),multiply(X_17,inverse(X_16))) = B,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))),inverse(B)),inverse(X_17)),multiply(X_17,inverse(X_16))),B) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
double_divide(multiply(multiply(X_35,inverse(X_33)),inverse(X_35)),multiply(X_35,inverse(X_35))) = X_33,
inference(subst,[],[refute_0_44:[bind(B,$fot(X_33)),bind(X_16,$fot(X_35)),bind(X_17,$fot(X_35))]]) ).
cnf(refute_0_46,plain,
multiply(multiply(X_17,inverse(X_16)),inverse(X_17)) = inverse(double_divide(inverse(X_17),multiply(X_17,inverse(X_16)))),
inference(subst,[],[multiply:[bind(A,$fot(multiply(X_17,inverse(X_16)))),bind(B,$fot(inverse(X_17)))]]) ).
cnf(refute_0_47,plain,
( multiply(multiply(X_17,inverse(X_16)),inverse(X_17)) != inverse(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))))
| double_divide(inverse(X_17),multiply(X_17,inverse(X_16))) != X_16
| multiply(multiply(X_17,inverse(X_16)),inverse(X_17)) = inverse(X_16) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_17,inverse(X_16)),inverse(X_17)),inverse(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))))) ),[1,0],$fot(X_16)]]) ).
cnf(refute_0_48,plain,
( multiply(multiply(X_17,inverse(X_16)),inverse(X_17)) != inverse(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))))
| multiply(multiply(X_17,inverse(X_16)),inverse(X_17)) = inverse(X_16) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))),X_16) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(multiply(X_17,inverse(X_16)),inverse(X_17)) = inverse(X_16),
inference(resolve,[$cnf( $equal(multiply(multiply(X_17,inverse(X_16)),inverse(X_17)),inverse(double_divide(inverse(X_17),multiply(X_17,inverse(X_16))))) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(multiply(X_35,inverse(X_33)),inverse(X_35)) = inverse(X_33),
inference(subst,[],[refute_0_49:[bind(X_16,$fot(X_33)),bind(X_17,$fot(X_35))]]) ).
cnf(refute_0_51,plain,
( multiply(multiply(X_35,inverse(X_33)),inverse(X_35)) != inverse(X_33)
| double_divide(multiply(multiply(X_35,inverse(X_33)),inverse(X_35)),multiply(X_35,inverse(X_35))) != X_33
| double_divide(inverse(X_33),multiply(X_35,inverse(X_35))) = X_33 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(X_35,inverse(X_33)),inverse(X_35)),multiply(X_35,inverse(X_35))),X_33) ),[0,0],$fot(inverse(X_33))]]) ).
cnf(refute_0_52,plain,
( double_divide(multiply(multiply(X_35,inverse(X_33)),inverse(X_35)),multiply(X_35,inverse(X_35))) != X_33
| double_divide(inverse(X_33),multiply(X_35,inverse(X_35))) = X_33 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_35,inverse(X_33)),inverse(X_35)),inverse(X_33)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
double_divide(inverse(X_33),multiply(X_35,inverse(X_35))) = X_33,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_35,inverse(X_33)),inverse(X_35)),multiply(X_35,inverse(X_35))),X_33) )],[refute_0_45,refute_0_52]) ).
cnf(refute_0_54,plain,
double_divide(inverse(X_36),multiply(X_37,inverse(X_37))) = X_36,
inference(subst,[],[refute_0_53:[bind(X_33,$fot(X_36)),bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_55,plain,
( multiply(multiply(X_37,inverse(X_37)),inverse(X_36)) != inverse(double_divide(inverse(X_36),multiply(X_37,inverse(X_37))))
| double_divide(inverse(X_36),multiply(X_37,inverse(X_37))) != X_36
| multiply(multiply(X_37,inverse(X_37)),inverse(X_36)) = inverse(X_36) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_37,inverse(X_37)),inverse(X_36)),inverse(double_divide(inverse(X_36),multiply(X_37,inverse(X_37))))) ),[1,0],$fot(X_36)]]) ).
cnf(refute_0_56,plain,
( multiply(multiply(X_37,inverse(X_37)),inverse(X_36)) != inverse(double_divide(inverse(X_36),multiply(X_37,inverse(X_37))))
| multiply(multiply(X_37,inverse(X_37)),inverse(X_36)) = inverse(X_36) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_36),multiply(X_37,inverse(X_37))),X_36) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(multiply(X_37,inverse(X_37)),inverse(X_36)) = inverse(X_36),
inference(resolve,[$cnf( $equal(multiply(multiply(X_37,inverse(X_37)),inverse(X_36)),inverse(double_divide(inverse(X_36),multiply(X_37,inverse(X_37))))) )],[refute_0_39,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(multiply(X_39,inverse(X_39)),inverse(B)) = inverse(B),
inference(subst,[],[refute_0_57:[bind(X_36,$fot(B)),bind(X_37,$fot(X_39))]]) ).
cnf(refute_0_59,plain,
( multiply(multiply(X_39,inverse(X_39)),inverse(B)) != inverse(B)
| double_divide(inverse(multiply(X_39,inverse(X_39))),multiply(multiply(X_39,inverse(X_39)),inverse(B))) != B
| double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(X_39,inverse(X_39))),multiply(multiply(X_39,inverse(X_39)),inverse(B))),B) ),[0,1],$fot(inverse(B))]]) ).
cnf(refute_0_60,plain,
( double_divide(inverse(multiply(X_39,inverse(X_39))),multiply(multiply(X_39,inverse(X_39)),inverse(B))) != B
| double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_39,inverse(X_39)),inverse(B)),inverse(B)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)) = B,
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_39,inverse(X_39))),multiply(multiply(X_39,inverse(X_39)),inverse(B))),B) )],[refute_0_38,refute_0_60]) ).
cnf(refute_0_62,plain,
double_divide(inverse(multiply(B,inverse(X_18))),multiply(multiply(B,inverse(X_18)),inverse(B))) = B,
inference(subst,[],[refute_0_37:[bind(X_3,$fot(multiply(B,inverse(X_18))))]]) ).
cnf(refute_0_63,plain,
multiply(multiply(B,inverse(X_18)),inverse(B)) = inverse(X_18),
inference(subst,[],[refute_0_49:[bind(X_16,$fot(X_18)),bind(X_17,$fot(B))]]) ).
cnf(refute_0_64,plain,
( multiply(multiply(B,inverse(X_18)),inverse(B)) != inverse(X_18)
| double_divide(inverse(multiply(B,inverse(X_18))),multiply(multiply(B,inverse(X_18)),inverse(B))) != B
| double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(B,inverse(X_18))),multiply(multiply(B,inverse(X_18)),inverse(B))),B) ),[0,1],$fot(inverse(X_18))]]) ).
cnf(refute_0_65,plain,
( double_divide(inverse(multiply(B,inverse(X_18))),multiply(multiply(B,inverse(X_18)),inverse(B))) != B
| double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,inverse(X_18)),inverse(B)),inverse(X_18)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)) = B,
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(B,inverse(X_18))),multiply(multiply(B,inverse(X_18)),inverse(B))),B) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
double_divide(inverse(multiply(multiply(X_21,inverse(X_16)),inverse(X_21))),inverse(X_21)) = multiply(X_21,inverse(X_16)),
inference(subst,[],[refute_0_66:[bind(B,$fot(multiply(X_21,inverse(X_16)))),bind(X_18,$fot(X_21))]]) ).
cnf(refute_0_68,plain,
multiply(multiply(X_21,inverse(X_16)),inverse(X_21)) = inverse(X_16),
inference(subst,[],[refute_0_49:[bind(X_17,$fot(X_21))]]) ).
cnf(refute_0_69,plain,
( multiply(multiply(X_21,inverse(X_16)),inverse(X_21)) != inverse(X_16)
| double_divide(inverse(multiply(multiply(X_21,inverse(X_16)),inverse(X_21))),inverse(X_21)) != multiply(X_21,inverse(X_16))
| double_divide(inverse(inverse(X_16)),inverse(X_21)) = multiply(X_21,inverse(X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(multiply(X_21,inverse(X_16)),inverse(X_21))),inverse(X_21)),multiply(X_21,inverse(X_16))) ),[0,0,0],$fot(inverse(X_16))]]) ).
cnf(refute_0_70,plain,
( double_divide(inverse(multiply(multiply(X_21,inverse(X_16)),inverse(X_21))),inverse(X_21)) != multiply(X_21,inverse(X_16))
| double_divide(inverse(inverse(X_16)),inverse(X_21)) = multiply(X_21,inverse(X_16)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,inverse(X_16)),inverse(X_21)),inverse(X_16)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
double_divide(inverse(inverse(X_16)),inverse(X_21)) = multiply(X_21,inverse(X_16)),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(multiply(X_21,inverse(X_16)),inverse(X_21))),inverse(X_21)),multiply(X_21,inverse(X_16))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
double_divide(inverse(inverse(double_divide(B,A))),inverse(X_30)) = multiply(X_30,inverse(double_divide(B,A))),
inference(subst,[],[refute_0_71:[bind(X_16,$fot(double_divide(B,A))),bind(X_21,$fot(X_30))]]) ).
cnf(refute_0_73,plain,
( double_divide(inverse(inverse(double_divide(B,A))),inverse(X_30)) != multiply(X_30,inverse(double_divide(B,A)))
| inverse(double_divide(B,A)) != multiply(A,B)
| double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(X_30,inverse(double_divide(B,A))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(double_divide(B,A))),inverse(X_30)),multiply(X_30,inverse(double_divide(B,A)))) ),[0,0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_74,plain,
( double_divide(inverse(inverse(double_divide(B,A))),inverse(X_30)) != multiply(X_30,inverse(double_divide(B,A)))
| double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(X_30,inverse(double_divide(B,A))) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_4,refute_0_73]) ).
cnf(refute_0_75,plain,
double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(X_30,inverse(double_divide(B,A))),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(double_divide(B,A))),inverse(X_30)),multiply(X_30,inverse(double_divide(B,A)))) )],[refute_0_72,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(X_30,inverse(double_divide(B,A))) = multiply(X_30,inverse(double_divide(B,A))),
introduced(tautology,[refl,[$fot(multiply(X_30,inverse(double_divide(B,A))))]]) ).
cnf(refute_0_77,plain,
( multiply(X_30,inverse(double_divide(B,A))) != multiply(X_30,inverse(double_divide(B,A)))
| inverse(double_divide(B,A)) != multiply(A,B)
| multiply(X_30,inverse(double_divide(B,A))) = multiply(X_30,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,inverse(double_divide(B,A))),multiply(X_30,inverse(double_divide(B,A)))) ),[1,1],$fot(multiply(A,B))]]) ).
cnf(refute_0_78,plain,
( inverse(double_divide(B,A)) != multiply(A,B)
| multiply(X_30,inverse(double_divide(B,A))) = multiply(X_30,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(double_divide(B,A))),multiply(X_30,inverse(double_divide(B,A)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(X_30,inverse(double_divide(B,A))) = multiply(X_30,multiply(A,B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_4,refute_0_78]) ).
cnf(refute_0_80,plain,
( multiply(X_30,inverse(double_divide(B,A))) != multiply(X_30,multiply(A,B))
| double_divide(inverse(multiply(A,B)),inverse(X_30)) != multiply(X_30,inverse(double_divide(B,A)))
| double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(X_30,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(A,B)),inverse(X_30)),multiply(X_30,inverse(double_divide(B,A)))) ),[1],$fot(multiply(X_30,multiply(A,B)))]]) ).
cnf(refute_0_81,plain,
( double_divide(inverse(multiply(A,B)),inverse(X_30)) != multiply(X_30,inverse(double_divide(B,A)))
| double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(X_30,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(double_divide(B,A))),multiply(X_30,multiply(A,B))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(X_30,multiply(A,B)),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(A,B)),inverse(X_30)),multiply(X_30,inverse(double_divide(B,A)))) )],[refute_0_75,refute_0_81]) ).
cnf(refute_0_83,plain,
double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)) = multiply(B,multiply(X_39,inverse(X_39))),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_39)),bind(B,$fot(inverse(X_39))),bind(X_30,$fot(B))]]) ).
cnf(refute_0_84,plain,
( double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)) != B
| double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)) != multiply(B,multiply(X_39,inverse(X_39)))
| multiply(B,multiply(X_39,inverse(X_39))) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)),B) ),[0],$fot(multiply(B,multiply(X_39,inverse(X_39))))]]) ).
cnf(refute_0_85,plain,
( double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)) != B
| multiply(B,multiply(X_39,inverse(X_39))) = B ),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)),multiply(B,multiply(X_39,inverse(X_39)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(B,multiply(X_39,inverse(X_39))) = B,
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_39,inverse(X_39))),inverse(B)),B) )],[refute_0_61,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(a2,multiply(b2,inverse(b2))) = a2,
inference(subst,[],[refute_0_86:[bind(B,$fot(a2)),bind(X_39,$fot(b2))]]) ).
cnf(refute_0_88,plain,
multiply(inverse(X_30),inverse(inverse(X_29))) = inverse(double_divide(inverse(inverse(X_29)),inverse(X_30))),
inference(subst,[],[multiply:[bind(A,$fot(inverse(X_30))),bind(B,$fot(inverse(inverse(X_29))))]]) ).
cnf(refute_0_89,plain,
double_divide(inverse(inverse(X_29)),inverse(X_30)) = multiply(X_30,inverse(X_29)),
inference(subst,[],[refute_0_71:[bind(X_16,$fot(X_29)),bind(X_21,$fot(X_30))]]) ).
cnf(refute_0_90,plain,
( multiply(inverse(X_30),inverse(inverse(X_29))) != inverse(double_divide(inverse(inverse(X_29)),inverse(X_30)))
| double_divide(inverse(inverse(X_29)),inverse(X_30)) != multiply(X_30,inverse(X_29))
| multiply(inverse(X_30),inverse(inverse(X_29))) = inverse(multiply(X_30,inverse(X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_30),inverse(inverse(X_29))),inverse(double_divide(inverse(inverse(X_29)),inverse(X_30)))) ),[1,0],$fot(multiply(X_30,inverse(X_29)))]]) ).
cnf(refute_0_91,plain,
( multiply(inverse(X_30),inverse(inverse(X_29))) != inverse(double_divide(inverse(inverse(X_29)),inverse(X_30)))
| multiply(inverse(X_30),inverse(inverse(X_29))) = inverse(multiply(X_30,inverse(X_29))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(X_29)),inverse(X_30)),multiply(X_30,inverse(X_29))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(inverse(X_30),inverse(inverse(X_29))) = inverse(multiply(X_30,inverse(X_29))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),inverse(inverse(X_29))),inverse(double_divide(inverse(inverse(X_29)),inverse(X_30)))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
double_divide(inverse(X_33),multiply(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),inverse(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))) = X_33,
inference(subst,[],[refute_0_53:[bind(X_35,$fot(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))]]) ).
cnf(refute_0_94,plain,
double_divide(inverse(double_divide(B,A)),multiply(double_divide(B,A),inverse(X_16))) = X_16,
inference(subst,[],[refute_0_37:[bind(B,$fot(X_16)),bind(X_3,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_95,plain,
( double_divide(inverse(double_divide(B,A)),multiply(double_divide(B,A),inverse(X_16))) != X_16
| inverse(double_divide(B,A)) != multiply(A,B)
| double_divide(multiply(A,B),multiply(double_divide(B,A),inverse(X_16))) = X_16 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(B,A)),multiply(double_divide(B,A),inverse(X_16))),X_16) ),[0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_96,plain,
( double_divide(inverse(double_divide(B,A)),multiply(double_divide(B,A),inverse(X_16))) != X_16
| double_divide(multiply(A,B),multiply(double_divide(B,A),inverse(X_16))) = X_16 ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_4,refute_0_95]) ).
cnf(refute_0_97,plain,
double_divide(multiply(A,B),multiply(double_divide(B,A),inverse(X_16))) = X_16,
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(B,A)),multiply(double_divide(B,A),inverse(X_16))),X_16) )],[refute_0_94,refute_0_96]) ).
cnf(refute_0_98,plain,
double_divide(multiply(X_52,multiply(B,inverse(X_52))),multiply(double_divide(multiply(B,inverse(X_52)),X_52),inverse(X_54))) = X_54,
inference(subst,[],[refute_0_97:[bind(A,$fot(X_52)),bind(B,$fot(multiply(B,inverse(X_52)))),bind(X_16,$fot(X_54))]]) ).
cnf(refute_0_99,plain,
double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)) = multiply(X_18,multiply(B,inverse(X_18))),
inference(subst,[],[refute_0_82:[bind(A,$fot(B)),bind(B,$fot(inverse(X_18))),bind(X_30,$fot(X_18))]]) ).
cnf(refute_0_100,plain,
( double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)) != B
| double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)) != multiply(X_18,multiply(B,inverse(X_18)))
| multiply(X_18,multiply(B,inverse(X_18))) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)),B) ),[0],$fot(multiply(X_18,multiply(B,inverse(X_18))))]]) ).
cnf(refute_0_101,plain,
( double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)) != B
| multiply(X_18,multiply(B,inverse(X_18))) = B ),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)),multiply(X_18,multiply(B,inverse(X_18)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(X_18,multiply(B,inverse(X_18))) = B,
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(B,inverse(X_18))),inverse(X_18)),B) )],[refute_0_66,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(X_52,multiply(B,inverse(X_52))) = B,
inference(subst,[],[refute_0_102:[bind(X_18,$fot(X_52))]]) ).
cnf(refute_0_104,plain,
( multiply(X_52,multiply(B,inverse(X_52))) != B
| double_divide(multiply(X_52,multiply(B,inverse(X_52))),multiply(double_divide(multiply(B,inverse(X_52)),X_52),inverse(X_54))) != X_54
| double_divide(B,multiply(double_divide(multiply(B,inverse(X_52)),X_52),inverse(X_54))) = X_54 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_52,multiply(B,inverse(X_52))),multiply(double_divide(multiply(B,inverse(X_52)),X_52),inverse(X_54))),X_54) ),[0,0],$fot(B)]]) ).
cnf(refute_0_105,plain,
( double_divide(multiply(X_52,multiply(B,inverse(X_52))),multiply(double_divide(multiply(B,inverse(X_52)),X_52),inverse(X_54))) != X_54
| double_divide(B,multiply(double_divide(multiply(B,inverse(X_52)),X_52),inverse(X_54))) = X_54 ),
inference(resolve,[$cnf( $equal(multiply(X_52,multiply(B,inverse(X_52))),B) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
double_divide(B,multiply(double_divide(multiply(B,inverse(X_52)),X_52),inverse(X_54))) = X_54,
inference(resolve,[$cnf( $equal(double_divide(multiply(X_52,multiply(B,inverse(X_52))),multiply(double_divide(multiply(B,inverse(X_52)),X_52),inverse(X_54))),X_54) )],[refute_0_98,refute_0_105]) ).
cnf(refute_0_107,plain,
double_divide(inverse(X_33),multiply(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),inverse(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))) = double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),
inference(subst,[],[refute_0_106:[bind(B,$fot(inverse(X_33))),bind(X_52,$fot(X_73)),bind(X_54,$fot(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))]]) ).
cnf(refute_0_108,plain,
( double_divide(inverse(X_33),multiply(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),inverse(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))) != X_33
| double_divide(inverse(X_33),multiply(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),inverse(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))) != double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)
| double_divide(multiply(inverse(X_33),inverse(X_73)),X_73) = X_33 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_33),multiply(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),inverse(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))),X_33) ),[0],$fot(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73))]]) ).
cnf(refute_0_109,plain,
( double_divide(inverse(X_33),multiply(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),inverse(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))) != X_33
| double_divide(multiply(inverse(X_33),inverse(X_73)),X_73) = X_33 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_33),multiply(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),inverse(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))),double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
double_divide(multiply(inverse(X_33),inverse(X_73)),X_73) = X_33,
inference(resolve,[$cnf( $equal(double_divide(inverse(X_33),multiply(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73),inverse(double_divide(multiply(inverse(X_33),inverse(X_73)),X_73)))),X_33) )],[refute_0_93,refute_0_109]) ).
cnf(refute_0_111,plain,
double_divide(multiply(inverse(X_33),inverse(inverse(inverse(X_33)))),inverse(inverse(X_33))) = X_33,
inference(subst,[],[refute_0_110:[bind(X_73,$fot(inverse(inverse(X_33))))]]) ).
cnf(refute_0_112,plain,
double_divide(multiply(multiply(X_16,inverse(B)),inverse(multiply(X_48,inverse(X_48)))),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) = B,
inference(subst,[],[refute_0_44:[bind(X_17,$fot(multiply(X_48,inverse(X_48))))]]) ).
cnf(refute_0_113,plain,
multiply(X_40,multiply(multiply(X_37,inverse(X_37)),inverse(multiply(X_37,inverse(X_37))))) = X_40,
inference(subst,[],[refute_0_86:[bind(B,$fot(X_40)),bind(X_39,$fot(multiply(X_37,inverse(X_37))))]]) ).
cnf(refute_0_114,plain,
multiply(multiply(X_37,inverse(X_37)),inverse(multiply(X_37,inverse(X_37)))) = inverse(multiply(X_37,inverse(X_37))),
inference(subst,[],[refute_0_57:[bind(X_36,$fot(multiply(X_37,inverse(X_37))))]]) ).
cnf(refute_0_115,plain,
( multiply(X_40,multiply(multiply(X_37,inverse(X_37)),inverse(multiply(X_37,inverse(X_37))))) != X_40
| multiply(multiply(X_37,inverse(X_37)),inverse(multiply(X_37,inverse(X_37)))) != inverse(multiply(X_37,inverse(X_37)))
| multiply(X_40,inverse(multiply(X_37,inverse(X_37)))) = X_40 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_40,multiply(multiply(X_37,inverse(X_37)),inverse(multiply(X_37,inverse(X_37))))),X_40) ),[0,1],$fot(inverse(multiply(X_37,inverse(X_37))))]]) ).
cnf(refute_0_116,plain,
( multiply(X_40,multiply(multiply(X_37,inverse(X_37)),inverse(multiply(X_37,inverse(X_37))))) != X_40
| multiply(X_40,inverse(multiply(X_37,inverse(X_37)))) = X_40 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_37,inverse(X_37)),inverse(multiply(X_37,inverse(X_37)))),inverse(multiply(X_37,inverse(X_37)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(X_40,inverse(multiply(X_37,inverse(X_37)))) = X_40,
inference(resolve,[$cnf( $equal(multiply(X_40,multiply(multiply(X_37,inverse(X_37)),inverse(multiply(X_37,inverse(X_37))))),X_40) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(multiply(X_16,inverse(B)),inverse(multiply(X_48,inverse(X_48)))) = multiply(X_16,inverse(B)),
inference(subst,[],[refute_0_117:[bind(X_37,$fot(X_48)),bind(X_40,$fot(multiply(X_16,inverse(B))))]]) ).
cnf(refute_0_119,plain,
( multiply(multiply(X_16,inverse(B)),inverse(multiply(X_48,inverse(X_48)))) != multiply(X_16,inverse(B))
| double_divide(multiply(multiply(X_16,inverse(B)),inverse(multiply(X_48,inverse(X_48)))),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) != B
| double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(X_16,inverse(B)),inverse(multiply(X_48,inverse(X_48)))),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))),B) ),[0,0],$fot(multiply(X_16,inverse(B)))]]) ).
cnf(refute_0_120,plain,
( double_divide(multiply(multiply(X_16,inverse(B)),inverse(multiply(X_48,inverse(X_48)))),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) != B
| double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_16,inverse(B)),inverse(multiply(X_48,inverse(X_48)))),multiply(X_16,inverse(B))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) = B,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_16,inverse(B)),inverse(multiply(X_48,inverse(X_48)))),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))),B) )],[refute_0_112,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(multiply(X_48,inverse(X_48)),inverse(X_16)) = inverse(X_16),
inference(subst,[],[refute_0_57:[bind(X_36,$fot(X_16)),bind(X_37,$fot(X_48))]]) ).
cnf(refute_0_123,plain,
double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) = double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))),
introduced(tautology,[refl,[$fot(double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))))]]) ).
cnf(refute_0_124,plain,
( multiply(multiply(X_48,inverse(X_48)),inverse(X_16)) != inverse(X_16)
| double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) != double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16)))
| double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) = double_divide(multiply(X_16,inverse(B)),inverse(X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))),double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16)))) ),[1,1],$fot(inverse(X_16))]]) ).
cnf(refute_0_125,plain,
( multiply(multiply(X_48,inverse(X_48)),inverse(X_16)) != inverse(X_16)
| double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) = double_divide(multiply(X_16,inverse(B)),inverse(X_16)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))),double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) = double_divide(multiply(X_16,inverse(B)),inverse(X_16)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_48,inverse(X_48)),inverse(X_16)),inverse(X_16)) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
( double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) != B
| double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) != double_divide(multiply(X_16,inverse(B)),inverse(X_16))
| double_divide(multiply(X_16,inverse(B)),inverse(X_16)) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))),B) ),[0],$fot(double_divide(multiply(X_16,inverse(B)),inverse(X_16)))]]) ).
cnf(refute_0_128,plain,
( double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))) != B
| double_divide(multiply(X_16,inverse(B)),inverse(X_16)) = B ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))),double_divide(multiply(X_16,inverse(B)),inverse(X_16))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
double_divide(multiply(X_16,inverse(B)),inverse(X_16)) = B,
inference(resolve,[$cnf( $equal(double_divide(multiply(X_16,inverse(B)),multiply(multiply(X_48,inverse(X_48)),inverse(X_16))),B) )],[refute_0_121,refute_0_128]) ).
cnf(refute_0_130,plain,
double_divide(multiply(inverse(X_33),inverse(inverse(inverse(X_33)))),inverse(inverse(X_33))) = inverse(inverse(X_33)),
inference(subst,[],[refute_0_129:[bind(B,$fot(inverse(inverse(X_33)))),bind(X_16,$fot(inverse(X_33)))]]) ).
cnf(refute_0_131,plain,
( double_divide(multiply(inverse(X_33),inverse(inverse(inverse(X_33)))),inverse(inverse(X_33))) != X_33
| double_divide(multiply(inverse(X_33),inverse(inverse(inverse(X_33)))),inverse(inverse(X_33))) != inverse(inverse(X_33))
| inverse(inverse(X_33)) = X_33 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(inverse(X_33),inverse(inverse(inverse(X_33)))),inverse(inverse(X_33))),X_33) ),[0],$fot(inverse(inverse(X_33)))]]) ).
cnf(refute_0_132,plain,
( double_divide(multiply(inverse(X_33),inverse(inverse(inverse(X_33)))),inverse(inverse(X_33))) != X_33
| inverse(inverse(X_33)) = X_33 ),
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_33),inverse(inverse(inverse(X_33)))),inverse(inverse(X_33))),inverse(inverse(X_33))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
inverse(inverse(X_33)) = X_33,
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_33),inverse(inverse(inverse(X_33)))),inverse(inverse(X_33))),X_33) )],[refute_0_111,refute_0_132]) ).
cnf(refute_0_134,plain,
inverse(inverse(X_29)) = X_29,
inference(subst,[],[refute_0_133:[bind(X_33,$fot(X_29))]]) ).
cnf(refute_0_135,plain,
multiply(inverse(X_30),inverse(inverse(X_29))) = multiply(inverse(X_30),inverse(inverse(X_29))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_30),inverse(inverse(X_29))))]]) ).
cnf(refute_0_136,plain,
( multiply(inverse(X_30),inverse(inverse(X_29))) != multiply(inverse(X_30),inverse(inverse(X_29)))
| inverse(inverse(X_29)) != X_29
| multiply(inverse(X_30),inverse(inverse(X_29))) = multiply(inverse(X_30),X_29) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_30),inverse(inverse(X_29))),multiply(inverse(X_30),inverse(inverse(X_29)))) ),[1,1],$fot(X_29)]]) ).
cnf(refute_0_137,plain,
( inverse(inverse(X_29)) != X_29
| multiply(inverse(X_30),inverse(inverse(X_29))) = multiply(inverse(X_30),X_29) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),inverse(inverse(X_29))),multiply(inverse(X_30),inverse(inverse(X_29)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(inverse(X_30),inverse(inverse(X_29))) = multiply(inverse(X_30),X_29),
inference(resolve,[$cnf( $equal(inverse(inverse(X_29)),X_29) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
( multiply(inverse(X_30),inverse(inverse(X_29))) != multiply(inverse(X_30),X_29)
| multiply(inverse(X_30),inverse(inverse(X_29))) != inverse(multiply(X_30,inverse(X_29)))
| multiply(inverse(X_30),X_29) = inverse(multiply(X_30,inverse(X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_30),inverse(inverse(X_29))),inverse(multiply(X_30,inverse(X_29)))) ),[0],$fot(multiply(inverse(X_30),X_29))]]) ).
cnf(refute_0_140,plain,
( multiply(inverse(X_30),inverse(inverse(X_29))) != inverse(multiply(X_30,inverse(X_29)))
| multiply(inverse(X_30),X_29) = inverse(multiply(X_30,inverse(X_29))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),inverse(inverse(X_29))),multiply(inverse(X_30),X_29)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(inverse(X_16),inverse(inverse(X_21))) = inverse(multiply(X_16,inverse(X_21))),
inference(subst,[],[refute_0_92:[bind(X_29,$fot(X_21)),bind(X_30,$fot(X_16))]]) ).
cnf(refute_0_142,plain,
double_divide(multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))),inverse(inverse(X_18))) = multiply(X_16,inverse(X_18)),
inference(subst,[],[refute_0_129:[bind(B,$fot(multiply(X_16,inverse(X_18)))),bind(X_16,$fot(inverse(X_18)))]]) ).
cnf(refute_0_143,plain,
multiply(multiply(multiply(X_16,inverse(X_18)),inverse(X_16)),inverse(multiply(X_16,inverse(X_18)))) = inverse(X_16),
inference(subst,[],[refute_0_49:[bind(X_17,$fot(multiply(X_16,inverse(X_18))))]]) ).
cnf(refute_0_144,plain,
multiply(multiply(X_16,inverse(X_18)),inverse(X_16)) = inverse(X_18),
inference(subst,[],[refute_0_49:[bind(X_16,$fot(X_18)),bind(X_17,$fot(X_16))]]) ).
cnf(refute_0_145,plain,
( multiply(multiply(X_16,inverse(X_18)),inverse(X_16)) != inverse(X_18)
| multiply(multiply(multiply(X_16,inverse(X_18)),inverse(X_16)),inverse(multiply(X_16,inverse(X_18)))) != inverse(X_16)
| multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))) = inverse(X_16) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(X_16,inverse(X_18)),inverse(X_16)),inverse(multiply(X_16,inverse(X_18)))),inverse(X_16)) ),[0,0],$fot(inverse(X_18))]]) ).
cnf(refute_0_146,plain,
( multiply(multiply(multiply(X_16,inverse(X_18)),inverse(X_16)),inverse(multiply(X_16,inverse(X_18)))) != inverse(X_16)
| multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))) = inverse(X_16) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_16,inverse(X_18)),inverse(X_16)),inverse(X_18)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))) = inverse(X_16),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_16,inverse(X_18)),inverse(X_16)),inverse(multiply(X_16,inverse(X_18)))),inverse(X_16)) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
( multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))) != inverse(X_16)
| double_divide(multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))),inverse(inverse(X_18))) != multiply(X_16,inverse(X_18))
| double_divide(inverse(X_16),inverse(inverse(X_18))) = multiply(X_16,inverse(X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))),inverse(inverse(X_18))),multiply(X_16,inverse(X_18))) ),[0,0],$fot(inverse(X_16))]]) ).
cnf(refute_0_149,plain,
( double_divide(multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))),inverse(inverse(X_18))) != multiply(X_16,inverse(X_18))
| double_divide(inverse(X_16),inverse(inverse(X_18))) = multiply(X_16,inverse(X_18)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))),inverse(X_16)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
double_divide(inverse(X_16),inverse(inverse(X_18))) = multiply(X_16,inverse(X_18)),
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_18),inverse(multiply(X_16,inverse(X_18)))),inverse(inverse(X_18))),multiply(X_16,inverse(X_18))) )],[refute_0_142,refute_0_149]) ).
cnf(refute_0_151,plain,
inverse(inverse(X_18)) = X_18,
inference(subst,[],[refute_0_133:[bind(X_33,$fot(X_18))]]) ).
cnf(refute_0_152,plain,
double_divide(inverse(X_16),inverse(inverse(X_18))) = double_divide(inverse(X_16),inverse(inverse(X_18))),
introduced(tautology,[refl,[$fot(double_divide(inverse(X_16),inverse(inverse(X_18))))]]) ).
cnf(refute_0_153,plain,
( double_divide(inverse(X_16),inverse(inverse(X_18))) != double_divide(inverse(X_16),inverse(inverse(X_18)))
| inverse(inverse(X_18)) != X_18
| double_divide(inverse(X_16),inverse(inverse(X_18))) = double_divide(inverse(X_16),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_16),inverse(inverse(X_18))),double_divide(inverse(X_16),inverse(inverse(X_18)))) ),[1,1],$fot(X_18)]]) ).
cnf(refute_0_154,plain,
( inverse(inverse(X_18)) != X_18
| double_divide(inverse(X_16),inverse(inverse(X_18))) = double_divide(inverse(X_16),X_18) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_16),inverse(inverse(X_18))),double_divide(inverse(X_16),inverse(inverse(X_18)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
double_divide(inverse(X_16),inverse(inverse(X_18))) = double_divide(inverse(X_16),X_18),
inference(resolve,[$cnf( $equal(inverse(inverse(X_18)),X_18) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
( double_divide(inverse(X_16),inverse(inverse(X_18))) != multiply(X_16,inverse(X_18))
| double_divide(inverse(X_16),inverse(inverse(X_18))) != double_divide(inverse(X_16),X_18)
| double_divide(inverse(X_16),X_18) = multiply(X_16,inverse(X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_16),inverse(inverse(X_18))),multiply(X_16,inverse(X_18))) ),[0],$fot(double_divide(inverse(X_16),X_18))]]) ).
cnf(refute_0_157,plain,
( double_divide(inverse(X_16),inverse(inverse(X_18))) != multiply(X_16,inverse(X_18))
| double_divide(inverse(X_16),X_18) = multiply(X_16,inverse(X_18)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_16),inverse(inverse(X_18))),double_divide(inverse(X_16),X_18)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
double_divide(inverse(X_16),X_18) = multiply(X_16,inverse(X_18)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_16),inverse(inverse(X_18))),multiply(X_16,inverse(X_18))) )],[refute_0_150,refute_0_157]) ).
cnf(refute_0_159,plain,
double_divide(inverse(inverse(X_16)),inverse(X_21)) = multiply(inverse(X_16),inverse(inverse(X_21))),
inference(subst,[],[refute_0_158:[bind(X_16,$fot(inverse(X_16))),bind(X_18,$fot(inverse(X_21)))]]) ).
cnf(refute_0_160,plain,
( multiply(inverse(X_16),inverse(inverse(X_21))) != inverse(multiply(X_16,inverse(X_21)))
| double_divide(inverse(inverse(X_16)),inverse(X_21)) != multiply(inverse(X_16),inverse(inverse(X_21)))
| double_divide(inverse(inverse(X_16)),inverse(X_21)) = inverse(multiply(X_16,inverse(X_21))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(double_divide(inverse(inverse(X_16)),inverse(X_21)))),bind(Y,$fot(multiply(inverse(X_16),inverse(inverse(X_21))))),bind(Z,$fot(inverse(multiply(X_16,inverse(X_21)))))]]) ).
cnf(refute_0_161,plain,
( multiply(inverse(X_16),inverse(inverse(X_21))) != inverse(multiply(X_16,inverse(X_21)))
| double_divide(inverse(inverse(X_16)),inverse(X_21)) = inverse(multiply(X_16,inverse(X_21))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(X_16)),inverse(X_21)),multiply(inverse(X_16),inverse(inverse(X_21)))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
double_divide(inverse(inverse(X_16)),inverse(X_21)) = inverse(multiply(X_16,inverse(X_21))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_16),inverse(inverse(X_21))),inverse(multiply(X_16,inverse(X_21)))) )],[refute_0_141,refute_0_161]) ).
cnf(refute_0_163,plain,
( double_divide(inverse(inverse(X_16)),inverse(X_21)) != multiply(X_21,inverse(X_16))
| double_divide(inverse(inverse(X_16)),inverse(X_21)) != inverse(multiply(X_16,inverse(X_21)))
| inverse(multiply(X_16,inverse(X_21))) = multiply(X_21,inverse(X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(X_16)),inverse(X_21)),multiply(X_21,inverse(X_16))) ),[0],$fot(inverse(multiply(X_16,inverse(X_21))))]]) ).
cnf(refute_0_164,plain,
( double_divide(inverse(inverse(X_16)),inverse(X_21)) != multiply(X_21,inverse(X_16))
| inverse(multiply(X_16,inverse(X_21))) = multiply(X_21,inverse(X_16)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(X_16)),inverse(X_21)),inverse(multiply(X_16,inverse(X_21)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
inverse(multiply(X_16,inverse(X_21))) = multiply(X_21,inverse(X_16)),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(X_16)),inverse(X_21)),multiply(X_21,inverse(X_16))) )],[refute_0_71,refute_0_164]) ).
cnf(refute_0_166,plain,
inverse(multiply(X_30,inverse(X_29))) = multiply(X_29,inverse(X_30)),
inference(subst,[],[refute_0_165:[bind(X_16,$fot(X_30)),bind(X_21,$fot(X_29))]]) ).
cnf(refute_0_167,plain,
( multiply(inverse(X_30),X_29) != inverse(multiply(X_30,inverse(X_29)))
| inverse(multiply(X_30,inverse(X_29))) != multiply(X_29,inverse(X_30))
| multiply(inverse(X_30),X_29) = multiply(X_29,inverse(X_30)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_30),X_29),multiply(X_29,inverse(X_30))) ),[0],$fot(inverse(multiply(X_30,inverse(X_29))))]]) ).
cnf(refute_0_168,plain,
( multiply(inverse(X_30),X_29) != inverse(multiply(X_30,inverse(X_29)))
| multiply(inverse(X_30),X_29) = multiply(X_29,inverse(X_30)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_30,inverse(X_29))),multiply(X_29,inverse(X_30))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
( multiply(inverse(X_30),inverse(inverse(X_29))) != inverse(multiply(X_30,inverse(X_29)))
| multiply(inverse(X_30),X_29) = multiply(X_29,inverse(X_30)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),X_29),inverse(multiply(X_30,inverse(X_29)))) )],[refute_0_140,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(inverse(X_30),X_29) = multiply(X_29,inverse(X_30)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),inverse(inverse(X_29))),inverse(multiply(X_30,inverse(X_29)))) )],[refute_0_92,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(inverse(b2),b2) = multiply(b2,inverse(b2)),
inference(subst,[],[refute_0_170:[bind(X_29,$fot(b2)),bind(X_30,$fot(b2))]]) ).
cnf(refute_0_172,plain,
multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(inverse(b2),b2)),
introduced(tautology,[refl,[$fot(multiply(a2,multiply(inverse(b2),b2)))]]) ).
cnf(refute_0_173,plain,
( multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(inverse(b2),b2))
| multiply(inverse(b2),b2) != multiply(b2,inverse(b2))
| multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(inverse(b2),b2))) ),[1,1],$fot(multiply(b2,inverse(b2)))]]) ).
cnf(refute_0_174,plain,
( multiply(inverse(b2),b2) != multiply(b2,inverse(b2))
| multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))) ),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(inverse(b2),b2))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),b2),multiply(b2,inverse(b2))) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(b2,inverse(b2)))
| multiply(a2,multiply(inverse(b2),b2)) = a2 ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiply(a2,multiply(inverse(b2),b2)))),bind(Y,$fot(multiply(a2,multiply(b2,inverse(b2))))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_177,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(a2,multiply(inverse(b2),b2)) = a2 ),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(b2,inverse(b2)))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
multiply(a2,multiply(inverse(b2),b2)) = a2,
inference(resolve,[$cnf( $equal(multiply(a2,multiply(b2,inverse(b2))),a2) )],[refute_0_87,refute_0_177]) ).
cnf(refute_0_179,plain,
inverse(inverse(X_30)) = X_30,
inference(subst,[],[refute_0_133:[bind(X_33,$fot(X_30))]]) ).
cnf(refute_0_180,plain,
multiply(multiply(A,B),inverse(inverse(X_30))) = multiply(multiply(A,B),inverse(inverse(X_30))),
introduced(tautology,[refl,[$fot(multiply(multiply(A,B),inverse(inverse(X_30))))]]) ).
cnf(refute_0_181,plain,
( multiply(multiply(A,B),inverse(inverse(X_30))) != multiply(multiply(A,B),inverse(inverse(X_30)))
| inverse(inverse(X_30)) != X_30
| multiply(multiply(A,B),inverse(inverse(X_30))) = multiply(multiply(A,B),X_30) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(A,B),inverse(inverse(X_30))),multiply(multiply(A,B),inverse(inverse(X_30)))) ),[1,1],$fot(X_30)]]) ).
cnf(refute_0_182,plain,
( inverse(inverse(X_30)) != X_30
| multiply(multiply(A,B),inverse(inverse(X_30))) = multiply(multiply(A,B),X_30) ),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),inverse(inverse(X_30))),multiply(multiply(A,B),inverse(inverse(X_30)))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(multiply(A,B),inverse(inverse(X_30))) = multiply(multiply(A,B),X_30),
inference(resolve,[$cnf( $equal(inverse(inverse(X_30)),X_30) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(multiply(A,B),inverse(inverse(X_30))),
inference(subst,[],[refute_0_158:[bind(X_16,$fot(multiply(A,B))),bind(X_18,$fot(inverse(X_30)))]]) ).
cnf(refute_0_185,plain,
( multiply(multiply(A,B),inverse(inverse(X_30))) != multiply(multiply(A,B),X_30)
| double_divide(inverse(multiply(A,B)),inverse(X_30)) != multiply(multiply(A,B),inverse(inverse(X_30)))
| double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(multiply(A,B),X_30) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(double_divide(inverse(multiply(A,B)),inverse(X_30)))),bind(Y,$fot(multiply(multiply(A,B),inverse(inverse(X_30))))),bind(Z,$fot(multiply(multiply(A,B),X_30)))]]) ).
cnf(refute_0_186,plain,
( multiply(multiply(A,B),inverse(inverse(X_30))) != multiply(multiply(A,B),X_30)
| double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(multiply(A,B),X_30) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(A,B)),inverse(X_30)),multiply(multiply(A,B),inverse(inverse(X_30)))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
double_divide(inverse(multiply(A,B)),inverse(X_30)) = multiply(multiply(A,B),X_30),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),inverse(inverse(X_30))),multiply(multiply(A,B),X_30)) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
( double_divide(inverse(multiply(A,B)),inverse(X_30)) != multiply(X_30,multiply(A,B))
| double_divide(inverse(multiply(A,B)),inverse(X_30)) != multiply(multiply(A,B),X_30)
| multiply(multiply(A,B),X_30) = multiply(X_30,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(A,B)),inverse(X_30)),multiply(X_30,multiply(A,B))) ),[0],$fot(multiply(multiply(A,B),X_30))]]) ).
cnf(refute_0_189,plain,
( double_divide(inverse(multiply(A,B)),inverse(X_30)) != multiply(X_30,multiply(A,B))
| multiply(multiply(A,B),X_30) = multiply(X_30,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(A,B)),inverse(X_30)),multiply(multiply(A,B),X_30)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
multiply(multiply(A,B),X_30) = multiply(X_30,multiply(A,B)),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(A,B)),inverse(X_30)),multiply(X_30,multiply(A,B))) )],[refute_0_82,refute_0_189]) ).
cnf(refute_0_191,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(inverse(b2),b2)),
inference(subst,[],[refute_0_190:[bind(A,$fot(inverse(b2))),bind(B,$fot(b2)),bind(X_30,$fot(a2))]]) ).
cnf(refute_0_192,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(a2,multiply(inverse(b2),b2))
| multiply(a2,multiply(inverse(b2),b2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiply(multiply(inverse(b2),b2),a2))),bind(Y,$fot(multiply(a2,multiply(inverse(b2),b2)))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_193,plain,
( multiply(a2,multiply(inverse(b2),b2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(a2,multiply(inverse(b2),b2))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),a2) )],[refute_0_178,refute_0_193]) ).
cnf(refute_0_195,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_196,plain,
( a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_196,prove_these_axioms_2]) ).
cnf(refute_0_198,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_199,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_198,refute_0_197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP606-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 12:10:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.60
% 0.41/0.60 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.47/0.65
%------------------------------------------------------------------------------