%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP607-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 50
% Syntax : Number of clauses : 184 ( 99 unt; 0 nHn; 90 RR)
% Number of literals : 311 ( 310 equ; 129 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 458 ( 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_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
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( $equal(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C),B) )],[single_axiom,refute_0_21]) ).
cnf(refute_0_23,plain,
double_divide(multiply(multiply(double_divide(X_2,X_4),inverse(double_divide(B,A))),X_2),X_4) = double_divide(B,A),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_2)),bind(B,$fot(double_divide(B,A))),bind(C,$fot(X_4))]]) ).
cnf(refute_0_24,plain,
( double_divide(multiply(multiply(double_divide(X_2,X_4),inverse(double_divide(B,A))),X_2),X_4) != double_divide(B,A)
| inverse(double_divide(B,A)) != multiply(A,B)
| double_divide(multiply(multiply(double_divide(X_2,X_4),multiply(A,B)),X_2),X_4) = double_divide(B,A) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(double_divide(X_2,X_4),inverse(double_divide(B,A))),X_2),X_4),double_divide(B,A)) ),[0,0,0,1],$fot(multiply(A,B))]]) ).
cnf(refute_0_25,plain,
( double_divide(multiply(multiply(double_divide(X_2,X_4),inverse(double_divide(B,A))),X_2),X_4) != double_divide(B,A)
| double_divide(multiply(multiply(double_divide(X_2,X_4),multiply(A,B)),X_2),X_4) = double_divide(B,A) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_4,refute_0_24]) ).
cnf(refute_0_26,plain,
double_divide(multiply(multiply(double_divide(X_2,X_4),multiply(A,B)),X_2),X_4) = double_divide(B,A),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(X_2,X_4),inverse(double_divide(B,A))),X_2),X_4),double_divide(B,A)) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(multiply(multiply(double_divide(X_41,X_42),multiply(X_39,inverse(double_divide(X_41,X_42)))),X_41),X_42) = double_divide(inverse(double_divide(X_41,X_42)),X_39),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_39)),bind(B,$fot(inverse(double_divide(X_41,X_42)))),bind(X_2,$fot(X_41)),bind(X_4,$fot(X_42))]]) ).
cnf(refute_0_28,plain,
double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C) = B,
inference(subst,[],[refute_0_22:[bind(A,$fot(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)))]]) ).
cnf(refute_0_29,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_30,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_31,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( $equal(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),X_3) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
double_divide(multiply(multiply(X_3,inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C) = B,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2),C),inverse(B)),multiply(multiply(double_divide(X_2,C),inverse(X_3)),X_2)),C),B) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
double_divide(multiply(multiply(X_11,inverse(X_8)),multiply(multiply(double_divide(X_10,multiply(X_11,inverse(X_8))),inverse(X_11)),X_10)),multiply(X_11,inverse(X_8))) = X_8,
inference(subst,[],[refute_0_32:[bind(B,$fot(X_8)),bind(C,$fot(multiply(X_11,inverse(X_8)))),bind(X_2,$fot(X_10)),bind(X_3,$fot(X_11))]]) ).
cnf(refute_0_34,plain,
multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) = inverse(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A)),
inference(subst,[],[multiply:[bind(B,$fot(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)))]]) ).
cnf(refute_0_35,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,$fot(A))]]) ).
cnf(refute_0_36,plain,
( multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) != inverse(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A))
| double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A) != X_3
| multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) = inverse(X_3) ),
introduced(tautology,[equality,[$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_37,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( $equal(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A),X_3) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)) = inverse(X_3),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2)),inverse(double_divide(multiply(multiply(double_divide(X_2,A),inverse(X_3)),X_2),A))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(multiply(X_11,inverse(X_8)),multiply(multiply(double_divide(X_10,multiply(X_11,inverse(X_8))),inverse(X_11)),X_10)) = inverse(X_11),
inference(subst,[],[refute_0_38:[bind(A,$fot(multiply(X_11,inverse(X_8)))),bind(X_2,$fot(X_10)),bind(X_3,$fot(X_11))]]) ).
cnf(refute_0_40,plain,
( multiply(multiply(X_11,inverse(X_8)),multiply(multiply(double_divide(X_10,multiply(X_11,inverse(X_8))),inverse(X_11)),X_10)) != inverse(X_11)
| double_divide(multiply(multiply(X_11,inverse(X_8)),multiply(multiply(double_divide(X_10,multiply(X_11,inverse(X_8))),inverse(X_11)),X_10)),multiply(X_11,inverse(X_8))) != X_8
| double_divide(inverse(X_11),multiply(X_11,inverse(X_8))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(X_11,inverse(X_8)),multiply(multiply(double_divide(X_10,multiply(X_11,inverse(X_8))),inverse(X_11)),X_10)),multiply(X_11,inverse(X_8))),X_8) ),[0,0],$fot(inverse(X_11))]]) ).
cnf(refute_0_41,plain,
( double_divide(multiply(multiply(X_11,inverse(X_8)),multiply(multiply(double_divide(X_10,multiply(X_11,inverse(X_8))),inverse(X_11)),X_10)),multiply(X_11,inverse(X_8))) != X_8
| double_divide(inverse(X_11),multiply(X_11,inverse(X_8))) = X_8 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,inverse(X_8)),multiply(multiply(double_divide(X_10,multiply(X_11,inverse(X_8))),inverse(X_11)),X_10)),inverse(X_11)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(inverse(X_11),multiply(X_11,inverse(X_8))) = X_8,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_11,inverse(X_8)),multiply(multiply(double_divide(X_10,multiply(X_11,inverse(X_8))),inverse(X_11)),X_10)),multiply(X_11,inverse(X_8))),X_8) )],[refute_0_33,refute_0_41]) ).
cnf(refute_0_43,plain,
double_divide(inverse(multiply(X_8,inverse(X_19))),multiply(multiply(X_8,inverse(X_19)),inverse(X_8))) = X_8,
inference(subst,[],[refute_0_42:[bind(X_11,$fot(multiply(X_8,inverse(X_19))))]]) ).
cnf(refute_0_44,plain,
multiply(multiply(X_12,inverse(X_13)),inverse(X_12)) = inverse(double_divide(inverse(X_12),multiply(X_12,inverse(X_13)))),
inference(subst,[],[multiply:[bind(A,$fot(multiply(X_12,inverse(X_13)))),bind(B,$fot(inverse(X_12)))]]) ).
cnf(refute_0_45,plain,
double_divide(inverse(X_12),multiply(X_12,inverse(X_13))) = X_13,
inference(subst,[],[refute_0_42:[bind(X_11,$fot(X_12)),bind(X_8,$fot(X_13))]]) ).
cnf(refute_0_46,plain,
( multiply(multiply(X_12,inverse(X_13)),inverse(X_12)) != inverse(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))))
| double_divide(inverse(X_12),multiply(X_12,inverse(X_13))) != X_13
| multiply(multiply(X_12,inverse(X_13)),inverse(X_12)) = inverse(X_13) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_12,inverse(X_13)),inverse(X_12)),inverse(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_47,plain,
( multiply(multiply(X_12,inverse(X_13)),inverse(X_12)) != inverse(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))))
| multiply(multiply(X_12,inverse(X_13)),inverse(X_12)) = inverse(X_13) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))),X_13) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(multiply(X_12,inverse(X_13)),inverse(X_12)) = inverse(X_13),
inference(resolve,[$cnf( $equal(multiply(multiply(X_12,inverse(X_13)),inverse(X_12)),inverse(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(multiply(X_8,inverse(X_19)),inverse(X_8)) = inverse(X_19),
inference(subst,[],[refute_0_48:[bind(X_12,$fot(X_8)),bind(X_13,$fot(X_19))]]) ).
cnf(refute_0_50,plain,
( multiply(multiply(X_8,inverse(X_19)),inverse(X_8)) != inverse(X_19)
| double_divide(inverse(multiply(X_8,inverse(X_19))),multiply(multiply(X_8,inverse(X_19)),inverse(X_8))) != X_8
| double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(X_8,inverse(X_19))),multiply(multiply(X_8,inverse(X_19)),inverse(X_8))),X_8) ),[0,1],$fot(inverse(X_19))]]) ).
cnf(refute_0_51,plain,
( double_divide(inverse(multiply(X_8,inverse(X_19))),multiply(multiply(X_8,inverse(X_19)),inverse(X_8))) != X_8
| double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)) = X_8 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,inverse(X_19)),inverse(X_8)),inverse(X_19)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)) = X_8,
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_8,inverse(X_19))),multiply(multiply(X_8,inverse(X_19)),inverse(X_8))),X_8) )],[refute_0_43,refute_0_51]) ).
cnf(refute_0_53,plain,
double_divide(inverse(multiply(multiply(X_20,inverse(X_13)),inverse(X_20))),inverse(X_20)) = multiply(X_20,inverse(X_13)),
inference(subst,[],[refute_0_52:[bind(X_19,$fot(X_20)),bind(X_8,$fot(multiply(X_20,inverse(X_13))))]]) ).
cnf(refute_0_54,plain,
multiply(multiply(X_20,inverse(X_13)),inverse(X_20)) = inverse(X_13),
inference(subst,[],[refute_0_48:[bind(X_12,$fot(X_20))]]) ).
cnf(refute_0_55,plain,
( multiply(multiply(X_20,inverse(X_13)),inverse(X_20)) != inverse(X_13)
| double_divide(inverse(multiply(multiply(X_20,inverse(X_13)),inverse(X_20))),inverse(X_20)) != multiply(X_20,inverse(X_13))
| double_divide(inverse(inverse(X_13)),inverse(X_20)) = multiply(X_20,inverse(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(multiply(X_20,inverse(X_13)),inverse(X_20))),inverse(X_20)),multiply(X_20,inverse(X_13))) ),[0,0,0],$fot(inverse(X_13))]]) ).
cnf(refute_0_56,plain,
( double_divide(inverse(multiply(multiply(X_20,inverse(X_13)),inverse(X_20))),inverse(X_20)) != multiply(X_20,inverse(X_13))
| double_divide(inverse(inverse(X_13)),inverse(X_20)) = multiply(X_20,inverse(X_13)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_20,inverse(X_13)),inverse(X_20)),inverse(X_13)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
double_divide(inverse(inverse(X_13)),inverse(X_20)) = multiply(X_20,inverse(X_13)),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(multiply(X_20,inverse(X_13)),inverse(X_20))),inverse(X_20)),multiply(X_20,inverse(X_13))) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
double_divide(inverse(inverse(double_divide(B,A))),inverse(X_25)) = multiply(X_25,inverse(double_divide(B,A))),
inference(subst,[],[refute_0_57:[bind(X_13,$fot(double_divide(B,A))),bind(X_20,$fot(X_25))]]) ).
cnf(refute_0_59,plain,
( double_divide(inverse(inverse(double_divide(B,A))),inverse(X_25)) != multiply(X_25,inverse(double_divide(B,A)))
| inverse(double_divide(B,A)) != multiply(A,B)
| double_divide(inverse(multiply(A,B)),inverse(X_25)) = multiply(X_25,inverse(double_divide(B,A))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(double_divide(B,A))),inverse(X_25)),multiply(X_25,inverse(double_divide(B,A)))) ),[0,0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_60,plain,
( double_divide(inverse(inverse(double_divide(B,A))),inverse(X_25)) != multiply(X_25,inverse(double_divide(B,A)))
| double_divide(inverse(multiply(A,B)),inverse(X_25)) = multiply(X_25,inverse(double_divide(B,A))) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_4,refute_0_59]) ).
cnf(refute_0_61,plain,
double_divide(inverse(multiply(A,B)),inverse(X_25)) = multiply(X_25,inverse(double_divide(B,A))),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(double_divide(B,A))),inverse(X_25)),multiply(X_25,inverse(double_divide(B,A)))) )],[refute_0_58,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(X_25,inverse(double_divide(B,A))) = multiply(X_25,inverse(double_divide(B,A))),
introduced(tautology,[refl,[$fot(multiply(X_25,inverse(double_divide(B,A))))]]) ).
cnf(refute_0_63,plain,
( multiply(X_25,inverse(double_divide(B,A))) != multiply(X_25,inverse(double_divide(B,A)))
| inverse(double_divide(B,A)) != multiply(A,B)
| multiply(X_25,inverse(double_divide(B,A))) = multiply(X_25,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_25,inverse(double_divide(B,A))),multiply(X_25,inverse(double_divide(B,A)))) ),[1,1],$fot(multiply(A,B))]]) ).
cnf(refute_0_64,plain,
( inverse(double_divide(B,A)) != multiply(A,B)
| multiply(X_25,inverse(double_divide(B,A))) = multiply(X_25,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(X_25,inverse(double_divide(B,A))),multiply(X_25,inverse(double_divide(B,A)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(X_25,inverse(double_divide(B,A))) = multiply(X_25,multiply(A,B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_4,refute_0_64]) ).
cnf(refute_0_66,plain,
( multiply(X_25,inverse(double_divide(B,A))) != multiply(X_25,multiply(A,B))
| double_divide(inverse(multiply(A,B)),inverse(X_25)) != multiply(X_25,inverse(double_divide(B,A)))
| double_divide(inverse(multiply(A,B)),inverse(X_25)) = multiply(X_25,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(A,B)),inverse(X_25)),multiply(X_25,inverse(double_divide(B,A)))) ),[1],$fot(multiply(X_25,multiply(A,B)))]]) ).
cnf(refute_0_67,plain,
( double_divide(inverse(multiply(A,B)),inverse(X_25)) != multiply(X_25,inverse(double_divide(B,A)))
| double_divide(inverse(multiply(A,B)),inverse(X_25)) = multiply(X_25,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(X_25,inverse(double_divide(B,A))),multiply(X_25,multiply(A,B))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
double_divide(inverse(multiply(A,B)),inverse(X_25)) = multiply(X_25,multiply(A,B)),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(A,B)),inverse(X_25)),multiply(X_25,inverse(double_divide(B,A)))) )],[refute_0_61,refute_0_67]) ).
cnf(refute_0_69,plain,
double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)) = multiply(X_19,multiply(X_8,inverse(X_19))),
inference(subst,[],[refute_0_68:[bind(A,$fot(X_8)),bind(B,$fot(inverse(X_19))),bind(X_25,$fot(X_19))]]) ).
cnf(refute_0_70,plain,
( double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)) != X_8
| double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)) != multiply(X_19,multiply(X_8,inverse(X_19)))
| multiply(X_19,multiply(X_8,inverse(X_19))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)),X_8) ),[0],$fot(multiply(X_19,multiply(X_8,inverse(X_19))))]]) ).
cnf(refute_0_71,plain,
( double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)) != X_8
| multiply(X_19,multiply(X_8,inverse(X_19))) = X_8 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)),multiply(X_19,multiply(X_8,inverse(X_19)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(X_19,multiply(X_8,inverse(X_19))) = X_8,
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_8,inverse(X_19))),inverse(X_19)),X_8) )],[refute_0_52,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(double_divide(X_41,X_42),multiply(X_39,inverse(double_divide(X_41,X_42)))) = X_39,
inference(subst,[],[refute_0_72:[bind(X_19,$fot(double_divide(X_41,X_42))),bind(X_8,$fot(X_39))]]) ).
cnf(refute_0_74,plain,
( multiply(double_divide(X_41,X_42),multiply(X_39,inverse(double_divide(X_41,X_42)))) != X_39
| double_divide(multiply(multiply(double_divide(X_41,X_42),multiply(X_39,inverse(double_divide(X_41,X_42)))),X_41),X_42) != double_divide(inverse(double_divide(X_41,X_42)),X_39)
| double_divide(multiply(X_39,X_41),X_42) = double_divide(inverse(double_divide(X_41,X_42)),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(double_divide(X_41,X_42),multiply(X_39,inverse(double_divide(X_41,X_42)))),X_41),X_42),double_divide(inverse(double_divide(X_41,X_42)),X_39)) ),[0,0,0],$fot(X_39)]]) ).
cnf(refute_0_75,plain,
( double_divide(multiply(multiply(double_divide(X_41,X_42),multiply(X_39,inverse(double_divide(X_41,X_42)))),X_41),X_42) != double_divide(inverse(double_divide(X_41,X_42)),X_39)
| double_divide(multiply(X_39,X_41),X_42) = double_divide(inverse(double_divide(X_41,X_42)),X_39) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_41,X_42),multiply(X_39,inverse(double_divide(X_41,X_42)))),X_39) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
double_divide(multiply(X_39,X_41),X_42) = double_divide(inverse(double_divide(X_41,X_42)),X_39),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(X_41,X_42),multiply(X_39,inverse(double_divide(X_41,X_42)))),X_41),X_42),double_divide(inverse(double_divide(X_41,X_42)),X_39)) )],[refute_0_27,refute_0_75]) ).
cnf(refute_0_77,plain,
inverse(double_divide(X_41,X_42)) = multiply(X_42,X_41),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_42)),bind(B,$fot(X_41))]]) ).
cnf(refute_0_78,plain,
double_divide(inverse(double_divide(X_41,X_42)),X_39) = double_divide(inverse(double_divide(X_41,X_42)),X_39),
introduced(tautology,[refl,[$fot(double_divide(inverse(double_divide(X_41,X_42)),X_39))]]) ).
cnf(refute_0_79,plain,
( double_divide(inverse(double_divide(X_41,X_42)),X_39) != double_divide(inverse(double_divide(X_41,X_42)),X_39)
| inverse(double_divide(X_41,X_42)) != multiply(X_42,X_41)
| double_divide(inverse(double_divide(X_41,X_42)),X_39) = double_divide(multiply(X_42,X_41),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(X_41,X_42)),X_39),double_divide(inverse(double_divide(X_41,X_42)),X_39)) ),[1,0],$fot(multiply(X_42,X_41))]]) ).
cnf(refute_0_80,plain,
( inverse(double_divide(X_41,X_42)) != multiply(X_42,X_41)
| double_divide(inverse(double_divide(X_41,X_42)),X_39) = double_divide(multiply(X_42,X_41),X_39) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(X_41,X_42)),X_39),double_divide(inverse(double_divide(X_41,X_42)),X_39)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
double_divide(inverse(double_divide(X_41,X_42)),X_39) = double_divide(multiply(X_42,X_41),X_39),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_41,X_42)),multiply(X_42,X_41)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( double_divide(multiply(X_39,X_41),X_42) != double_divide(inverse(double_divide(X_41,X_42)),X_39)
| double_divide(inverse(double_divide(X_41,X_42)),X_39) != double_divide(multiply(X_42,X_41),X_39)
| double_divide(multiply(X_39,X_41),X_42) = double_divide(multiply(X_42,X_41),X_39) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double_divide(multiply(X_39,X_41),X_42),double_divide(multiply(X_42,X_41),X_39)) ),[0],$fot(double_divide(inverse(double_divide(X_41,X_42)),X_39))]]) ).
cnf(refute_0_83,plain,
( double_divide(multiply(X_39,X_41),X_42) != double_divide(inverse(double_divide(X_41,X_42)),X_39)
| double_divide(multiply(X_39,X_41),X_42) = double_divide(multiply(X_42,X_41),X_39) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(X_41,X_42)),X_39),double_divide(multiply(X_42,X_41),X_39)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
double_divide(multiply(X_39,X_41),X_42) = double_divide(multiply(X_42,X_41),X_39),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_39,X_41),X_42),double_divide(inverse(double_divide(X_41,X_42)),X_39)) )],[refute_0_76,refute_0_83]) ).
cnf(refute_0_85,plain,
double_divide(multiply(X_49,multiply(X_33,inverse(X_33))),X_51) = double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49),
inference(subst,[],[refute_0_84:[bind(X_39,$fot(X_49)),bind(X_41,$fot(multiply(X_33,inverse(X_33)))),bind(X_42,$fot(X_51))]]) ).
cnf(refute_0_86,plain,
double_divide(inverse(multiply(X_33,inverse(X_33))),multiply(multiply(X_33,inverse(X_33)),inverse(X_8))) = X_8,
inference(subst,[],[refute_0_42:[bind(X_11,$fot(multiply(X_33,inverse(X_33))))]]) ).
cnf(refute_0_87,plain,
multiply(X_5,multiply(multiply(double_divide(multiply(multiply(double_divide(A,X_5),inverse(B)),A),X_5),inverse(X_7)),multiply(multiply(double_divide(A,X_5),inverse(B)),A))) = inverse(X_7),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_5)),bind(X_2,$fot(multiply(multiply(double_divide(A,X_5),inverse(B)),A))),bind(X_3,$fot(X_7))]]) ).
cnf(refute_0_88,plain,
double_divide(multiply(multiply(double_divide(A,X_5),inverse(B)),A),X_5) = B,
inference(subst,[],[refute_0_22:[bind(C,$fot(X_5))]]) ).
cnf(refute_0_89,plain,
( multiply(X_5,multiply(multiply(double_divide(multiply(multiply(double_divide(A,X_5),inverse(B)),A),X_5),inverse(X_7)),multiply(multiply(double_divide(A,X_5),inverse(B)),A))) != inverse(X_7)
| double_divide(multiply(multiply(double_divide(A,X_5),inverse(B)),A),X_5) != B
| multiply(X_5,multiply(multiply(B,inverse(X_7)),multiply(multiply(double_divide(A,X_5),inverse(B)),A))) = inverse(X_7) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_5,multiply(multiply(double_divide(multiply(multiply(double_divide(A,X_5),inverse(B)),A),X_5),inverse(X_7)),multiply(multiply(double_divide(A,X_5),inverse(B)),A))),inverse(X_7)) ),[0,1,0,0],$fot(B)]]) ).
cnf(refute_0_90,plain,
( multiply(X_5,multiply(multiply(double_divide(multiply(multiply(double_divide(A,X_5),inverse(B)),A),X_5),inverse(X_7)),multiply(multiply(double_divide(A,X_5),inverse(B)),A))) != inverse(X_7)
| multiply(X_5,multiply(multiply(B,inverse(X_7)),multiply(multiply(double_divide(A,X_5),inverse(B)),A))) = inverse(X_7) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(A,X_5),inverse(B)),A),X_5),B) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(X_5,multiply(multiply(B,inverse(X_7)),multiply(multiply(double_divide(A,X_5),inverse(B)),A))) = inverse(X_7),
inference(resolve,[$cnf( $equal(multiply(X_5,multiply(multiply(double_divide(multiply(multiply(double_divide(A,X_5),inverse(B)),A),X_5),inverse(X_7)),multiply(multiply(double_divide(A,X_5),inverse(B)),A))),inverse(X_7)) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(double_divide(inverse(X_31),multiply(X_32,inverse(X_32))),inverse(B)),inverse(X_31)))) = inverse(X_7),
inference(subst,[],[refute_0_91:[bind(A,$fot(inverse(X_31))),bind(X_5,$fot(multiply(X_32,inverse(X_32))))]]) ).
cnf(refute_0_93,plain,
double_divide(multiply(multiply(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))),inverse(B)),inverse(X_12)),multiply(X_12,inverse(X_13))) = B,
inference(subst,[],[refute_0_22:[bind(A,$fot(inverse(X_12))),bind(C,$fot(multiply(X_12,inverse(X_13))))]]) ).
cnf(refute_0_94,plain,
( double_divide(multiply(multiply(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))),inverse(B)),inverse(X_12)),multiply(X_12,inverse(X_13))) != B
| double_divide(inverse(X_12),multiply(X_12,inverse(X_13))) != X_13
| double_divide(multiply(multiply(X_13,inverse(B)),inverse(X_12)),multiply(X_12,inverse(X_13))) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))),inverse(B)),inverse(X_12)),multiply(X_12,inverse(X_13))),B) ),[0,0,0,0],$fot(X_13)]]) ).
cnf(refute_0_95,plain,
( double_divide(multiply(multiply(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))),inverse(B)),inverse(X_12)),multiply(X_12,inverse(X_13))) != B
| double_divide(multiply(multiply(X_13,inverse(B)),inverse(X_12)),multiply(X_12,inverse(X_13))) = B ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))),X_13) )],[refute_0_45,refute_0_94]) ).
cnf(refute_0_96,plain,
double_divide(multiply(multiply(X_13,inverse(B)),inverse(X_12)),multiply(X_12,inverse(X_13))) = B,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(double_divide(inverse(X_12),multiply(X_12,inverse(X_13))),inverse(B)),inverse(X_12)),multiply(X_12,inverse(X_13))),B) )],[refute_0_93,refute_0_95]) ).
cnf(refute_0_97,plain,
double_divide(multiply(multiply(X_29,inverse(X_28)),inverse(X_29)),multiply(X_29,inverse(X_29))) = X_28,
inference(subst,[],[refute_0_96:[bind(B,$fot(X_28)),bind(X_12,$fot(X_29)),bind(X_13,$fot(X_29))]]) ).
cnf(refute_0_98,plain,
multiply(multiply(X_29,inverse(X_28)),inverse(X_29)) = inverse(X_28),
inference(subst,[],[refute_0_48:[bind(X_12,$fot(X_29)),bind(X_13,$fot(X_28))]]) ).
cnf(refute_0_99,plain,
( multiply(multiply(X_29,inverse(X_28)),inverse(X_29)) != inverse(X_28)
| double_divide(multiply(multiply(X_29,inverse(X_28)),inverse(X_29)),multiply(X_29,inverse(X_29))) != X_28
| double_divide(inverse(X_28),multiply(X_29,inverse(X_29))) = X_28 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(X_29,inverse(X_28)),inverse(X_29)),multiply(X_29,inverse(X_29))),X_28) ),[0,0],$fot(inverse(X_28))]]) ).
cnf(refute_0_100,plain,
( double_divide(multiply(multiply(X_29,inverse(X_28)),inverse(X_29)),multiply(X_29,inverse(X_29))) != X_28
| double_divide(inverse(X_28),multiply(X_29,inverse(X_29))) = X_28 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_29,inverse(X_28)),inverse(X_29)),inverse(X_28)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
double_divide(inverse(X_28),multiply(X_29,inverse(X_29))) = X_28,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_29,inverse(X_28)),inverse(X_29)),multiply(X_29,inverse(X_29))),X_28) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
double_divide(inverse(X_31),multiply(X_32,inverse(X_32))) = X_31,
inference(subst,[],[refute_0_101:[bind(X_28,$fot(X_31)),bind(X_29,$fot(X_32))]]) ).
cnf(refute_0_103,plain,
( multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(double_divide(inverse(X_31),multiply(X_32,inverse(X_32))),inverse(B)),inverse(X_31)))) != inverse(X_7)
| double_divide(inverse(X_31),multiply(X_32,inverse(X_32))) != X_31
| multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) = inverse(X_7) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(double_divide(inverse(X_31),multiply(X_32,inverse(X_32))),inverse(B)),inverse(X_31)))),inverse(X_7)) ),[0,1,1,0,0],$fot(X_31)]]) ).
cnf(refute_0_104,plain,
( multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(double_divide(inverse(X_31),multiply(X_32,inverse(X_32))),inverse(B)),inverse(X_31)))) != inverse(X_7)
| multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) = inverse(X_7) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_31),multiply(X_32,inverse(X_32))),X_31) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) = inverse(X_7),
inference(resolve,[$cnf( $equal(multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(double_divide(inverse(X_31),multiply(X_32,inverse(X_32))),inverse(B)),inverse(X_31)))),inverse(X_7)) )],[refute_0_92,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(multiply(B,inverse(X_7)),inverse(B)) = inverse(X_7),
inference(subst,[],[refute_0_48:[bind(X_12,$fot(B)),bind(X_13,$fot(X_7))]]) ).
cnf(refute_0_107,plain,
multiply(multiply(X_31,inverse(B)),inverse(X_31)) = inverse(B),
inference(subst,[],[refute_0_48:[bind(X_12,$fot(X_31)),bind(X_13,$fot(B))]]) ).
cnf(refute_0_108,plain,
multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) = multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))),
introduced(tautology,[refl,[$fot(multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))))]]) ).
cnf(refute_0_109,plain,
( multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) != multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))
| multiply(multiply(X_31,inverse(B)),inverse(X_31)) != inverse(B)
| multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) = multiply(multiply(B,inverse(X_7)),inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_110,plain,
( multiply(multiply(X_31,inverse(B)),inverse(X_31)) != inverse(B)
| multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) = multiply(multiply(B,inverse(X_7)),inverse(B)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) = multiply(multiply(B,inverse(X_7)),inverse(B)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_31,inverse(B)),inverse(X_31)),inverse(B)) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
( multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) != multiply(multiply(B,inverse(X_7)),inverse(B))
| multiply(multiply(B,inverse(X_7)),inverse(B)) != inverse(X_7)
| multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) = inverse(X_7) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))))),bind(Y,$fot(multiply(multiply(B,inverse(X_7)),inverse(B)))),bind(Z,$fot(inverse(X_7)))]]) ).
cnf(refute_0_113,plain,
( multiply(multiply(B,inverse(X_7)),inverse(B)) != inverse(X_7)
| multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) = inverse(X_7) ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))),multiply(multiply(B,inverse(X_7)),inverse(B))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) = inverse(X_7),
inference(resolve,[$cnf( $equal(multiply(multiply(B,inverse(X_7)),inverse(B)),inverse(X_7)) )],[refute_0_106,refute_0_113]) ).
cnf(refute_0_115,plain,
multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) = multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))),
introduced(tautology,[refl,[$fot(multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))))]]) ).
cnf(refute_0_116,plain,
( multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) != inverse(X_7)
| multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) != multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))))
| multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) = multiply(multiply(X_32,inverse(X_32)),inverse(X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))),multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))))) ),[1,1],$fot(inverse(X_7))]]) ).
cnf(refute_0_117,plain,
( multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))) != inverse(X_7)
| multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) = multiply(multiply(X_32,inverse(X_32)),inverse(X_7)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))),multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) = multiply(multiply(X_32,inverse(X_32)),inverse(X_7)),
inference(resolve,[$cnf( $equal(multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31))),inverse(X_7)) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
( multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) != multiply(multiply(X_32,inverse(X_32)),inverse(X_7))
| multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) != inverse(X_7)
| multiply(multiply(X_32,inverse(X_32)),inverse(X_7)) = inverse(X_7) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))),inverse(X_7)) ),[0],$fot(multiply(multiply(X_32,inverse(X_32)),inverse(X_7)))]]) ).
cnf(refute_0_120,plain,
( multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))) != inverse(X_7)
| multiply(multiply(X_32,inverse(X_32)),inverse(X_7)) = inverse(X_7) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))),multiply(multiply(X_32,inverse(X_32)),inverse(X_7))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(multiply(X_32,inverse(X_32)),inverse(X_7)) = inverse(X_7),
inference(resolve,[$cnf( $equal(multiply(multiply(X_32,inverse(X_32)),multiply(multiply(B,inverse(X_7)),multiply(multiply(X_31,inverse(B)),inverse(X_31)))),inverse(X_7)) )],[refute_0_105,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(multiply(X_33,inverse(X_33)),inverse(X_8)) = inverse(X_8),
inference(subst,[],[refute_0_121:[bind(X_32,$fot(X_33)),bind(X_7,$fot(X_8))]]) ).
cnf(refute_0_123,plain,
( multiply(multiply(X_33,inverse(X_33)),inverse(X_8)) != inverse(X_8)
| double_divide(inverse(multiply(X_33,inverse(X_33))),multiply(multiply(X_33,inverse(X_33)),inverse(X_8))) != X_8
| double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(X_33,inverse(X_33))),multiply(multiply(X_33,inverse(X_33)),inverse(X_8))),X_8) ),[0,1],$fot(inverse(X_8))]]) ).
cnf(refute_0_124,plain,
( double_divide(inverse(multiply(X_33,inverse(X_33))),multiply(multiply(X_33,inverse(X_33)),inverse(X_8))) != X_8
| double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_33,inverse(X_33)),inverse(X_8)),inverse(X_8)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)) = X_8,
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_33,inverse(X_33))),multiply(multiply(X_33,inverse(X_33)),inverse(X_8))),X_8) )],[refute_0_86,refute_0_124]) ).
cnf(refute_0_126,plain,
double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)) = multiply(X_8,multiply(X_33,inverse(X_33))),
inference(subst,[],[refute_0_68:[bind(A,$fot(X_33)),bind(B,$fot(inverse(X_33))),bind(X_25,$fot(X_8))]]) ).
cnf(refute_0_127,plain,
( double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)) != X_8
| double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)) != multiply(X_8,multiply(X_33,inverse(X_33)))
| multiply(X_8,multiply(X_33,inverse(X_33))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)),X_8) ),[0],$fot(multiply(X_8,multiply(X_33,inverse(X_33))))]]) ).
cnf(refute_0_128,plain,
( double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)) != X_8
| multiply(X_8,multiply(X_33,inverse(X_33))) = X_8 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)),multiply(X_8,multiply(X_33,inverse(X_33)))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
multiply(X_8,multiply(X_33,inverse(X_33))) = X_8,
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_33,inverse(X_33))),inverse(X_8)),X_8) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(X_49,multiply(X_33,inverse(X_33))) = X_49,
inference(subst,[],[refute_0_129:[bind(X_8,$fot(X_49))]]) ).
cnf(refute_0_131,plain,
( multiply(X_49,multiply(X_33,inverse(X_33))) != X_49
| double_divide(multiply(X_49,multiply(X_33,inverse(X_33))),X_51) != double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)
| double_divide(X_49,X_51) = double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_49,multiply(X_33,inverse(X_33))),X_51),double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)) ),[0,0],$fot(X_49)]]) ).
cnf(refute_0_132,plain,
( double_divide(multiply(X_49,multiply(X_33,inverse(X_33))),X_51) != double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)
| double_divide(X_49,X_51) = double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49) ),
inference(resolve,[$cnf( $equal(multiply(X_49,multiply(X_33,inverse(X_33))),X_49) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
double_divide(X_49,X_51) = double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_49,multiply(X_33,inverse(X_33))),X_51),double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)) )],[refute_0_85,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(X_51,multiply(X_33,inverse(X_33))) = X_51,
inference(subst,[],[refute_0_129:[bind(X_8,$fot(X_51))]]) ).
cnf(refute_0_135,plain,
double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49) = double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49),
introduced(tautology,[refl,[$fot(double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49))]]) ).
cnf(refute_0_136,plain,
( multiply(X_51,multiply(X_33,inverse(X_33))) != X_51
| double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49) != double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)
| double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49) = double_divide(X_51,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49),double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)) ),[1,0],$fot(X_51)]]) ).
cnf(refute_0_137,plain,
( multiply(X_51,multiply(X_33,inverse(X_33))) != X_51
| double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49) = double_divide(X_51,X_49) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49),double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49) = double_divide(X_51,X_49),
inference(resolve,[$cnf( $equal(multiply(X_51,multiply(X_33,inverse(X_33))),X_51) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
( double_divide(X_49,X_51) != double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)
| double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49) != double_divide(X_51,X_49)
| double_divide(X_49,X_51) = double_divide(X_51,X_49) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double_divide(X_49,X_51),double_divide(X_51,X_49)) ),[0],$fot(double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49))]]) ).
cnf(refute_0_140,plain,
( double_divide(X_49,X_51) != double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)
| double_divide(X_49,X_51) = double_divide(X_51,X_49) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49),double_divide(X_51,X_49)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
double_divide(X_49,X_51) = double_divide(X_51,X_49),
inference(resolve,[$cnf( $equal(double_divide(X_49,X_51),double_divide(multiply(X_51,multiply(X_33,inverse(X_33))),X_49)) )],[refute_0_133,refute_0_140]) ).
cnf(refute_0_142,plain,
double_divide(B,A) = double_divide(A,B),
inference(subst,[],[refute_0_141:[bind(X_49,$fot(B)),bind(X_51,$fot(A))]]) ).
cnf(refute_0_143,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| double_divide(B,A) != double_divide(A,B)
| multiply(A,B) = inverse(double_divide(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) ),[1,0],$fot(double_divide(A,B))]]) ).
cnf(refute_0_144,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| multiply(A,B) = inverse(double_divide(A,B)) ),
inference(resolve,[$cnf( $equal(double_divide(B,A),double_divide(A,B)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
multiply(A,B) = inverse(double_divide(A,B)),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[multiply,refute_0_144]) ).
cnf(refute_0_146,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(subst,[],[refute_0_4:[bind(A,$fot(B)),bind(B,$fot(A))]]) ).
cnf(refute_0_147,plain,
( multiply(A,B) != inverse(double_divide(A,B))
| inverse(double_divide(A,B)) != multiply(B,A)
| multiply(A,B) = multiply(B,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),multiply(B,A)) ),[0],$fot(inverse(double_divide(A,B)))]]) ).
cnf(refute_0_148,plain,
( multiply(A,B) != inverse(double_divide(A,B))
| multiply(A,B) = multiply(B,A) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(A,B)),multiply(B,A)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(A,B) = multiply(B,A),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(A,B))) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( multiply(A,B) != multiply(B,A)
| multiply(B,A) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(multiply(B,A)))]]) ).
cnf(refute_0_151,plain,
multiply(B,A) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),multiply(B,A)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
multiply(c3,b3) = multiply(b3,c3),
inference(subst,[],[refute_0_151:[bind(A,$fot(b3)),bind(B,$fot(c3))]]) ).
cnf(refute_0_153,plain,
multiply(a3,multiply(c3,b3)) = multiply(a3,multiply(c3,b3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(c3,b3)))]]) ).
cnf(refute_0_154,plain,
( multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(c3,b3))
| multiply(c3,b3) != multiply(b3,c3)
| multiply(a3,multiply(c3,b3)) = multiply(a3,multiply(b3,c3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(c3,b3))) ),[1,1],$fot(multiply(b3,c3))]]) ).
cnf(refute_0_155,plain,
( multiply(c3,b3) != multiply(b3,c3)
| multiply(a3,multiply(c3,b3)) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(c3,b3))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(a3,multiply(c3,b3)) = multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(c3,b3),multiply(b3,c3)) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(A,multiply(X_49,X_50)) = inverse(double_divide(multiply(X_49,X_50),A)),
inference(subst,[],[multiply:[bind(B,$fot(multiply(X_49,X_50)))]]) ).
cnf(refute_0_158,plain,
double_divide(multiply(X_49,X_50),A) = double_divide(multiply(A,X_50),X_49),
inference(subst,[],[refute_0_84:[bind(X_39,$fot(X_49)),bind(X_41,$fot(X_50)),bind(X_42,$fot(A))]]) ).
cnf(refute_0_159,plain,
( multiply(A,multiply(X_49,X_50)) != inverse(double_divide(multiply(X_49,X_50),A))
| double_divide(multiply(X_49,X_50),A) != double_divide(multiply(A,X_50),X_49)
| multiply(A,multiply(X_49,X_50)) = inverse(double_divide(multiply(A,X_50),X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_49,X_50)),inverse(double_divide(multiply(X_49,X_50),A))) ),[1,0],$fot(double_divide(multiply(A,X_50),X_49))]]) ).
cnf(refute_0_160,plain,
( multiply(A,multiply(X_49,X_50)) != inverse(double_divide(multiply(X_49,X_50),A))
| multiply(A,multiply(X_49,X_50)) = inverse(double_divide(multiply(A,X_50),X_49)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_49,X_50),A),double_divide(multiply(A,X_50),X_49)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
multiply(A,multiply(X_49,X_50)) = inverse(double_divide(multiply(A,X_50),X_49)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_49,X_50)),inverse(double_divide(multiply(X_49,X_50),A))) )],[refute_0_157,refute_0_160]) ).
cnf(refute_0_162,plain,
inverse(double_divide(multiply(A,X_50),X_49)) = multiply(X_49,multiply(A,X_50)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_49)),bind(B,$fot(multiply(A,X_50)))]]) ).
cnf(refute_0_163,plain,
( multiply(A,multiply(X_49,X_50)) != inverse(double_divide(multiply(A,X_50),X_49))
| inverse(double_divide(multiply(A,X_50),X_49)) != multiply(X_49,multiply(A,X_50))
| multiply(A,multiply(X_49,X_50)) = multiply(X_49,multiply(A,X_50)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,multiply(X_49,X_50)),multiply(X_49,multiply(A,X_50))) ),[0],$fot(inverse(double_divide(multiply(A,X_50),X_49)))]]) ).
cnf(refute_0_164,plain,
( multiply(A,multiply(X_49,X_50)) != inverse(double_divide(multiply(A,X_50),X_49))
| multiply(A,multiply(X_49,X_50)) = multiply(X_49,multiply(A,X_50)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(multiply(A,X_50),X_49)),multiply(X_49,multiply(A,X_50))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(A,multiply(X_49,X_50)) = multiply(X_49,multiply(A,X_50)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_49,X_50)),inverse(double_divide(multiply(A,X_50),X_49))) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( multiply(A,multiply(X_49,X_50)) != multiply(X_49,multiply(A,X_50))
| multiply(X_49,multiply(A,X_50)) = multiply(A,multiply(X_49,X_50)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,multiply(X_49,X_50)))),bind(Y,$fot(multiply(X_49,multiply(A,X_50))))]]) ).
cnf(refute_0_167,plain,
multiply(X_49,multiply(A,X_50)) = multiply(A,multiply(X_49,X_50)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_49,X_50)),multiply(X_49,multiply(A,X_50))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(c3,b3)),
inference(subst,[],[refute_0_167:[bind(A,$fot(a3)),bind(X_49,$fot(c3)),bind(X_50,$fot(b3))]]) ).
cnf(refute_0_169,plain,
multiply(multiply(a3,b3),c3) = multiply(c3,multiply(a3,b3)),
inference(subst,[],[refute_0_151:[bind(A,$fot(c3)),bind(B,$fot(multiply(a3,b3)))]]) ).
cnf(refute_0_170,plain,
( multiply(multiply(a3,b3),c3) != multiply(c3,multiply(a3,b3))
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(c3,b3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(c3,b3)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiply(multiply(a3,b3),c3))),bind(Y,$fot(multiply(c3,multiply(a3,b3)))),bind(Z,$fot(multiply(a3,multiply(c3,b3))))]]) ).
cnf(refute_0_171,plain,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(c3,b3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(c3,b3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(c3,multiply(a3,b3))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(c3,b3)),
inference(resolve,[$cnf( $equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(c3,b3))) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(c3,b3))
| multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(multiply(multiply(a3,b3),c3))),bind(Y,$fot(multiply(a3,multiply(c3,b3)))),bind(Z,$fot(multiply(a3,multiply(b3,c3))))]]) ).
cnf(refute_0_174,plain,
( multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(c3,b3))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))) )],[refute_0_156,refute_0_174]) ).
cnf(refute_0_176,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),[0],$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_177,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_177,prove_these_axioms_3]) ).
cnf(refute_0_179,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_180,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_179,refute_0_178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP607-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 10:03:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.50
%------------------------------------------------------------------------------