TSTP Solution File: GRP455-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP455-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 10:40:45 EDT 2022
% Result : Unsatisfiable 0.18s 0.35s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 64
% Syntax : Number of clauses : 223 ( 113 unt; 0 nHn; 116 RR)
% Number of literals : 382 ( 381 equ; 162 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 : 353 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(identity,B)) ).
cnf(inverse,axiom,
inverse(A) = divide(identity,A) ).
cnf(identity,axiom,
identity = divide(A,A) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(identity,a2) != a2 ).
cnf(refute_0_0,plain,
inverse(inverse(X_3)) = divide(identity,inverse(X_3)),
inference(subst,[],[inverse:[bind(A,$fot(inverse(X_3)))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_2,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_3,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( inverse(A) != divide(identity,A)
| divide(identity,A) = inverse(A) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(identity,A)))]]) ).
cnf(refute_0_5,plain,
divide(identity,A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(identity,A)) )],[inverse,refute_0_4]) ).
cnf(refute_0_6,plain,
divide(identity,B) = inverse(B),
inference(subst,[],[refute_0_5:[bind(A,$fot(B))]]) ).
cnf(refute_0_7,plain,
divide(A,divide(identity,B)) = divide(A,divide(identity,B)),
introduced(tautology,[refl,[$fot(divide(A,divide(identity,B)))]]) ).
cnf(refute_0_8,plain,
( divide(A,divide(identity,B)) != divide(A,divide(identity,B))
| divide(identity,B) != inverse(B)
| divide(A,divide(identity,B)) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(identity,B)),divide(A,divide(identity,B))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_9,plain,
( divide(identity,B) != inverse(B)
| divide(A,divide(identity,B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(identity,B)),divide(A,divide(identity,B))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
divide(A,divide(identity,B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(identity,B),inverse(B)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( multiply(A,B) != divide(A,divide(identity,B))
| divide(A,divide(identity,B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(identity,B)))]]) ).
cnf(refute_0_12,plain,
( multiply(A,B) != divide(A,divide(identity,B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(identity,B)),divide(A,inverse(B))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(identity,B))) )],[multiply,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(identity,X_3) = divide(identity,inverse(X_3)),
inference(subst,[],[refute_0_13:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_15,plain,
( multiply(identity,X_3) != divide(identity,inverse(X_3))
| divide(identity,inverse(X_3)) = multiply(identity,X_3) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(identity,X_3))),bind(Y,$fot(divide(identity,inverse(X_3))))]]) ).
cnf(refute_0_16,plain,
divide(identity,inverse(X_3)) = multiply(identity,X_3),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),divide(identity,inverse(X_3))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( divide(identity,inverse(X_3)) != multiply(identity,X_3)
| inverse(inverse(X_3)) != divide(identity,inverse(X_3))
| inverse(inverse(X_3)) = multiply(identity,X_3) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_3)),divide(identity,inverse(X_3))) ),[1],$fot(multiply(identity,X_3))]]) ).
cnf(refute_0_18,plain,
( inverse(inverse(X_3)) != divide(identity,inverse(X_3))
| inverse(inverse(X_3)) = multiply(identity,X_3) ),
inference(resolve,[$cnf( $equal(divide(identity,inverse(X_3)),multiply(identity,X_3)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(inverse(X_3)) = multiply(identity,X_3),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),divide(identity,inverse(X_3))) )],[refute_0_0,refute_0_18]) ).
cnf(refute_0_20,plain,
( inverse(inverse(X_3)) != multiply(identity,X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(inverse(X_3)))),bind(Y,$fot(multiply(identity,X_3)))]]) ).
cnf(refute_0_21,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),multiply(identity,X_3)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(identity,a2) = inverse(inverse(a2)),
inference(subst,[],[refute_0_21:[bind(X_3,$fot(a2))]]) ).
cnf(refute_0_23,plain,
( multiply(identity,a2) != inverse(inverse(a2))
| inverse(inverse(a2)) != a2
| multiply(identity,a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,a2),a2) ),[0],$fot(inverse(inverse(a2)))]]) ).
cnf(refute_0_24,plain,
( inverse(inverse(a2)) != a2
| multiply(identity,a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(identity,a2),inverse(inverse(a2))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
inverse(inverse(a2)) != a2,
inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_24,prove_these_axioms_2]) ).
cnf(refute_0_26,plain,
( identity != divide(A,A)
| divide(A,A) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(divide(A,A)))]]) ).
cnf(refute_0_27,plain,
divide(A,A) = identity,
inference(resolve,[$cnf( $equal(identity,divide(A,A)) )],[identity,refute_0_26]) ).
cnf(refute_0_28,plain,
divide(divide(A,A),A) = divide(divide(A,A),A),
introduced(tautology,[refl,[$fot(divide(divide(A,A),A))]]) ).
cnf(refute_0_29,plain,
( divide(A,A) != identity
| divide(divide(A,A),A) != divide(divide(A,A),A)
| divide(divide(A,A),A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(A,A),A),divide(divide(A,A),A)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_30,plain,
( divide(A,A) != identity
| divide(divide(A,A),A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(A,A),A),divide(divide(A,A),A)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
divide(divide(A,A),A) = divide(identity,A),
inference(resolve,[$cnf( $equal(divide(A,A),identity) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_33,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_3,refute_0_32]) ).
cnf(refute_0_34,plain,
( divide(divide(A,A),A) != divide(identity,A)
| divide(identity,A) != inverse(A)
| divide(divide(A,A),A) = inverse(A) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(divide(divide(A,A),A))),bind(Y,$fot(divide(identity,A))),bind(Z,$fot(inverse(A)))]]) ).
cnf(refute_0_35,plain,
( divide(identity,A) != inverse(A)
| divide(divide(A,A),A) = inverse(A) ),
inference(resolve,[$cnf( $equal(divide(divide(A,A),A),divide(identity,A)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
divide(divide(A,A),A) = inverse(A),
inference(resolve,[$cnf( $equal(divide(identity,A),inverse(A)) )],[refute_0_5,refute_0_35]) ).
cnf(refute_0_37,plain,
divide(divide(divide(A,A),A),C) = divide(divide(divide(A,A),A),C),
introduced(tautology,[refl,[$fot(divide(divide(divide(A,A),A),C))]]) ).
cnf(refute_0_38,plain,
( divide(divide(A,A),A) != inverse(A)
| divide(divide(divide(A,A),A),C) != divide(divide(divide(A,A),A),C)
| divide(divide(divide(A,A),A),C) = divide(inverse(A),C) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(A,A),A),C),divide(divide(divide(A,A),A),C)) ),[1,0],$fot(inverse(A))]]) ).
cnf(refute_0_39,plain,
( divide(divide(A,A),A) != inverse(A)
| divide(divide(divide(A,A),A),C) = divide(inverse(A),C) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(A,A),A),C),divide(divide(divide(A,A),A),C)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
divide(divide(divide(A,A),A),C) = divide(inverse(A),C),
inference(resolve,[$cnf( $equal(divide(divide(A,A),A),inverse(A)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
divide(B,divide(divide(divide(A,A),A),C)) = divide(B,divide(divide(divide(A,A),A),C)),
introduced(tautology,[refl,[$fot(divide(B,divide(divide(divide(A,A),A),C)))]]) ).
cnf(refute_0_42,plain,
( divide(B,divide(divide(divide(A,A),A),C)) != divide(B,divide(divide(divide(A,A),A),C))
| divide(divide(divide(A,A),A),C) != divide(inverse(A),C)
| divide(B,divide(divide(divide(A,A),A),C)) = divide(B,divide(inverse(A),C)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(B,divide(divide(divide(A,A),A),C)),divide(B,divide(divide(divide(A,A),A),C))) ),[1,1],$fot(divide(inverse(A),C))]]) ).
cnf(refute_0_43,plain,
( divide(divide(divide(A,A),A),C) != divide(inverse(A),C)
| divide(B,divide(divide(divide(A,A),A),C)) = divide(B,divide(inverse(A),C)) ),
inference(resolve,[$cnf( $equal(divide(B,divide(divide(divide(A,A),A),C)),divide(B,divide(divide(divide(A,A),A),C))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
divide(B,divide(divide(divide(A,A),A),C)) = divide(B,divide(inverse(A),C)),
inference(resolve,[$cnf( $equal(divide(divide(divide(A,A),A),C),divide(inverse(A),C)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
divide(A,divide(B,divide(divide(divide(A,A),A),C))) = divide(A,divide(B,divide(divide(divide(A,A),A),C))),
introduced(tautology,[refl,[$fot(divide(A,divide(B,divide(divide(divide(A,A),A),C))))]]) ).
cnf(refute_0_46,plain,
( divide(A,divide(B,divide(divide(divide(A,A),A),C))) != divide(A,divide(B,divide(divide(divide(A,A),A),C)))
| divide(B,divide(divide(divide(A,A),A),C)) != divide(B,divide(inverse(A),C))
| divide(A,divide(B,divide(divide(divide(A,A),A),C))) = divide(A,divide(B,divide(inverse(A),C))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(B,divide(divide(divide(A,A),A),C))),divide(A,divide(B,divide(divide(divide(A,A),A),C)))) ),[1,1],$fot(divide(B,divide(inverse(A),C)))]]) ).
cnf(refute_0_47,plain,
( divide(B,divide(divide(divide(A,A),A),C)) != divide(B,divide(inverse(A),C))
| divide(A,divide(B,divide(divide(divide(A,A),A),C))) = divide(A,divide(B,divide(inverse(A),C))) ),
inference(resolve,[$cnf( $equal(divide(A,divide(B,divide(divide(divide(A,A),A),C))),divide(A,divide(B,divide(divide(divide(A,A),A),C)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
divide(A,divide(B,divide(divide(divide(A,A),A),C))) = divide(A,divide(B,divide(inverse(A),C))),
inference(resolve,[$cnf( $equal(divide(B,divide(divide(divide(A,A),A),C)),divide(B,divide(inverse(A),C))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))) = inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))),
introduced(tautology,[refl,[$fot(inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))))]]) ).
cnf(refute_0_50,plain,
( divide(A,divide(B,divide(divide(divide(A,A),A),C))) != divide(A,divide(B,divide(inverse(A),C)))
| inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))) != inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C))))
| inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))) = inverse(divide(A,divide(B,divide(inverse(A),C)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))),inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C))))) ),[1,0],$fot(divide(A,divide(B,divide(inverse(A),C))))]]) ).
cnf(refute_0_51,plain,
( divide(A,divide(B,divide(divide(divide(A,A),A),C))) != divide(A,divide(B,divide(inverse(A),C)))
| inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))) = inverse(divide(A,divide(B,divide(inverse(A),C)))) ),
inference(resolve,[$cnf( $equal(inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))),inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C))))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))) = inverse(divide(A,divide(B,divide(inverse(A),C)))),
inference(resolve,[$cnf( $equal(divide(A,divide(B,divide(divide(divide(A,A),A),C))),divide(A,divide(B,divide(inverse(A),C)))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))) = inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))),
inference(subst,[],[refute_0_5:[bind(A,$fot(divide(A,divide(B,divide(divide(divide(A,A),A),C)))))]]) ).
cnf(refute_0_54,plain,
( divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))) != inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C))))
| inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))) != inverse(divide(A,divide(B,divide(inverse(A),C))))
| divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))) = inverse(divide(A,divide(B,divide(inverse(A),C)))) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))))),bind(Y,$fot(inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))))),bind(Z,$fot(inverse(divide(A,divide(B,divide(inverse(A),C))))))]]) ).
cnf(refute_0_55,plain,
( inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))) != inverse(divide(A,divide(B,divide(inverse(A),C))))
| divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))) = inverse(divide(A,divide(B,divide(inverse(A),C)))) ),
inference(resolve,[$cnf( $equal(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C))))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))) = inverse(divide(A,divide(B,divide(inverse(A),C)))),
inference(resolve,[$cnf( $equal(inverse(divide(A,divide(B,divide(divide(divide(A,A),A),C)))),inverse(divide(A,divide(B,divide(inverse(A),C))))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C),
introduced(tautology,[refl,[$fot(divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C))]]) ).
cnf(refute_0_58,plain,
( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) != divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)
| divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))) != inverse(divide(A,divide(B,divide(inverse(A),C))))
| divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C),divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)) ),[1,0],$fot(inverse(divide(A,divide(B,divide(inverse(A),C)))))]]) ).
cnf(refute_0_59,plain,
( divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))) != inverse(divide(A,divide(B,divide(inverse(A),C))))
| divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C),divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C),
inference(resolve,[$cnf( $equal(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),inverse(divide(A,divide(B,divide(inverse(A),C))))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) != B
| divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) != divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C)
| divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C),B) ),[0],$fot(divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C))]]) ).
cnf(refute_0_62,plain,
( divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) != B
| divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) = B ),
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C),divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) = B,
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C),B) )],[single_axiom,refute_0_62]) ).
cnf(refute_0_64,plain,
divide(inverse(divide(X_7,divide(X_8,divide(inverse(X_7),inverse(X_7))))),inverse(X_7)) = X_8,
inference(subst,[],[refute_0_63:[bind(A,$fot(X_7)),bind(B,$fot(X_8)),bind(C,$fot(inverse(X_7)))]]) ).
cnf(refute_0_65,plain,
identity = divide(inverse(X_7),inverse(X_7)),
inference(subst,[],[identity:[bind(A,$fot(inverse(X_7)))]]) ).
cnf(refute_0_66,plain,
( identity != divide(inverse(X_7),inverse(X_7))
| divide(inverse(X_7),inverse(X_7)) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(divide(inverse(X_7),inverse(X_7))))]]) ).
cnf(refute_0_67,plain,
divide(inverse(X_7),inverse(X_7)) = identity,
inference(resolve,[$cnf( $equal(identity,divide(inverse(X_7),inverse(X_7))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( divide(inverse(X_7),inverse(X_7)) != identity
| divide(inverse(divide(X_7,divide(X_8,divide(inverse(X_7),inverse(X_7))))),inverse(X_7)) != X_8
| divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(divide(X_7,divide(X_8,divide(inverse(X_7),inverse(X_7))))),inverse(X_7)),X_8) ),[0,0,0,1,1],$fot(identity)]]) ).
cnf(refute_0_69,plain,
( divide(inverse(divide(X_7,divide(X_8,divide(inverse(X_7),inverse(X_7))))),inverse(X_7)) != X_8
| divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) = X_8 ),
inference(resolve,[$cnf( $equal(divide(inverse(X_7),inverse(X_7)),identity) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) = X_8,
inference(resolve,[$cnf( $equal(divide(inverse(divide(X_7,divide(X_8,divide(inverse(X_7),inverse(X_7))))),inverse(X_7)),X_8) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_2,identity) = divide(X_2,inverse(identity)),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_2)),bind(B,$fot(identity))]]) ).
cnf(refute_0_72,plain,
identity = divide(identity,identity),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_73,plain,
inverse(identity) = divide(identity,identity),
inference(subst,[],[inverse:[bind(A,$fot(identity))]]) ).
cnf(refute_0_74,plain,
( inverse(identity) != divide(identity,identity)
| divide(identity,identity) = inverse(identity) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(identity))),bind(Y,$fot(divide(identity,identity)))]]) ).
cnf(refute_0_75,plain,
divide(identity,identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),divide(identity,identity)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( divide(identity,identity) != inverse(identity)
| identity != divide(identity,identity)
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,divide(identity,identity)) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_77,plain,
( identity != divide(identity,identity)
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(divide(identity,identity),inverse(identity)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,divide(identity,identity)) )],[refute_0_72,refute_0_77]) ).
cnf(refute_0_79,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_80,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(X_2,identity) != divide(X_2,inverse(identity))
| inverse(identity) != identity
| multiply(X_2,identity) = divide(X_2,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,identity),divide(X_2,inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_82,plain,
( multiply(X_2,identity) != divide(X_2,inverse(identity))
| multiply(X_2,identity) = divide(X_2,identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(X_2,identity) = divide(X_2,identity),
inference(resolve,[$cnf( $equal(multiply(X_2,identity),divide(X_2,inverse(identity))) )],[refute_0_71,refute_0_82]) ).
cnf(refute_0_84,plain,
( multiply(X_2,identity) != divide(X_2,identity)
| divide(X_2,identity) = multiply(X_2,identity) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(X_2,identity))),bind(Y,$fot(divide(X_2,identity)))]]) ).
cnf(refute_0_85,plain,
divide(X_2,identity) = multiply(X_2,identity),
inference(resolve,[$cnf( $equal(multiply(X_2,identity),divide(X_2,identity)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
divide(X_8,identity) = multiply(X_8,identity),
inference(subst,[],[refute_0_85:[bind(X_2,$fot(X_8))]]) ).
cnf(refute_0_87,plain,
divide(X_7,divide(X_8,identity)) = divide(X_7,divide(X_8,identity)),
introduced(tautology,[refl,[$fot(divide(X_7,divide(X_8,identity)))]]) ).
cnf(refute_0_88,plain,
( divide(X_7,divide(X_8,identity)) != divide(X_7,divide(X_8,identity))
| divide(X_8,identity) != multiply(X_8,identity)
| divide(X_7,divide(X_8,identity)) = divide(X_7,multiply(X_8,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(X_8,identity)),divide(X_7,divide(X_8,identity))) ),[1,1],$fot(multiply(X_8,identity))]]) ).
cnf(refute_0_89,plain,
( divide(X_8,identity) != multiply(X_8,identity)
| divide(X_7,divide(X_8,identity)) = divide(X_7,multiply(X_8,identity)) ),
inference(resolve,[$cnf( $equal(divide(X_7,divide(X_8,identity)),divide(X_7,divide(X_8,identity))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
divide(X_7,divide(X_8,identity)) = divide(X_7,multiply(X_8,identity)),
inference(resolve,[$cnf( $equal(divide(X_8,identity),multiply(X_8,identity)) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
inverse(divide(X_7,divide(X_8,identity))) = inverse(divide(X_7,divide(X_8,identity))),
introduced(tautology,[refl,[$fot(inverse(divide(X_7,divide(X_8,identity))))]]) ).
cnf(refute_0_92,plain,
( divide(X_7,divide(X_8,identity)) != divide(X_7,multiply(X_8,identity))
| inverse(divide(X_7,divide(X_8,identity))) != inverse(divide(X_7,divide(X_8,identity)))
| inverse(divide(X_7,divide(X_8,identity))) = inverse(divide(X_7,multiply(X_8,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(X_7,divide(X_8,identity))),inverse(divide(X_7,divide(X_8,identity)))) ),[1,0],$fot(divide(X_7,multiply(X_8,identity)))]]) ).
cnf(refute_0_93,plain,
( divide(X_7,divide(X_8,identity)) != divide(X_7,multiply(X_8,identity))
| inverse(divide(X_7,divide(X_8,identity))) = inverse(divide(X_7,multiply(X_8,identity))) ),
inference(resolve,[$cnf( $equal(inverse(divide(X_7,divide(X_8,identity))),inverse(divide(X_7,divide(X_8,identity)))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
inverse(divide(X_7,divide(X_8,identity))) = inverse(divide(X_7,multiply(X_8,identity))),
inference(resolve,[$cnf( $equal(divide(X_7,divide(X_8,identity)),divide(X_7,multiply(X_8,identity))) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(inverse(divide(X_7,divide(X_8,identity))),X_7) = multiply(inverse(divide(X_7,divide(X_8,identity))),X_7),
introduced(tautology,[refl,[$fot(multiply(inverse(divide(X_7,divide(X_8,identity))),X_7))]]) ).
cnf(refute_0_96,plain,
( multiply(inverse(divide(X_7,divide(X_8,identity))),X_7) != multiply(inverse(divide(X_7,divide(X_8,identity))),X_7)
| inverse(divide(X_7,divide(X_8,identity))) != inverse(divide(X_7,multiply(X_8,identity)))
| multiply(inverse(divide(X_7,divide(X_8,identity))),X_7) = multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(X_7,divide(X_8,identity))),X_7),multiply(inverse(divide(X_7,divide(X_8,identity))),X_7)) ),[1,0],$fot(inverse(divide(X_7,multiply(X_8,identity))))]]) ).
cnf(refute_0_97,plain,
( inverse(divide(X_7,divide(X_8,identity))) != inverse(divide(X_7,multiply(X_8,identity)))
| multiply(inverse(divide(X_7,divide(X_8,identity))),X_7) = multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_7,divide(X_8,identity))),X_7),multiply(inverse(divide(X_7,divide(X_8,identity))),X_7)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(inverse(divide(X_7,divide(X_8,identity))),X_7) = multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7),
inference(resolve,[$cnf( $equal(inverse(divide(X_7,divide(X_8,identity))),inverse(divide(X_7,multiply(X_8,identity)))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_100,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_13,refute_0_99]) ).
cnf(refute_0_101,plain,
divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) = multiply(inverse(divide(X_7,divide(X_8,identity))),X_7),
inference(subst,[],[refute_0_100:[bind(A,$fot(inverse(divide(X_7,divide(X_8,identity))))),bind(B,$fot(X_7))]]) ).
cnf(refute_0_102,plain,
( multiply(inverse(divide(X_7,divide(X_8,identity))),X_7) != multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7)
| divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) != multiply(inverse(divide(X_7,divide(X_8,identity))),X_7)
| divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) = multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)))),bind(Y,$fot(multiply(inverse(divide(X_7,divide(X_8,identity))),X_7))),bind(Z,$fot(multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7)))]]) ).
cnf(refute_0_103,plain,
( multiply(inverse(divide(X_7,divide(X_8,identity))),X_7) != multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7)
| divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) = multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)),multiply(inverse(divide(X_7,divide(X_8,identity))),X_7)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) = multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_7,divide(X_8,identity))),X_7),multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7)) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
( divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) != X_8
| divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) != multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7)
| multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)),X_8) ),[0],$fot(multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7))]]) ).
cnf(refute_0_106,plain,
( divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)) != X_8
| multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) = X_8 ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)),multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) = X_8,
inference(resolve,[$cnf( $equal(divide(inverse(divide(X_7,divide(X_8,identity))),inverse(X_7)),X_8) )],[refute_0_70,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(inverse(divide(X_12,multiply(inverse(divide(identity,multiply(X_8,identity))),identity))),X_12) = inverse(divide(identity,multiply(X_8,identity))),
inference(subst,[],[refute_0_107:[bind(X_7,$fot(X_12)),bind(X_8,$fot(inverse(divide(identity,multiply(X_8,identity)))))]]) ).
cnf(refute_0_109,plain,
multiply(inverse(divide(identity,multiply(X_8,identity))),identity) = X_8,
inference(subst,[],[refute_0_107:[bind(X_7,$fot(identity))]]) ).
cnf(refute_0_110,plain,
( multiply(inverse(divide(X_12,multiply(inverse(divide(identity,multiply(X_8,identity))),identity))),X_12) != inverse(divide(identity,multiply(X_8,identity)))
| multiply(inverse(divide(identity,multiply(X_8,identity))),identity) != X_8
| multiply(inverse(divide(X_12,X_8)),X_12) = inverse(divide(identity,multiply(X_8,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(X_12,multiply(inverse(divide(identity,multiply(X_8,identity))),identity))),X_12),inverse(divide(identity,multiply(X_8,identity)))) ),[0,0,0,1],$fot(X_8)]]) ).
cnf(refute_0_111,plain,
( multiply(inverse(divide(X_12,multiply(inverse(divide(identity,multiply(X_8,identity))),identity))),X_12) != inverse(divide(identity,multiply(X_8,identity)))
| multiply(inverse(divide(X_12,X_8)),X_12) = inverse(divide(identity,multiply(X_8,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(identity,multiply(X_8,identity))),identity),X_8) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(inverse(divide(X_12,X_8)),X_12) = inverse(divide(identity,multiply(X_8,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_12,multiply(inverse(divide(identity,multiply(X_8,identity))),identity))),X_12),inverse(divide(identity,multiply(X_8,identity)))) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
multiply(inverse(divide(X_7,multiply(inverse(divide(identity,multiply(X_13,identity))),identity))),X_7) = inverse(divide(identity,multiply(X_13,identity))),
inference(subst,[],[refute_0_107:[bind(X_8,$fot(inverse(divide(identity,multiply(X_13,identity)))))]]) ).
cnf(refute_0_114,plain,
multiply(inverse(divide(identity,multiply(X_13,identity))),identity) = X_13,
inference(subst,[],[refute_0_107:[bind(X_7,$fot(identity)),bind(X_8,$fot(X_13))]]) ).
cnf(refute_0_115,plain,
( multiply(inverse(divide(X_7,multiply(inverse(divide(identity,multiply(X_13,identity))),identity))),X_7) != inverse(divide(identity,multiply(X_13,identity)))
| multiply(inverse(divide(identity,multiply(X_13,identity))),identity) != X_13
| multiply(inverse(divide(X_7,X_13)),X_7) = inverse(divide(identity,multiply(X_13,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(X_7,multiply(inverse(divide(identity,multiply(X_13,identity))),identity))),X_7),inverse(divide(identity,multiply(X_13,identity)))) ),[0,0,0,1],$fot(X_13)]]) ).
cnf(refute_0_116,plain,
( multiply(inverse(divide(X_7,multiply(inverse(divide(identity,multiply(X_13,identity))),identity))),X_7) != inverse(divide(identity,multiply(X_13,identity)))
| multiply(inverse(divide(X_7,X_13)),X_7) = inverse(divide(identity,multiply(X_13,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(identity,multiply(X_13,identity))),identity),X_13) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(inverse(divide(X_7,X_13)),X_7) = inverse(divide(identity,multiply(X_13,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_7,multiply(inverse(divide(identity,multiply(X_13,identity))),identity))),X_7),inverse(divide(identity,multiply(X_13,identity)))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
divide(identity,multiply(X_13,identity)) = inverse(multiply(X_13,identity)),
inference(subst,[],[refute_0_5:[bind(A,$fot(multiply(X_13,identity)))]]) ).
cnf(refute_0_119,plain,
inverse(divide(identity,multiply(X_13,identity))) = inverse(divide(identity,multiply(X_13,identity))),
introduced(tautology,[refl,[$fot(inverse(divide(identity,multiply(X_13,identity))))]]) ).
cnf(refute_0_120,plain,
( divide(identity,multiply(X_13,identity)) != inverse(multiply(X_13,identity))
| inverse(divide(identity,multiply(X_13,identity))) != inverse(divide(identity,multiply(X_13,identity)))
| inverse(divide(identity,multiply(X_13,identity))) = inverse(inverse(multiply(X_13,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(identity,multiply(X_13,identity))),inverse(divide(identity,multiply(X_13,identity)))) ),[1,0],$fot(inverse(multiply(X_13,identity)))]]) ).
cnf(refute_0_121,plain,
( divide(identity,multiply(X_13,identity)) != inverse(multiply(X_13,identity))
| inverse(divide(identity,multiply(X_13,identity))) = inverse(inverse(multiply(X_13,identity))) ),
inference(resolve,[$cnf( $equal(inverse(divide(identity,multiply(X_13,identity))),inverse(divide(identity,multiply(X_13,identity)))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
inverse(divide(identity,multiply(X_13,identity))) = inverse(inverse(multiply(X_13,identity))),
inference(resolve,[$cnf( $equal(divide(identity,multiply(X_13,identity)),inverse(multiply(X_13,identity))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
( multiply(inverse(divide(X_7,X_13)),X_7) != inverse(divide(identity,multiply(X_13,identity)))
| inverse(divide(identity,multiply(X_13,identity))) != inverse(inverse(multiply(X_13,identity)))
| multiply(inverse(divide(X_7,X_13)),X_7) = inverse(inverse(multiply(X_13,identity))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(divide(X_7,X_13)),X_7),inverse(inverse(multiply(X_13,identity)))) ),[0],$fot(inverse(divide(identity,multiply(X_13,identity))))]]) ).
cnf(refute_0_124,plain,
( multiply(inverse(divide(X_7,X_13)),X_7) != inverse(divide(identity,multiply(X_13,identity)))
| multiply(inverse(divide(X_7,X_13)),X_7) = inverse(inverse(multiply(X_13,identity))) ),
inference(resolve,[$cnf( $equal(inverse(divide(identity,multiply(X_13,identity))),inverse(inverse(multiply(X_13,identity)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
multiply(inverse(divide(X_7,X_13)),X_7) = inverse(inverse(multiply(X_13,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_7,X_13)),X_7),inverse(divide(identity,multiply(X_13,identity)))) )],[refute_0_117,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(inverse(divide(X_12,X_8)),X_12) = inverse(inverse(multiply(X_8,identity))),
inference(subst,[],[refute_0_125:[bind(X_13,$fot(X_8)),bind(X_7,$fot(X_12))]]) ).
cnf(refute_0_127,plain,
( multiply(inverse(divide(X_12,X_8)),X_12) != inverse(divide(identity,multiply(X_8,identity)))
| multiply(inverse(divide(X_12,X_8)),X_12) != inverse(inverse(multiply(X_8,identity)))
| inverse(inverse(multiply(X_8,identity))) = inverse(divide(identity,multiply(X_8,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(X_12,X_8)),X_12),inverse(divide(identity,multiply(X_8,identity)))) ),[0],$fot(inverse(inverse(multiply(X_8,identity))))]]) ).
cnf(refute_0_128,plain,
( multiply(inverse(divide(X_12,X_8)),X_12) != inverse(divide(identity,multiply(X_8,identity)))
| inverse(inverse(multiply(X_8,identity))) = inverse(divide(identity,multiply(X_8,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_12,X_8)),X_12),inverse(inverse(multiply(X_8,identity)))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
divide(inverse(inverse(X_8)),identity) = multiply(inverse(inverse(X_8)),identity),
inference(subst,[],[refute_0_85:[bind(X_2,$fot(inverse(inverse(X_8))))]]) ).
cnf(refute_0_130,plain,
divide(inverse(divide(identity,divide(X_8,divide(inverse(identity),X_9)))),X_9) = X_8,
inference(subst,[],[refute_0_63:[bind(A,$fot(identity)),bind(B,$fot(X_8)),bind(C,$fot(X_9))]]) ).
cnf(refute_0_131,plain,
( divide(inverse(divide(identity,divide(X_8,divide(inverse(identity),X_9)))),X_9) != X_8
| inverse(identity) != identity
| divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(divide(identity,divide(X_8,divide(inverse(identity),X_9)))),X_9),X_8) ),[0,0,0,1,1,0],$fot(identity)]]) ).
cnf(refute_0_132,plain,
( divide(inverse(divide(identity,divide(X_8,divide(inverse(identity),X_9)))),X_9) != X_8
| divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) = X_8 ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_80,refute_0_131]) ).
cnf(refute_0_133,plain,
divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) = X_8,
inference(resolve,[$cnf( $equal(divide(inverse(divide(identity,divide(X_8,divide(inverse(identity),X_9)))),X_9),X_8) )],[refute_0_130,refute_0_132]) ).
cnf(refute_0_134,plain,
divide(X_8,inverse(X_9)) = multiply(X_8,X_9),
inference(subst,[],[refute_0_100:[bind(A,$fot(X_8)),bind(B,$fot(X_9))]]) ).
cnf(refute_0_135,plain,
divide(identity,X_9) = inverse(X_9),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_9))]]) ).
cnf(refute_0_136,plain,
divide(X_8,divide(identity,X_9)) = divide(X_8,divide(identity,X_9)),
introduced(tautology,[refl,[$fot(divide(X_8,divide(identity,X_9)))]]) ).
cnf(refute_0_137,plain,
( divide(X_8,divide(identity,X_9)) != divide(X_8,divide(identity,X_9))
| divide(identity,X_9) != inverse(X_9)
| divide(X_8,divide(identity,X_9)) = divide(X_8,inverse(X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_8,divide(identity,X_9)),divide(X_8,divide(identity,X_9))) ),[1,1],$fot(inverse(X_9))]]) ).
cnf(refute_0_138,plain,
( divide(identity,X_9) != inverse(X_9)
| divide(X_8,divide(identity,X_9)) = divide(X_8,inverse(X_9)) ),
inference(resolve,[$cnf( $equal(divide(X_8,divide(identity,X_9)),divide(X_8,divide(identity,X_9))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
divide(X_8,divide(identity,X_9)) = divide(X_8,inverse(X_9)),
inference(resolve,[$cnf( $equal(divide(identity,X_9),inverse(X_9)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
( divide(X_8,divide(identity,X_9)) != divide(X_8,inverse(X_9))
| divide(X_8,inverse(X_9)) != multiply(X_8,X_9)
| divide(X_8,divide(identity,X_9)) = multiply(X_8,X_9) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(divide(X_8,divide(identity,X_9)))),bind(Y,$fot(divide(X_8,inverse(X_9)))),bind(Z,$fot(multiply(X_8,X_9)))]]) ).
cnf(refute_0_141,plain,
( divide(X_8,inverse(X_9)) != multiply(X_8,X_9)
| divide(X_8,divide(identity,X_9)) = multiply(X_8,X_9) ),
inference(resolve,[$cnf( $equal(divide(X_8,divide(identity,X_9)),divide(X_8,inverse(X_9))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
divide(X_8,divide(identity,X_9)) = multiply(X_8,X_9),
inference(resolve,[$cnf( $equal(divide(X_8,inverse(X_9)),multiply(X_8,X_9)) )],[refute_0_134,refute_0_141]) ).
cnf(refute_0_143,plain,
inverse(divide(X_8,divide(identity,X_9))) = inverse(divide(X_8,divide(identity,X_9))),
introduced(tautology,[refl,[$fot(inverse(divide(X_8,divide(identity,X_9))))]]) ).
cnf(refute_0_144,plain,
( divide(X_8,divide(identity,X_9)) != multiply(X_8,X_9)
| inverse(divide(X_8,divide(identity,X_9))) != inverse(divide(X_8,divide(identity,X_9)))
| inverse(divide(X_8,divide(identity,X_9))) = inverse(multiply(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(X_8,divide(identity,X_9))),inverse(divide(X_8,divide(identity,X_9)))) ),[1,0],$fot(multiply(X_8,X_9))]]) ).
cnf(refute_0_145,plain,
( divide(X_8,divide(identity,X_9)) != multiply(X_8,X_9)
| inverse(divide(X_8,divide(identity,X_9))) = inverse(multiply(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(inverse(divide(X_8,divide(identity,X_9))),inverse(divide(X_8,divide(identity,X_9)))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
inverse(divide(X_8,divide(identity,X_9))) = inverse(multiply(X_8,X_9)),
inference(resolve,[$cnf( $equal(divide(X_8,divide(identity,X_9)),multiply(X_8,X_9)) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
divide(identity,divide(X_8,divide(identity,X_9))) = inverse(divide(X_8,divide(identity,X_9))),
inference(subst,[],[refute_0_5:[bind(A,$fot(divide(X_8,divide(identity,X_9))))]]) ).
cnf(refute_0_148,plain,
( divide(identity,divide(X_8,divide(identity,X_9))) != inverse(divide(X_8,divide(identity,X_9)))
| inverse(divide(X_8,divide(identity,X_9))) != inverse(multiply(X_8,X_9))
| divide(identity,divide(X_8,divide(identity,X_9))) = inverse(multiply(X_8,X_9)) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(divide(identity,divide(X_8,divide(identity,X_9))))),bind(Y,$fot(inverse(divide(X_8,divide(identity,X_9))))),bind(Z,$fot(inverse(multiply(X_8,X_9))))]]) ).
cnf(refute_0_149,plain,
( inverse(divide(X_8,divide(identity,X_9))) != inverse(multiply(X_8,X_9))
| divide(identity,divide(X_8,divide(identity,X_9))) = inverse(multiply(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(divide(identity,divide(X_8,divide(identity,X_9))),inverse(divide(X_8,divide(identity,X_9)))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
divide(identity,divide(X_8,divide(identity,X_9))) = inverse(multiply(X_8,X_9)),
inference(resolve,[$cnf( $equal(inverse(divide(X_8,divide(identity,X_9))),inverse(multiply(X_8,X_9))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
inverse(divide(identity,divide(X_8,divide(identity,X_9)))) = inverse(divide(identity,divide(X_8,divide(identity,X_9)))),
introduced(tautology,[refl,[$fot(inverse(divide(identity,divide(X_8,divide(identity,X_9)))))]]) ).
cnf(refute_0_152,plain,
( divide(identity,divide(X_8,divide(identity,X_9))) != inverse(multiply(X_8,X_9))
| inverse(divide(identity,divide(X_8,divide(identity,X_9)))) != inverse(divide(identity,divide(X_8,divide(identity,X_9))))
| inverse(divide(identity,divide(X_8,divide(identity,X_9)))) = inverse(inverse(multiply(X_8,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),inverse(divide(identity,divide(X_8,divide(identity,X_9))))) ),[1,0],$fot(inverse(multiply(X_8,X_9)))]]) ).
cnf(refute_0_153,plain,
( divide(identity,divide(X_8,divide(identity,X_9))) != inverse(multiply(X_8,X_9))
| inverse(divide(identity,divide(X_8,divide(identity,X_9)))) = inverse(inverse(multiply(X_8,X_9))) ),
inference(resolve,[$cnf( $equal(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),inverse(divide(identity,divide(X_8,divide(identity,X_9))))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
inverse(divide(identity,divide(X_8,divide(identity,X_9)))) = inverse(inverse(multiply(X_8,X_9))),
inference(resolve,[$cnf( $equal(divide(identity,divide(X_8,divide(identity,X_9))),inverse(multiply(X_8,X_9))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) = divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9),
introduced(tautology,[refl,[$fot(divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9))]]) ).
cnf(refute_0_156,plain,
( divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) != divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9)
| inverse(divide(identity,divide(X_8,divide(identity,X_9)))) != inverse(inverse(multiply(X_8,X_9)))
| divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) = divide(inverse(inverse(multiply(X_8,X_9))),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9),divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9)) ),[1,0],$fot(inverse(inverse(multiply(X_8,X_9))))]]) ).
cnf(refute_0_157,plain,
( inverse(divide(identity,divide(X_8,divide(identity,X_9)))) != inverse(inverse(multiply(X_8,X_9)))
| divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) = divide(inverse(inverse(multiply(X_8,X_9))),X_9) ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9),divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) = divide(inverse(inverse(multiply(X_8,X_9))),X_9),
inference(resolve,[$cnf( $equal(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),inverse(inverse(multiply(X_8,X_9)))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
( divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) != X_8
| divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) != divide(inverse(inverse(multiply(X_8,X_9))),X_9)
| divide(inverse(inverse(multiply(X_8,X_9))),X_9) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9),X_8) ),[0],$fot(divide(inverse(inverse(multiply(X_8,X_9))),X_9))]]) ).
cnf(refute_0_160,plain,
( divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9) != X_8
| divide(inverse(inverse(multiply(X_8,X_9))),X_9) = X_8 ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9),divide(inverse(inverse(multiply(X_8,X_9))),X_9)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
divide(inverse(inverse(multiply(X_8,X_9))),X_9) = X_8,
inference(resolve,[$cnf( $equal(divide(inverse(divide(identity,divide(X_8,divide(identity,X_9)))),X_9),X_8) )],[refute_0_133,refute_0_160]) ).
cnf(refute_0_162,plain,
divide(inverse(inverse(multiply(inverse(divide(X_9,multiply(X_13,identity))),X_9))),X_9) = inverse(divide(X_9,multiply(X_13,identity))),
inference(subst,[],[refute_0_161:[bind(X_8,$fot(inverse(divide(X_9,multiply(X_13,identity)))))]]) ).
cnf(refute_0_163,plain,
multiply(inverse(divide(X_9,multiply(X_13,identity))),X_9) = X_13,
inference(subst,[],[refute_0_107:[bind(X_7,$fot(X_9)),bind(X_8,$fot(X_13))]]) ).
cnf(refute_0_164,plain,
( multiply(inverse(divide(X_9,multiply(X_13,identity))),X_9) != X_13
| divide(inverse(inverse(multiply(inverse(divide(X_9,multiply(X_13,identity))),X_9))),X_9) != inverse(divide(X_9,multiply(X_13,identity)))
| divide(inverse(inverse(X_13)),X_9) = inverse(divide(X_9,multiply(X_13,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(inverse(multiply(inverse(divide(X_9,multiply(X_13,identity))),X_9))),X_9),inverse(divide(X_9,multiply(X_13,identity)))) ),[0,0,0,0],$fot(X_13)]]) ).
cnf(refute_0_165,plain,
( divide(inverse(inverse(multiply(inverse(divide(X_9,multiply(X_13,identity))),X_9))),X_9) != inverse(divide(X_9,multiply(X_13,identity)))
| divide(inverse(inverse(X_13)),X_9) = inverse(divide(X_9,multiply(X_13,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_9,multiply(X_13,identity))),X_9),X_13) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
divide(inverse(inverse(X_13)),X_9) = inverse(divide(X_9,multiply(X_13,identity))),
inference(resolve,[$cnf( $equal(divide(inverse(inverse(multiply(inverse(divide(X_9,multiply(X_13,identity))),X_9))),X_9),inverse(divide(X_9,multiply(X_13,identity)))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
( divide(inverse(inverse(X_13)),X_9) != inverse(divide(X_9,multiply(X_13,identity)))
| inverse(divide(X_9,multiply(X_13,identity))) = divide(inverse(inverse(X_13)),X_9) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(divide(inverse(inverse(X_13)),X_9))),bind(Y,$fot(inverse(divide(X_9,multiply(X_13,identity)))))]]) ).
cnf(refute_0_168,plain,
inverse(divide(X_9,multiply(X_13,identity))) = divide(inverse(inverse(X_13)),X_9),
inference(resolve,[$cnf( $equal(divide(inverse(inverse(X_13)),X_9),inverse(divide(X_9,multiply(X_13,identity)))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
inverse(divide(identity,multiply(X_8,identity))) = divide(inverse(inverse(X_8)),identity),
inference(subst,[],[refute_0_168:[bind(X_13,$fot(X_8)),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_170,plain,
( divide(inverse(inverse(X_8)),identity) != multiply(inverse(inverse(X_8)),identity)
| inverse(divide(identity,multiply(X_8,identity))) != divide(inverse(inverse(X_8)),identity)
| inverse(divide(identity,multiply(X_8,identity))) = multiply(inverse(inverse(X_8)),identity) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(inverse(divide(identity,multiply(X_8,identity))))),bind(Y,$fot(divide(inverse(inverse(X_8)),identity))),bind(Z,$fot(multiply(inverse(inverse(X_8)),identity)))]]) ).
cnf(refute_0_171,plain,
( divide(inverse(inverse(X_8)),identity) != multiply(inverse(inverse(X_8)),identity)
| inverse(divide(identity,multiply(X_8,identity))) = multiply(inverse(inverse(X_8)),identity) ),
inference(resolve,[$cnf( $equal(inverse(divide(identity,multiply(X_8,identity))),divide(inverse(inverse(X_8)),identity)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
inverse(divide(identity,multiply(X_8,identity))) = multiply(inverse(inverse(X_8)),identity),
inference(resolve,[$cnf( $equal(divide(inverse(inverse(X_8)),identity),multiply(inverse(inverse(X_8)),identity)) )],[refute_0_129,refute_0_171]) ).
cnf(refute_0_173,plain,
( inverse(divide(identity,multiply(X_8,identity))) != multiply(inverse(inverse(X_8)),identity)
| inverse(inverse(multiply(X_8,identity))) != inverse(divide(identity,multiply(X_8,identity)))
| inverse(inverse(multiply(X_8,identity))) = multiply(inverse(inverse(X_8)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_8,identity))),inverse(divide(identity,multiply(X_8,identity)))) ),[1],$fot(multiply(inverse(inverse(X_8)),identity))]]) ).
cnf(refute_0_174,plain,
( inverse(inverse(multiply(X_8,identity))) != inverse(divide(identity,multiply(X_8,identity)))
| inverse(inverse(multiply(X_8,identity))) = multiply(inverse(inverse(X_8)),identity) ),
inference(resolve,[$cnf( $equal(inverse(divide(identity,multiply(X_8,identity))),multiply(inverse(inverse(X_8)),identity)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
( multiply(inverse(divide(X_12,X_8)),X_12) != inverse(divide(identity,multiply(X_8,identity)))
| inverse(inverse(multiply(X_8,identity))) = multiply(inverse(inverse(X_8)),identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_8,identity))),inverse(divide(identity,multiply(X_8,identity)))) )],[refute_0_128,refute_0_174]) ).
cnf(refute_0_176,plain,
inverse(inverse(multiply(X_8,identity))) = multiply(inverse(inverse(X_8)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_12,X_8)),X_12),inverse(divide(identity,multiply(X_8,identity)))) )],[refute_0_112,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(inverse(divide(multiply(X_13,identity),multiply(X_13,identity))),multiply(X_13,identity)) = X_13,
inference(subst,[],[refute_0_107:[bind(X_7,$fot(multiply(X_13,identity))),bind(X_8,$fot(X_13))]]) ).
cnf(refute_0_178,plain,
identity = divide(multiply(X_13,identity),multiply(X_13,identity)),
inference(subst,[],[identity:[bind(A,$fot(multiply(X_13,identity)))]]) ).
cnf(refute_0_179,plain,
( identity != divide(multiply(X_13,identity),multiply(X_13,identity))
| divide(multiply(X_13,identity),multiply(X_13,identity)) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(divide(multiply(X_13,identity),multiply(X_13,identity))))]]) ).
cnf(refute_0_180,plain,
divide(multiply(X_13,identity),multiply(X_13,identity)) = identity,
inference(resolve,[$cnf( $equal(identity,divide(multiply(X_13,identity),multiply(X_13,identity))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
( multiply(inverse(divide(multiply(X_13,identity),multiply(X_13,identity))),multiply(X_13,identity)) != X_13
| divide(multiply(X_13,identity),multiply(X_13,identity)) != identity
| multiply(inverse(identity),multiply(X_13,identity)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(multiply(X_13,identity),multiply(X_13,identity))),multiply(X_13,identity)),X_13) ),[0,0,0],$fot(identity)]]) ).
cnf(refute_0_182,plain,
( multiply(inverse(divide(multiply(X_13,identity),multiply(X_13,identity))),multiply(X_13,identity)) != X_13
| multiply(inverse(identity),multiply(X_13,identity)) = X_13 ),
inference(resolve,[$cnf( $equal(divide(multiply(X_13,identity),multiply(X_13,identity)),identity) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(inverse(identity),multiply(X_13,identity)) = X_13,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(multiply(X_13,identity),multiply(X_13,identity))),multiply(X_13,identity)),X_13) )],[refute_0_177,refute_0_182]) ).
cnf(refute_0_184,plain,
multiply(identity,multiply(X_13,identity)) = inverse(inverse(multiply(X_13,identity))),
inference(subst,[],[refute_0_21:[bind(X_3,$fot(multiply(X_13,identity)))]]) ).
cnf(refute_0_185,plain,
multiply(inverse(identity),multiply(X_13,identity)) = multiply(inverse(identity),multiply(X_13,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),multiply(X_13,identity)))]]) ).
cnf(refute_0_186,plain,
( multiply(inverse(identity),multiply(X_13,identity)) != multiply(inverse(identity),multiply(X_13,identity))
| inverse(identity) != identity
| multiply(inverse(identity),multiply(X_13,identity)) = multiply(identity,multiply(X_13,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),multiply(X_13,identity)),multiply(inverse(identity),multiply(X_13,identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_187,plain,
( inverse(identity) != identity
| multiply(inverse(identity),multiply(X_13,identity)) = multiply(identity,multiply(X_13,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),multiply(X_13,identity)),multiply(inverse(identity),multiply(X_13,identity))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
multiply(inverse(identity),multiply(X_13,identity)) = multiply(identity,multiply(X_13,identity)),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_80,refute_0_187]) ).
cnf(refute_0_189,plain,
( multiply(identity,multiply(X_13,identity)) != inverse(inverse(multiply(X_13,identity)))
| multiply(inverse(identity),multiply(X_13,identity)) != multiply(identity,multiply(X_13,identity))
| multiply(inverse(identity),multiply(X_13,identity)) = inverse(inverse(multiply(X_13,identity))) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(multiply(inverse(identity),multiply(X_13,identity)))),bind(Y,$fot(multiply(identity,multiply(X_13,identity)))),bind(Z,$fot(inverse(inverse(multiply(X_13,identity)))))]]) ).
cnf(refute_0_190,plain,
( multiply(identity,multiply(X_13,identity)) != inverse(inverse(multiply(X_13,identity)))
| multiply(inverse(identity),multiply(X_13,identity)) = inverse(inverse(multiply(X_13,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),multiply(X_13,identity)),multiply(identity,multiply(X_13,identity))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
multiply(inverse(identity),multiply(X_13,identity)) = inverse(inverse(multiply(X_13,identity))),
inference(resolve,[$cnf( $equal(multiply(identity,multiply(X_13,identity)),inverse(inverse(multiply(X_13,identity)))) )],[refute_0_184,refute_0_190]) ).
cnf(refute_0_192,plain,
( multiply(inverse(identity),multiply(X_13,identity)) != X_13
| multiply(inverse(identity),multiply(X_13,identity)) != inverse(inverse(multiply(X_13,identity)))
| inverse(inverse(multiply(X_13,identity))) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),multiply(X_13,identity)),X_13) ),[0],$fot(inverse(inverse(multiply(X_13,identity))))]]) ).
cnf(refute_0_193,plain,
( multiply(inverse(identity),multiply(X_13,identity)) != X_13
| inverse(inverse(multiply(X_13,identity))) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),multiply(X_13,identity)),inverse(inverse(multiply(X_13,identity)))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
inverse(inverse(multiply(X_13,identity))) = X_13,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),multiply(X_13,identity)),X_13) )],[refute_0_183,refute_0_193]) ).
cnf(refute_0_195,plain,
inverse(inverse(multiply(X_8,identity))) = X_8,
inference(subst,[],[refute_0_194:[bind(X_13,$fot(X_8))]]) ).
cnf(refute_0_196,plain,
( inverse(inverse(multiply(X_8,identity))) != X_8
| inverse(inverse(multiply(X_8,identity))) != multiply(inverse(inverse(X_8)),identity)
| X_8 = multiply(inverse(inverse(X_8)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_8,identity))),multiply(inverse(inverse(X_8)),identity)) ),[0],$fot(X_8)]]) ).
cnf(refute_0_197,plain,
( inverse(inverse(multiply(X_8,identity))) != multiply(inverse(inverse(X_8)),identity)
| X_8 = multiply(inverse(inverse(X_8)),identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_8,identity))),X_8) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
( multiply(inverse(divide(X_7,X_13)),X_7) != inverse(inverse(multiply(X_13,identity)))
| inverse(inverse(multiply(X_13,identity))) != X_13
| multiply(inverse(divide(X_7,X_13)),X_7) = X_13 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(divide(X_7,X_13)),X_7),X_13) ),[0],$fot(inverse(inverse(multiply(X_13,identity))))]]) ).
cnf(refute_0_199,plain,
( multiply(inverse(divide(X_7,X_13)),X_7) != inverse(inverse(multiply(X_13,identity)))
| multiply(inverse(divide(X_7,X_13)),X_7) = X_13 ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_13,identity))),X_13) )],[refute_0_194,refute_0_198]) ).
cnf(refute_0_200,plain,
multiply(inverse(divide(X_7,X_13)),X_7) = X_13,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_7,X_13)),X_7),inverse(inverse(multiply(X_13,identity)))) )],[refute_0_125,refute_0_199]) ).
cnf(refute_0_201,plain,
multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) = multiply(X_8,identity),
inference(subst,[],[refute_0_200:[bind(X_13,$fot(multiply(X_8,identity)))]]) ).
cnf(refute_0_202,plain,
( multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) != X_8
| multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) != multiply(X_8,identity)
| multiply(X_8,identity) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7),X_8) ),[0],$fot(multiply(X_8,identity))]]) ).
cnf(refute_0_203,plain,
( multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7) != X_8
| multiply(X_8,identity) = X_8 ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7),multiply(X_8,identity)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
multiply(X_8,identity) = X_8,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_7,multiply(X_8,identity))),X_7),X_8) )],[refute_0_107,refute_0_203]) ).
cnf(refute_0_205,plain,
multiply(inverse(inverse(X_8)),identity) = inverse(inverse(X_8)),
inference(subst,[],[refute_0_204:[bind(X_8,$fot(inverse(inverse(X_8))))]]) ).
cnf(refute_0_206,plain,
( X_8 != multiply(inverse(inverse(X_8)),identity)
| multiply(inverse(inverse(X_8)),identity) != inverse(inverse(X_8))
| X_8 = inverse(inverse(X_8)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_8,inverse(inverse(X_8))) ),[0],$fot(multiply(inverse(inverse(X_8)),identity))]]) ).
cnf(refute_0_207,plain,
( X_8 != multiply(inverse(inverse(X_8)),identity)
| X_8 = inverse(inverse(X_8)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_8)),identity),inverse(inverse(X_8))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
( inverse(inverse(multiply(X_8,identity))) != multiply(inverse(inverse(X_8)),identity)
| X_8 = inverse(inverse(X_8)) ),
inference(resolve,[$cnf( $equal(X_8,multiply(inverse(inverse(X_8)),identity)) )],[refute_0_197,refute_0_207]) ).
cnf(refute_0_209,plain,
X_8 = inverse(inverse(X_8)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_8,identity))),multiply(inverse(inverse(X_8)),identity)) )],[refute_0_176,refute_0_208]) ).
cnf(refute_0_210,plain,
( X_8 != inverse(inverse(X_8))
| inverse(inverse(X_8)) = X_8 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_8)),bind(Y,$fot(inverse(inverse(X_8))))]]) ).
cnf(refute_0_211,plain,
inverse(inverse(X_8)) = X_8,
inference(resolve,[$cnf( $equal(X_8,inverse(inverse(X_8))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
inverse(inverse(a2)) = a2,
inference(subst,[],[refute_0_211:[bind(X_8,$fot(a2))]]) ).
cnf(refute_0_213,plain,
( a2 != a2
| inverse(inverse(a2)) != a2
| inverse(inverse(a2)) = a2 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a2)),a2) ),[0,0,0],$fot(a2)]]) ).
cnf(refute_0_214,plain,
( a2 != a2
| inverse(inverse(a2)) = a2 ),
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_214,refute_0_25]) ).
cnf(refute_0_216,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_217,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_216,refute_0_215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP455-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 09:35:18 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.35
% 0.18/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.40
%------------------------------------------------------------------------------