%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP532-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 10:42:10 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 47
% Syntax : Number of clauses : 188 ( 103 unt; 0 nHn; 83 RR)
% Number of literals : 311 ( 310 equ; 125 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 398 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(A,divide(B,C)),divide(A,B)) = C ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)) ).
cnf(inverse,axiom,
inverse(A) = divide(divide(B,B),A) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
cnf(refute_0_0,plain,
divide(divide(divide(B,B),divide(X_9,X_10)),divide(divide(B,B),X_9)) = X_10,
inference(subst,[],[single_axiom:[bind(A,$fot(divide(B,B))),bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_1,plain,
inverse(X_9) = divide(divide(B,B),X_9),
inference(subst,[],[inverse:[bind(A,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( inverse(X_9) != divide(divide(B,B),X_9)
| divide(divide(B,B),X_9) = inverse(X_9) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_9))),bind(Y,$fot(divide(divide(B,B),X_9)))]]) ).
cnf(refute_0_6,plain,
divide(divide(B,B),X_9) = inverse(X_9),
inference(resolve,[$cnf( $equal(inverse(X_9),divide(divide(B,B),X_9)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( divide(divide(B,B),X_9) != inverse(X_9)
| divide(divide(divide(B,B),divide(X_9,X_10)),divide(divide(B,B),X_9)) != X_10
| divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(B,B),divide(X_9,X_10)),divide(divide(B,B),X_9)),X_10) ),[0,1],$fot(inverse(X_9))]]) ).
cnf(refute_0_8,plain,
( divide(divide(divide(B,B),divide(X_9,X_10)),divide(divide(B,B),X_9)) != X_10
| divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),X_9),inverse(X_9)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) = X_10,
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_9,X_10)),divide(divide(B,B),X_9)),X_10) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_11,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_10]) ).
cnf(refute_0_12,plain,
divide(divide(B,B),divide(X_9,X_10)) = inverse(divide(X_9,X_10)),
inference(subst,[],[refute_0_11:[bind(A,$fot(divide(X_9,X_10)))]]) ).
cnf(refute_0_13,plain,
multiply(divide(divide(B,B),divide(X_9,X_10)),X_9) = multiply(divide(divide(B,B),divide(X_9,X_10)),X_9),
introduced(tautology,[refl,[$fot(multiply(divide(divide(B,B),divide(X_9,X_10)),X_9))]]) ).
cnf(refute_0_14,plain,
( multiply(divide(divide(B,B),divide(X_9,X_10)),X_9) != multiply(divide(divide(B,B),divide(X_9,X_10)),X_9)
| divide(divide(B,B),divide(X_9,X_10)) != inverse(divide(X_9,X_10))
| multiply(divide(divide(B,B),divide(X_9,X_10)),X_9) = multiply(inverse(divide(X_9,X_10)),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(divide(B,B),divide(X_9,X_10)),X_9),multiply(divide(divide(B,B),divide(X_9,X_10)),X_9)) ),[1,0],$fot(inverse(divide(X_9,X_10)))]]) ).
cnf(refute_0_15,plain,
( divide(divide(B,B),divide(X_9,X_10)) != inverse(divide(X_9,X_10))
| multiply(divide(divide(B,B),divide(X_9,X_10)),X_9) = multiply(inverse(divide(X_9,X_10)),X_9) ),
inference(resolve,[$cnf( $equal(multiply(divide(divide(B,B),divide(X_9,X_10)),X_9),multiply(divide(divide(B,B),divide(X_9,X_10)),X_9)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(divide(divide(B,B),divide(X_9,X_10)),X_9) = multiply(inverse(divide(X_9,X_10)),X_9),
inference(resolve,[$cnf( $equal(divide(divide(B,B),divide(X_9,X_10)),inverse(divide(X_9,X_10))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_11:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_18,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_19,plain,
( divide(A,divide(divide(C,C),B)) != divide(A,divide(divide(C,C),B))
| divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_20,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_23,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_26,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) = multiply(divide(divide(B,B),divide(X_9,X_10)),X_9),
inference(subst,[],[refute_0_26:[bind(A,$fot(divide(divide(B,B),divide(X_9,X_10)))),bind(B,$fot(X_9))]]) ).
cnf(refute_0_28,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_29,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
( multiply(divide(divide(B,B),divide(X_9,X_10)),X_9) != multiply(inverse(divide(X_9,X_10)),X_9)
| divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) != multiply(divide(divide(B,B),divide(X_9,X_10)),X_9)
| divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) = multiply(inverse(divide(X_9,X_10)),X_9) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)))),bind(Y,$fot(multiply(divide(divide(B,B),divide(X_9,X_10)),X_9))),bind(Z,$fot(multiply(inverse(divide(X_9,X_10)),X_9)))]]) ).
cnf(refute_0_31,plain,
( multiply(divide(divide(B,B),divide(X_9,X_10)),X_9) != multiply(inverse(divide(X_9,X_10)),X_9)
| divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) = multiply(inverse(divide(X_9,X_10)),X_9) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)),multiply(divide(divide(B,B),divide(X_9,X_10)),X_9)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) = multiply(inverse(divide(X_9,X_10)),X_9),
inference(resolve,[$cnf( $equal(multiply(divide(divide(B,B),divide(X_9,X_10)),X_9),multiply(inverse(divide(X_9,X_10)),X_9)) )],[refute_0_16,refute_0_31]) ).
cnf(refute_0_33,plain,
( divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) != X_10
| divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) != multiply(inverse(divide(X_9,X_10)),X_9)
| multiply(inverse(divide(X_9,X_10)),X_9) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)),X_10) ),[0],$fot(multiply(inverse(divide(X_9,X_10)),X_9))]]) ).
cnf(refute_0_34,plain,
( divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)) != X_10
| multiply(inverse(divide(X_9,X_10)),X_9) = X_10 ),
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)),multiply(inverse(divide(X_9,X_10)),X_9)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(inverse(divide(X_9,X_10)),X_9) = X_10,
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_9,X_10)),inverse(X_9)),X_10) )],[refute_0_9,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(inverse(divide(divide(X_10,X_25),X_10)),divide(X_10,X_25)) = X_10,
inference(subst,[],[refute_0_35:[bind(X_9,$fot(divide(X_10,X_25)))]]) ).
cnf(refute_0_37,plain,
inverse(divide(divide(X_9,X_10),X_9)) = divide(divide(divide(X_9,X_10),divide(X_9,X_10)),divide(divide(X_9,X_10),X_9)),
inference(subst,[],[inverse:[bind(A,$fot(divide(divide(X_9,X_10),X_9))),bind(B,$fot(divide(X_9,X_10)))]]) ).
cnf(refute_0_38,plain,
divide(divide(divide(X_9,X_10),divide(X_9,X_10)),divide(divide(X_9,X_10),X_9)) = X_10,
inference(subst,[],[single_axiom:[bind(A,$fot(divide(X_9,X_10))),bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_39,plain,
( divide(divide(divide(X_9,X_10),divide(X_9,X_10)),divide(divide(X_9,X_10),X_9)) != X_10
| inverse(divide(divide(X_9,X_10),X_9)) != divide(divide(divide(X_9,X_10),divide(X_9,X_10)),divide(divide(X_9,X_10),X_9))
| inverse(divide(divide(X_9,X_10),X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(X_9,X_10),X_9)),divide(divide(divide(X_9,X_10),divide(X_9,X_10)),divide(divide(X_9,X_10),X_9))) ),[1],$fot(X_10)]]) ).
cnf(refute_0_40,plain,
( inverse(divide(divide(X_9,X_10),X_9)) != divide(divide(divide(X_9,X_10),divide(X_9,X_10)),divide(divide(X_9,X_10),X_9))
| inverse(divide(divide(X_9,X_10),X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_9,X_10),divide(X_9,X_10)),divide(divide(X_9,X_10),X_9)),X_10) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
inverse(divide(divide(X_9,X_10),X_9)) = X_10,
inference(resolve,[$cnf( $equal(inverse(divide(divide(X_9,X_10),X_9)),divide(divide(divide(X_9,X_10),divide(X_9,X_10)),divide(divide(X_9,X_10),X_9))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
inverse(divide(divide(X_10,X_25),X_10)) = X_25,
inference(subst,[],[refute_0_41:[bind(X_10,$fot(X_25)),bind(X_9,$fot(X_10))]]) ).
cnf(refute_0_43,plain,
( multiply(inverse(divide(divide(X_10,X_25),X_10)),divide(X_10,X_25)) != X_10
| inverse(divide(divide(X_10,X_25),X_10)) != X_25
| multiply(X_25,divide(X_10,X_25)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(divide(X_10,X_25),X_10)),divide(X_10,X_25)),X_10) ),[0,0],$fot(X_25)]]) ).
cnf(refute_0_44,plain,
( multiply(inverse(divide(divide(X_10,X_25),X_10)),divide(X_10,X_25)) != X_10
| multiply(X_25,divide(X_10,X_25)) = X_10 ),
inference(resolve,[$cnf( $equal(inverse(divide(divide(X_10,X_25),X_10)),X_25) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(X_25,divide(X_10,X_25)) = X_10,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(divide(X_10,X_25),X_10)),divide(X_10,X_25)),X_10) )],[refute_0_36,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(X_58,divide(X_58,X_58)) = X_58,
inference(subst,[],[refute_0_45:[bind(X_10,$fot(X_58)),bind(X_25,$fot(X_58))]]) ).
cnf(refute_0_47,plain,
divide(divide(X_8,divide(inverse(divide(X_1,X_1)),X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = X_10,
inference(subst,[],[single_axiom:[bind(A,$fot(X_8)),bind(B,$fot(inverse(divide(X_1,X_1)))),bind(C,$fot(X_10))]]) ).
cnf(refute_0_48,plain,
inverse(A) = divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A),
inference(subst,[],[inverse:[bind(B,$fot(divide(X_1,X_1)))]]) ).
cnf(refute_0_49,plain,
inverse(divide(X_1,X_1)) = divide(divide(X_1,X_1),divide(X_1,X_1)),
inference(subst,[],[inverse:[bind(A,$fot(divide(X_1,X_1))),bind(B,$fot(X_1))]]) ).
cnf(refute_0_50,plain,
( inverse(divide(X_1,X_1)) != divide(divide(X_1,X_1),divide(X_1,X_1))
| divide(divide(X_1,X_1),divide(X_1,X_1)) = inverse(divide(X_1,X_1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(divide(X_1,X_1)))),bind(Y,$fot(divide(divide(X_1,X_1),divide(X_1,X_1))))]]) ).
cnf(refute_0_51,plain,
divide(divide(X_1,X_1),divide(X_1,X_1)) = inverse(divide(X_1,X_1)),
inference(resolve,[$cnf( $equal(inverse(divide(X_1,X_1)),divide(divide(X_1,X_1),divide(X_1,X_1))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( divide(divide(X_1,X_1),divide(X_1,X_1)) != inverse(divide(X_1,X_1))
| inverse(A) != divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)
| inverse(A) = divide(inverse(divide(X_1,X_1)),A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(A),divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)) ),[1,0],$fot(inverse(divide(X_1,X_1)))]]) ).
cnf(refute_0_53,plain,
( inverse(A) != divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)
| inverse(A) = divide(inverse(divide(X_1,X_1)),A) ),
inference(resolve,[$cnf( $equal(divide(divide(X_1,X_1),divide(X_1,X_1)),inverse(divide(X_1,X_1))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
inverse(A) = divide(inverse(divide(X_1,X_1)),A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
inverse(X_10) = divide(inverse(divide(X_1,X_1)),X_10),
inference(subst,[],[refute_0_54:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_56,plain,
( inverse(X_10) != divide(inverse(divide(X_1,X_1)),X_10)
| divide(inverse(divide(X_1,X_1)),X_10) = inverse(X_10) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_10))),bind(Y,$fot(divide(inverse(divide(X_1,X_1)),X_10)))]]) ).
cnf(refute_0_57,plain,
divide(inverse(divide(X_1,X_1)),X_10) = inverse(X_10),
inference(resolve,[$cnf( $equal(inverse(X_10),divide(inverse(divide(X_1,X_1)),X_10)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( divide(divide(X_8,divide(inverse(divide(X_1,X_1)),X_10)),divide(X_8,inverse(divide(X_1,X_1)))) != X_10
| divide(inverse(divide(X_1,X_1)),X_10) != inverse(X_10)
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_8,divide(inverse(divide(X_1,X_1)),X_10)),divide(X_8,inverse(divide(X_1,X_1)))),X_10) ),[0,0,1],$fot(inverse(X_10))]]) ).
cnf(refute_0_59,plain,
( divide(divide(X_8,divide(inverse(divide(X_1,X_1)),X_10)),divide(X_8,inverse(divide(X_1,X_1)))) != X_10
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = X_10 ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(X_1,X_1)),X_10),inverse(X_10)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = X_10,
inference(resolve,[$cnf( $equal(divide(divide(X_8,divide(inverse(divide(X_1,X_1)),X_10)),divide(X_8,inverse(divide(X_1,X_1)))),X_10) )],[refute_0_47,refute_0_59]) ).
cnf(refute_0_61,plain,
divide(X_8,inverse(divide(X_1,X_1))) = multiply(X_8,divide(X_1,X_1)),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_8)),bind(B,$fot(divide(X_1,X_1)))]]) ).
cnf(refute_0_62,plain,
divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))),
introduced(tautology,[refl,[$fot(divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))))]]) ).
cnf(refute_0_63,plain,
( divide(X_8,inverse(divide(X_1,X_1))) != multiply(X_8,divide(X_1,X_1))
| divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) != divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1))))
| divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))),divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1))))) ),[1,1],$fot(multiply(X_8,divide(X_1,X_1)))]]) ).
cnf(refute_0_64,plain,
( divide(X_8,inverse(divide(X_1,X_1))) != multiply(X_8,divide(X_1,X_1))
| divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))),divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1))))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))),
inference(resolve,[$cnf( $equal(divide(X_8,inverse(divide(X_1,X_1))),multiply(X_8,divide(X_1,X_1))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
divide(X_8,inverse(X_10)) = multiply(X_8,X_10),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_8)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_67,plain,
divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))),
introduced(tautology,[refl,[$fot(divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))))]]) ).
cnf(refute_0_68,plain,
( divide(X_8,inverse(X_10)) != multiply(X_8,X_10)
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) != divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1))))
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))),divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1))))) ),[1,0],$fot(multiply(X_8,X_10))]]) ).
cnf(refute_0_69,plain,
( divide(X_8,inverse(X_10)) != multiply(X_8,X_10)
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) ),
inference(resolve,[$cnf( $equal(divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))),divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1))))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))),
inference(resolve,[$cnf( $equal(divide(X_8,inverse(X_10)),multiply(X_8,X_10)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) != divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) != divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1))))
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))))),bind(Y,$fot(divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))))),bind(Z,$fot(divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))))]]) ).
cnf(refute_0_72,plain,
( divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))) != divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) ),
inference(resolve,[$cnf( $equal(divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))),divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1))))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) = divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))),
inference(resolve,[$cnf( $equal(divide(multiply(X_8,X_10),divide(X_8,inverse(divide(X_1,X_1)))),divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))) )],[refute_0_65,refute_0_72]) ).
cnf(refute_0_74,plain,
( divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) != X_10
| divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) != divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))
| divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))),X_10) ),[0],$fot(divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))))]]) ).
cnf(refute_0_75,plain,
( divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))) != X_10
| divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) = X_10 ),
inference(resolve,[$cnf( $equal(divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))),divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) = X_10,
inference(resolve,[$cnf( $equal(divide(divide(X_8,inverse(X_10)),divide(X_8,inverse(divide(X_1,X_1)))),X_10) )],[refute_0_60,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(inverse(divide(divide(B,B),X_13)),divide(B,B)) = X_13,
inference(subst,[],[refute_0_35:[bind(X_10,$fot(X_13)),bind(X_9,$fot(divide(B,B)))]]) ).
cnf(refute_0_78,plain,
inverse(X_13) = divide(divide(B,B),X_13),
inference(subst,[],[inverse:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_79,plain,
( inverse(X_13) != divide(divide(B,B),X_13)
| divide(divide(B,B),X_13) = inverse(X_13) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_13))),bind(Y,$fot(divide(divide(B,B),X_13)))]]) ).
cnf(refute_0_80,plain,
divide(divide(B,B),X_13) = inverse(X_13),
inference(resolve,[$cnf( $equal(inverse(X_13),divide(divide(B,B),X_13)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(inverse(divide(divide(B,B),X_13)),divide(B,B)) != X_13
| divide(divide(B,B),X_13) != inverse(X_13)
| multiply(inverse(inverse(X_13)),divide(B,B)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(divide(B,B),X_13)),divide(B,B)),X_13) ),[0,0,0],$fot(inverse(X_13))]]) ).
cnf(refute_0_82,plain,
( multiply(inverse(divide(divide(B,B),X_13)),divide(B,B)) != X_13
| multiply(inverse(inverse(X_13)),divide(B,B)) = X_13 ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),X_13),inverse(X_13)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(inverse(inverse(X_13)),divide(B,B)) = X_13,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(divide(B,B),X_13)),divide(B,B)),X_13) )],[refute_0_77,refute_0_82]) ).
cnf(refute_0_84,plain,
inverse(divide(divide(X_25,X_25),X_25)) = X_25,
inference(subst,[],[refute_0_41:[bind(X_10,$fot(X_25)),bind(X_9,$fot(X_25))]]) ).
cnf(refute_0_85,plain,
inverse(X_25) = divide(divide(X_25,X_25),X_25),
inference(subst,[],[inverse:[bind(A,$fot(X_25)),bind(B,$fot(X_25))]]) ).
cnf(refute_0_86,plain,
( inverse(X_25) != divide(divide(X_25,X_25),X_25)
| divide(divide(X_25,X_25),X_25) = inverse(X_25) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_25))),bind(Y,$fot(divide(divide(X_25,X_25),X_25)))]]) ).
cnf(refute_0_87,plain,
divide(divide(X_25,X_25),X_25) = inverse(X_25),
inference(resolve,[$cnf( $equal(inverse(X_25),divide(divide(X_25,X_25),X_25)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( divide(divide(X_25,X_25),X_25) != inverse(X_25)
| inverse(divide(divide(X_25,X_25),X_25)) != X_25
| inverse(inverse(X_25)) = X_25 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(X_25,X_25),X_25)),X_25) ),[0,0],$fot(inverse(X_25))]]) ).
cnf(refute_0_89,plain,
( inverse(divide(divide(X_25,X_25),X_25)) != X_25
| inverse(inverse(X_25)) = X_25 ),
inference(resolve,[$cnf( $equal(divide(divide(X_25,X_25),X_25),inverse(X_25)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
inverse(inverse(X_25)) = X_25,
inference(resolve,[$cnf( $equal(inverse(divide(divide(X_25,X_25),X_25)),X_25) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
inverse(inverse(X_13)) = X_13,
inference(subst,[],[refute_0_90:[bind(X_25,$fot(X_13))]]) ).
cnf(refute_0_92,plain,
multiply(inverse(inverse(X_13)),divide(B,B)) = multiply(inverse(inverse(X_13)),divide(B,B)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_13)),divide(B,B)))]]) ).
cnf(refute_0_93,plain,
( multiply(inverse(inverse(X_13)),divide(B,B)) != multiply(inverse(inverse(X_13)),divide(B,B))
| inverse(inverse(X_13)) != X_13
| multiply(inverse(inverse(X_13)),divide(B,B)) = multiply(X_13,divide(B,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_13)),divide(B,B)),multiply(inverse(inverse(X_13)),divide(B,B))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_94,plain,
( inverse(inverse(X_13)) != X_13
| multiply(inverse(inverse(X_13)),divide(B,B)) = multiply(X_13,divide(B,B)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),divide(B,B)),multiply(inverse(inverse(X_13)),divide(B,B))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(inverse(inverse(X_13)),divide(B,B)) = multiply(X_13,divide(B,B)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_13)),X_13) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( multiply(inverse(inverse(X_13)),divide(B,B)) != X_13
| multiply(inverse(inverse(X_13)),divide(B,B)) != multiply(X_13,divide(B,B))
| multiply(X_13,divide(B,B)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_13)),divide(B,B)),X_13) ),[0],$fot(multiply(X_13,divide(B,B)))]]) ).
cnf(refute_0_97,plain,
( multiply(inverse(inverse(X_13)),divide(B,B)) != X_13
| multiply(X_13,divide(B,B)) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),divide(B,B)),multiply(X_13,divide(B,B))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(X_13,divide(B,B)) = X_13,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),divide(B,B)),X_13) )],[refute_0_83,refute_0_97]) ).
cnf(refute_0_99,plain,
multiply(X_8,divide(X_1,X_1)) = X_8,
inference(subst,[],[refute_0_98:[bind(B,$fot(X_1)),bind(X_13,$fot(X_8))]]) ).
cnf(refute_0_100,plain,
divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) = divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))),
introduced(tautology,[refl,[$fot(divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))))]]) ).
cnf(refute_0_101,plain,
( multiply(X_8,divide(X_1,X_1)) != X_8
| divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) != divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))
| divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) = divide(multiply(X_8,X_10),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))),divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))) ),[1,1],$fot(X_8)]]) ).
cnf(refute_0_102,plain,
( multiply(X_8,divide(X_1,X_1)) != X_8
| divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) = divide(multiply(X_8,X_10),X_8) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))),divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1)))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) = divide(multiply(X_8,X_10),X_8),
inference(resolve,[$cnf( $equal(multiply(X_8,divide(X_1,X_1)),X_8) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
( divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) != X_10
| divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) != divide(multiply(X_8,X_10),X_8)
| divide(multiply(X_8,X_10),X_8) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))),X_10) ),[0],$fot(divide(multiply(X_8,X_10),X_8))]]) ).
cnf(refute_0_105,plain,
( divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))) != X_10
| divide(multiply(X_8,X_10),X_8) = X_10 ),
inference(resolve,[$cnf( $equal(divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))),divide(multiply(X_8,X_10),X_8)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
divide(multiply(X_8,X_10),X_8) = X_10,
inference(resolve,[$cnf( $equal(divide(multiply(X_8,X_10),multiply(X_8,divide(X_1,X_1))),X_10) )],[refute_0_76,refute_0_105]) ).
cnf(refute_0_107,plain,
divide(multiply(X_46,multiply(inverse(X_31),X_31)),X_46) = multiply(inverse(X_31),X_31),
inference(subst,[],[refute_0_106:[bind(X_10,$fot(multiply(inverse(X_31),X_31))),bind(X_8,$fot(X_46))]]) ).
cnf(refute_0_108,plain,
multiply(inverse(divide(multiply(inverse(X_31),X_31),X_10)),multiply(inverse(X_31),X_31)) = X_10,
inference(subst,[],[refute_0_35:[bind(X_9,$fot(multiply(inverse(X_31),X_31)))]]) ).
cnf(refute_0_109,plain,
inverse(A) = divide(divide(inverse(X_12),inverse(X_12)),A),
inference(subst,[],[inverse:[bind(B,$fot(inverse(X_12)))]]) ).
cnf(refute_0_110,plain,
multiply(inverse(X_12),X_12) = divide(inverse(X_12),inverse(X_12)),
inference(subst,[],[refute_0_24:[bind(A,$fot(inverse(X_12))),bind(B,$fot(X_12))]]) ).
cnf(refute_0_111,plain,
( multiply(inverse(X_12),X_12) != divide(inverse(X_12),inverse(X_12))
| divide(inverse(X_12),inverse(X_12)) = multiply(inverse(X_12),X_12) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(inverse(X_12),X_12))),bind(Y,$fot(divide(inverse(X_12),inverse(X_12))))]]) ).
cnf(refute_0_112,plain,
divide(inverse(X_12),inverse(X_12)) = multiply(inverse(X_12),X_12),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),X_12),divide(inverse(X_12),inverse(X_12))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( divide(inverse(X_12),inverse(X_12)) != multiply(inverse(X_12),X_12)
| inverse(A) != divide(divide(inverse(X_12),inverse(X_12)),A)
| inverse(A) = divide(multiply(inverse(X_12),X_12),A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(A),divide(divide(inverse(X_12),inverse(X_12)),A)) ),[1,0],$fot(multiply(inverse(X_12),X_12))]]) ).
cnf(refute_0_114,plain,
( inverse(A) != divide(divide(inverse(X_12),inverse(X_12)),A)
| inverse(A) = divide(multiply(inverse(X_12),X_12),A) ),
inference(resolve,[$cnf( $equal(divide(inverse(X_12),inverse(X_12)),multiply(inverse(X_12),X_12)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
inverse(A) = divide(multiply(inverse(X_12),X_12),A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(inverse(X_12),inverse(X_12)),A)) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
inverse(X_10) = divide(multiply(inverse(X_31),X_31),X_10),
inference(subst,[],[refute_0_115:[bind(A,$fot(X_10)),bind(X_12,$fot(X_31))]]) ).
cnf(refute_0_117,plain,
( inverse(X_10) != divide(multiply(inverse(X_31),X_31),X_10)
| divide(multiply(inverse(X_31),X_31),X_10) = inverse(X_10) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_10))),bind(Y,$fot(divide(multiply(inverse(X_31),X_31),X_10)))]]) ).
cnf(refute_0_118,plain,
divide(multiply(inverse(X_31),X_31),X_10) = inverse(X_10),
inference(resolve,[$cnf( $equal(inverse(X_10),divide(multiply(inverse(X_31),X_31),X_10)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( multiply(inverse(divide(multiply(inverse(X_31),X_31),X_10)),multiply(inverse(X_31),X_31)) != X_10
| divide(multiply(inverse(X_31),X_31),X_10) != inverse(X_10)
| multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(multiply(inverse(X_31),X_31),X_10)),multiply(inverse(X_31),X_31)),X_10) ),[0,0,0],$fot(inverse(X_10))]]) ).
cnf(refute_0_120,plain,
( multiply(inverse(divide(multiply(inverse(X_31),X_31),X_10)),multiply(inverse(X_31),X_31)) != X_10
| multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) = X_10 ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(X_31),X_31),X_10),inverse(X_10)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) = X_10,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(multiply(inverse(X_31),X_31),X_10)),multiply(inverse(X_31),X_31)),X_10) )],[refute_0_108,refute_0_120]) ).
cnf(refute_0_122,plain,
inverse(inverse(X_10)) = X_10,
inference(subst,[],[refute_0_90:[bind(X_25,$fot(X_10))]]) ).
cnf(refute_0_123,plain,
multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) = multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)))]]) ).
cnf(refute_0_124,plain,
( multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) != multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31))
| inverse(inverse(X_10)) != X_10
| multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) = multiply(X_10,multiply(inverse(X_31),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)),multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_125,plain,
( inverse(inverse(X_10)) != X_10
| multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) = multiply(X_10,multiply(inverse(X_31),X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)),multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) = multiply(X_10,multiply(inverse(X_31),X_31)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),X_10) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
( multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) != X_10
| multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) != multiply(X_10,multiply(inverse(X_31),X_31))
| multiply(X_10,multiply(inverse(X_31),X_31)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)),X_10) ),[0],$fot(multiply(X_10,multiply(inverse(X_31),X_31)))]]) ).
cnf(refute_0_128,plain,
( multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)) != X_10
| multiply(X_10,multiply(inverse(X_31),X_31)) = X_10 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)),multiply(X_10,multiply(inverse(X_31),X_31))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
multiply(X_10,multiply(inverse(X_31),X_31)) = X_10,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_10)),multiply(inverse(X_31),X_31)),X_10) )],[refute_0_121,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(X_46,multiply(inverse(X_31),X_31)) = X_46,
inference(subst,[],[refute_0_129:[bind(X_10,$fot(X_46))]]) ).
cnf(refute_0_131,plain,
( multiply(X_46,multiply(inverse(X_31),X_31)) != X_46
| divide(multiply(X_46,multiply(inverse(X_31),X_31)),X_46) != multiply(inverse(X_31),X_31)
| divide(X_46,X_46) = multiply(inverse(X_31),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(X_46,multiply(inverse(X_31),X_31)),X_46),multiply(inverse(X_31),X_31)) ),[0,0],$fot(X_46)]]) ).
cnf(refute_0_132,plain,
( divide(multiply(X_46,multiply(inverse(X_31),X_31)),X_46) != multiply(inverse(X_31),X_31)
| divide(X_46,X_46) = multiply(inverse(X_31),X_31) ),
inference(resolve,[$cnf( $equal(multiply(X_46,multiply(inverse(X_31),X_31)),X_46) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
divide(X_46,X_46) = multiply(inverse(X_31),X_31),
inference(resolve,[$cnf( $equal(divide(multiply(X_46,multiply(inverse(X_31),X_31)),X_46),multiply(inverse(X_31),X_31)) )],[refute_0_107,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(inverse(divide(multiply(X_10,X_45),X_10)),multiply(X_10,X_45)) = X_10,
inference(subst,[],[refute_0_35:[bind(X_9,$fot(multiply(X_10,X_45)))]]) ).
cnf(refute_0_135,plain,
divide(multiply(X_10,X_45),X_10) = X_45,
inference(subst,[],[refute_0_106:[bind(X_10,$fot(X_45)),bind(X_8,$fot(X_10))]]) ).
cnf(refute_0_136,plain,
( multiply(inverse(divide(multiply(X_10,X_45),X_10)),multiply(X_10,X_45)) != X_10
| divide(multiply(X_10,X_45),X_10) != X_45
| multiply(inverse(X_45),multiply(X_10,X_45)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(multiply(X_10,X_45),X_10)),multiply(X_10,X_45)),X_10) ),[0,0,0],$fot(X_45)]]) ).
cnf(refute_0_137,plain,
( multiply(inverse(divide(multiply(X_10,X_45),X_10)),multiply(X_10,X_45)) != X_10
| multiply(inverse(X_45),multiply(X_10,X_45)) = X_10 ),
inference(resolve,[$cnf( $equal(divide(multiply(X_10,X_45),X_10),X_45) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(inverse(X_45),multiply(X_10,X_45)) = X_10,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(multiply(X_10,X_45),X_10)),multiply(X_10,X_45)),X_10) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(inverse(X_48),multiply(inverse(divide(X_48,X_10)),X_48)) = inverse(divide(X_48,X_10)),
inference(subst,[],[refute_0_138:[bind(X_10,$fot(inverse(divide(X_48,X_10)))),bind(X_45,$fot(X_48))]]) ).
cnf(refute_0_140,plain,
multiply(inverse(divide(X_48,X_10)),X_48) = X_10,
inference(subst,[],[refute_0_35:[bind(X_9,$fot(X_48))]]) ).
cnf(refute_0_141,plain,
( multiply(inverse(X_48),multiply(inverse(divide(X_48,X_10)),X_48)) != inverse(divide(X_48,X_10))
| multiply(inverse(divide(X_48,X_10)),X_48) != X_10
| multiply(inverse(X_48),X_10) = inverse(divide(X_48,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_48),multiply(inverse(divide(X_48,X_10)),X_48)),inverse(divide(X_48,X_10))) ),[0,1],$fot(X_10)]]) ).
cnf(refute_0_142,plain,
( multiply(inverse(X_48),multiply(inverse(divide(X_48,X_10)),X_48)) != inverse(divide(X_48,X_10))
| multiply(inverse(X_48),X_10) = inverse(divide(X_48,X_10)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_48,X_10)),X_48),X_10) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(inverse(X_48),X_10) = inverse(divide(X_48,X_10)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_48),multiply(inverse(divide(X_48,X_10)),X_48)),inverse(divide(X_48,X_10))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
multiply(inverse(X_31),X_31) = inverse(divide(X_31,X_31)),
inference(subst,[],[refute_0_143:[bind(X_10,$fot(X_31)),bind(X_48,$fot(X_31))]]) ).
cnf(refute_0_145,plain,
( multiply(inverse(X_31),X_31) != inverse(divide(X_31,X_31))
| divide(X_46,X_46) != multiply(inverse(X_31),X_31)
| divide(X_46,X_46) = inverse(divide(X_31,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_46,X_46),multiply(inverse(X_31),X_31)) ),[1],$fot(inverse(divide(X_31,X_31)))]]) ).
cnf(refute_0_146,plain,
( divide(X_46,X_46) != multiply(inverse(X_31),X_31)
| divide(X_46,X_46) = inverse(divide(X_31,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_31),X_31),inverse(divide(X_31,X_31))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
divide(X_46,X_46) = inverse(divide(X_31,X_31)),
inference(resolve,[$cnf( $equal(divide(X_46,X_46),multiply(inverse(X_31),X_31)) )],[refute_0_133,refute_0_146]) ).
cnf(refute_0_148,plain,
divide(X_58,X_58) = inverse(divide(X_31,X_31)),
inference(subst,[],[refute_0_147:[bind(X_46,$fot(X_58))]]) ).
cnf(refute_0_149,plain,
( multiply(X_58,divide(X_58,X_58)) != X_58
| divide(X_58,X_58) != inverse(divide(X_31,X_31))
| multiply(X_58,inverse(divide(X_31,X_31))) = X_58 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_58,divide(X_58,X_58)),X_58) ),[0,1],$fot(inverse(divide(X_31,X_31)))]]) ).
cnf(refute_0_150,plain,
( multiply(X_58,divide(X_58,X_58)) != X_58
| multiply(X_58,inverse(divide(X_31,X_31))) = X_58 ),
inference(resolve,[$cnf( $equal(divide(X_58,X_58),inverse(divide(X_31,X_31))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(X_58,inverse(divide(X_31,X_31))) = X_58,
inference(resolve,[$cnf( $equal(multiply(X_58,divide(X_58,X_58)),X_58) )],[refute_0_46,refute_0_150]) ).
cnf(refute_0_152,plain,
multiply(divide(A,B),divide(divide(A,divide(B,C)),divide(A,B))) = divide(A,divide(B,C)),
inference(subst,[],[refute_0_45:[bind(X_10,$fot(divide(A,divide(B,C)))),bind(X_25,$fot(divide(A,B)))]]) ).
cnf(refute_0_153,plain,
( multiply(divide(A,B),divide(divide(A,divide(B,C)),divide(A,B))) != divide(A,divide(B,C))
| divide(divide(A,divide(B,C)),divide(A,B)) != C
| multiply(divide(A,B),C) = divide(A,divide(B,C)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(A,B),divide(divide(A,divide(B,C)),divide(A,B))),divide(A,divide(B,C))) ),[0,1],$fot(C)]]) ).
cnf(refute_0_154,plain,
( multiply(divide(A,B),divide(divide(A,divide(B,C)),divide(A,B))) != divide(A,divide(B,C))
| multiply(divide(A,B),C) = divide(A,divide(B,C)) ),
inference(resolve,[$cnf( $equal(divide(divide(A,divide(B,C)),divide(A,B)),C) )],[single_axiom,refute_0_153]) ).
cnf(refute_0_155,plain,
multiply(divide(A,B),C) = divide(A,divide(B,C)),
inference(resolve,[$cnf( $equal(multiply(divide(A,B),divide(divide(A,divide(B,C)),divide(A,B))),divide(A,divide(B,C))) )],[refute_0_152,refute_0_154]) ).
cnf(refute_0_156,plain,
( multiply(divide(A,B),C) != divide(A,divide(B,C))
| divide(A,divide(B,C)) = multiply(divide(A,B),C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(divide(A,B),C))),bind(Y,$fot(divide(A,divide(B,C))))]]) ).
cnf(refute_0_157,plain,
divide(A,divide(B,C)) = multiply(divide(A,B),C),
inference(resolve,[$cnf( $equal(multiply(divide(A,B),C),divide(A,divide(B,C))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
divide(X_58,divide(X_31,X_31)) = multiply(divide(X_58,X_31),X_31),
inference(subst,[],[refute_0_157:[bind(A,$fot(X_58)),bind(B,$fot(X_31)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_159,plain,
multiply(A,inverse(X_27)) = divide(A,inverse(inverse(X_27))),
inference(subst,[],[refute_0_24:[bind(B,$fot(inverse(X_27)))]]) ).
cnf(refute_0_160,plain,
inverse(inverse(X_27)) = X_27,
inference(subst,[],[refute_0_90:[bind(X_25,$fot(X_27))]]) ).
cnf(refute_0_161,plain,
( multiply(A,inverse(X_27)) != divide(A,inverse(inverse(X_27)))
| inverse(inverse(X_27)) != X_27
| multiply(A,inverse(X_27)) = divide(A,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,inverse(X_27)),divide(A,inverse(inverse(X_27)))) ),[1,1],$fot(X_27)]]) ).
cnf(refute_0_162,plain,
( multiply(A,inverse(X_27)) != divide(A,inverse(inverse(X_27)))
| multiply(A,inverse(X_27)) = divide(A,X_27) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_27)),X_27) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
multiply(A,inverse(X_27)) = divide(A,X_27),
inference(resolve,[$cnf( $equal(multiply(A,inverse(X_27)),divide(A,inverse(inverse(X_27)))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(X_58,inverse(divide(X_31,X_31))) = divide(X_58,divide(X_31,X_31)),
inference(subst,[],[refute_0_163:[bind(A,$fot(X_58)),bind(X_27,$fot(divide(X_31,X_31)))]]) ).
cnf(refute_0_165,plain,
( multiply(X_58,inverse(divide(X_31,X_31))) != divide(X_58,divide(X_31,X_31))
| divide(X_58,divide(X_31,X_31)) != multiply(divide(X_58,X_31),X_31)
| multiply(X_58,inverse(divide(X_31,X_31))) = multiply(divide(X_58,X_31),X_31) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(multiply(X_58,inverse(divide(X_31,X_31))))),bind(Y,$fot(divide(X_58,divide(X_31,X_31)))),bind(Z,$fot(multiply(divide(X_58,X_31),X_31)))]]) ).
cnf(refute_0_166,plain,
( divide(X_58,divide(X_31,X_31)) != multiply(divide(X_58,X_31),X_31)
| multiply(X_58,inverse(divide(X_31,X_31))) = multiply(divide(X_58,X_31),X_31) ),
inference(resolve,[$cnf( $equal(multiply(X_58,inverse(divide(X_31,X_31))),divide(X_58,divide(X_31,X_31))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
multiply(X_58,inverse(divide(X_31,X_31))) = multiply(divide(X_58,X_31),X_31),
inference(resolve,[$cnf( $equal(divide(X_58,divide(X_31,X_31)),multiply(divide(X_58,X_31),X_31)) )],[refute_0_158,refute_0_166]) ).
cnf(refute_0_168,plain,
( multiply(X_58,inverse(divide(X_31,X_31))) != X_58
| multiply(X_58,inverse(divide(X_31,X_31))) != multiply(divide(X_58,X_31),X_31)
| multiply(divide(X_58,X_31),X_31) = X_58 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_58,inverse(divide(X_31,X_31))),X_58) ),[0],$fot(multiply(divide(X_58,X_31),X_31))]]) ).
cnf(refute_0_169,plain,
( multiply(X_58,inverse(divide(X_31,X_31))) != X_58
| multiply(divide(X_58,X_31),X_31) = X_58 ),
inference(resolve,[$cnf( $equal(multiply(X_58,inverse(divide(X_31,X_31))),multiply(divide(X_58,X_31),X_31)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(divide(X_58,X_31),X_31) = X_58,
inference(resolve,[$cnf( $equal(multiply(X_58,inverse(divide(X_31,X_31))),X_58) )],[refute_0_151,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(divide(multiply(X_59,X_10),X_59),X_59) = multiply(X_59,X_10),
inference(subst,[],[refute_0_170:[bind(X_31,$fot(X_59)),bind(X_58,$fot(multiply(X_59,X_10)))]]) ).
cnf(refute_0_172,plain,
divide(multiply(X_59,X_10),X_59) = X_10,
inference(subst,[],[refute_0_106:[bind(X_8,$fot(X_59))]]) ).
cnf(refute_0_173,plain,
( multiply(divide(multiply(X_59,X_10),X_59),X_59) != multiply(X_59,X_10)
| divide(multiply(X_59,X_10),X_59) != X_10
| multiply(X_10,X_59) = multiply(X_59,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(multiply(X_59,X_10),X_59),X_59),multiply(X_59,X_10)) ),[0,0],$fot(X_10)]]) ).
cnf(refute_0_174,plain,
( multiply(divide(multiply(X_59,X_10),X_59),X_59) != multiply(X_59,X_10)
| multiply(X_10,X_59) = multiply(X_59,X_10) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_59,X_10),X_59),X_10) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
multiply(X_10,X_59) = multiply(X_59,X_10),
inference(resolve,[$cnf( $equal(multiply(divide(multiply(X_59,X_10),X_59),X_59),multiply(X_59,X_10)) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
( multiply(X_10,X_59) != multiply(X_59,X_10)
| multiply(X_59,X_10) = multiply(X_10,X_59) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(X_10,X_59))),bind(Y,$fot(multiply(X_59,X_10)))]]) ).
cnf(refute_0_177,plain,
multiply(X_59,X_10) = multiply(X_10,X_59),
inference(resolve,[$cnf( $equal(multiply(X_10,X_59),multiply(X_59,X_10)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
multiply(b,a) = multiply(a,b),
inference(subst,[],[refute_0_177:[bind(X_10,$fot(a)),bind(X_59,$fot(b))]]) ).
cnf(refute_0_179,plain,
( multiply(a,b) != multiply(a,b)
| multiply(b,a) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,b),multiply(b,a)) ),[1],$fot(multiply(a,b))]]) ).
cnf(refute_0_180,plain,
( multiply(a,b) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
multiply(a,b) != multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(b,a)) )],[refute_0_180,prove_these_axioms_4]) ).
cnf(refute_0_182,plain,
multiply(a,b) = multiply(a,b),
introduced(tautology,[refl,[$fot(multiply(a,b))]]) ).
cnf(refute_0_183,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(a,b)) )],[refute_0_182,refute_0_181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP532-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.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 23:45:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41
% 0.18/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.44
%------------------------------------------------------------------------------