TSTP Solution File: GRP522-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 10:42:07 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 49
% Syntax : Number of clauses : 183 ( 98 unt; 0 nHn; 85 RR)
% Number of literals : 306 ( 305 equ; 126 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 416 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(A,divide(B,divide(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_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
inverse(inverse(X_12)) = divide(divide(B,B),inverse(X_12)),
inference(subst,[],[inverse:[bind(A,$fot(inverse(X_12)))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_5,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_4]) ).
cnf(refute_0_6,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_5:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_7,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_8,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_9,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_12,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(divide(B,B),X_12) = divide(divide(B,B),inverse(X_12)),
inference(subst,[],[refute_0_13:[bind(A,$fot(divide(B,B))),bind(B,$fot(X_12))]]) ).
cnf(refute_0_15,plain,
( multiply(divide(B,B),X_12) != divide(divide(B,B),inverse(X_12))
| divide(divide(B,B),inverse(X_12)) = multiply(divide(B,B),X_12) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(divide(B,B),X_12))),bind(Y,$fot(divide(divide(B,B),inverse(X_12))))]]) ).
cnf(refute_0_16,plain,
divide(divide(B,B),inverse(X_12)) = multiply(divide(B,B),X_12),
inference(resolve,[$cnf( $equal(multiply(divide(B,B),X_12),divide(divide(B,B),inverse(X_12))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( divide(divide(B,B),inverse(X_12)) != multiply(divide(B,B),X_12)
| inverse(inverse(X_12)) != divide(divide(B,B),inverse(X_12))
| inverse(inverse(X_12)) = multiply(divide(B,B),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_12)),divide(divide(B,B),inverse(X_12))) ),[1],$fot(multiply(divide(B,B),X_12))]]) ).
cnf(refute_0_18,plain,
( inverse(inverse(X_12)) != divide(divide(B,B),inverse(X_12))
| inverse(inverse(X_12)) = multiply(divide(B,B),X_12) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),inverse(X_12)),multiply(divide(B,B),X_12)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(inverse(X_12)) = multiply(divide(B,B),X_12),
inference(resolve,[$cnf( $equal(inverse(inverse(X_12)),divide(divide(B,B),inverse(X_12))) )],[refute_0_0,refute_0_18]) ).
cnf(refute_0_20,plain,
inverse(inverse(X_14)) = multiply(divide(inverse(B),inverse(B)),X_14),
inference(subst,[],[refute_0_19:[bind(B,$fot(inverse(B))),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_21,plain,
multiply(inverse(B),B) = divide(inverse(B),inverse(B)),
inference(subst,[],[refute_0_13:[bind(A,$fot(inverse(B)))]]) ).
cnf(refute_0_22,plain,
( multiply(inverse(B),B) != divide(inverse(B),inverse(B))
| divide(inverse(B),inverse(B)) = multiply(inverse(B),B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(inverse(B),B))),bind(Y,$fot(divide(inverse(B),inverse(B))))]]) ).
cnf(refute_0_23,plain,
divide(inverse(B),inverse(B)) = multiply(inverse(B),B),
inference(resolve,[$cnf( $equal(multiply(inverse(B),B),divide(inverse(B),inverse(B))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( divide(inverse(B),inverse(B)) != multiply(inverse(B),B)
| inverse(inverse(X_14)) != multiply(divide(inverse(B),inverse(B)),X_14)
| inverse(inverse(X_14)) = multiply(multiply(inverse(B),B),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_14)),multiply(divide(inverse(B),inverse(B)),X_14)) ),[1,0],$fot(multiply(inverse(B),B))]]) ).
cnf(refute_0_25,plain,
( inverse(inverse(X_14)) != multiply(divide(inverse(B),inverse(B)),X_14)
| inverse(inverse(X_14)) = multiply(multiply(inverse(B),B),X_14) ),
inference(resolve,[$cnf( $equal(divide(inverse(B),inverse(B)),multiply(inverse(B),B)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
inverse(inverse(X_14)) = multiply(multiply(inverse(B),B),X_14),
inference(resolve,[$cnf( $equal(inverse(inverse(X_14)),multiply(divide(inverse(B),inverse(B)),X_14)) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
( inverse(inverse(X_14)) != multiply(multiply(inverse(B),B),X_14)
| multiply(multiply(inverse(B),B),X_14) = inverse(inverse(X_14)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(inverse(X_14)))),bind(Y,$fot(multiply(multiply(inverse(B),B),X_14)))]]) ).
cnf(refute_0_28,plain,
multiply(multiply(inverse(B),B),X_14) = inverse(inverse(X_14)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_14)),multiply(multiply(inverse(B),B),X_14)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(multiply(inverse(b2),b2),a2) = inverse(inverse(a2)),
inference(subst,[],[refute_0_28:[bind(B,$fot(b2)),bind(X_14,$fot(a2))]]) ).
cnf(refute_0_30,plain,
( multiply(multiply(inverse(b2),b2),a2) != inverse(inverse(a2))
| inverse(inverse(a2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(inverse(inverse(a2)))]]) ).
cnf(refute_0_31,plain,
( inverse(inverse(a2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),inverse(inverse(a2))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
inverse(inverse(a2)) != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_31,prove_these_axioms_2]) ).
cnf(refute_0_33,plain,
inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) = divide(divide(B,B),divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),
inference(subst,[],[inverse:[bind(A,$fot(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))))]]) ).
cnf(refute_0_34,plain,
divide(divide(B,B),divide(X_9,divide(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,$fot(X_10))]]) ).
cnf(refute_0_35,plain,
( divide(divide(B,B),divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) != X_10
| inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) != divide(divide(B,B),divide(X_9,divide(X_10,divide(divide(B,B),X_9))))
| inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),divide(divide(B,B),divide(X_9,divide(X_10,divide(divide(B,B),X_9))))) ),[1],$fot(X_10)]]) ).
cnf(refute_0_36,plain,
( inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) != divide(divide(B,B),divide(X_9,divide(X_10,divide(divide(B,B),X_9))))
| inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) = X_10 ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),X_10) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) = X_10,
inference(resolve,[$cnf( $equal(inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),divide(divide(B,B),divide(X_9,divide(X_10,divide(divide(B,B),X_9))))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_39,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_13,refute_0_38]) ).
cnf(refute_0_40,plain,
divide(X_10,inverse(X_9)) = multiply(X_10,X_9),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_10)),bind(B,$fot(X_9))]]) ).
cnf(refute_0_41,plain,
divide(divide(B,B),X_9) = inverse(X_9),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_9))]]) ).
cnf(refute_0_42,plain,
divide(X_10,divide(divide(B,B),X_9)) = divide(X_10,divide(divide(B,B),X_9)),
introduced(tautology,[refl,[$fot(divide(X_10,divide(divide(B,B),X_9)))]]) ).
cnf(refute_0_43,plain,
( divide(X_10,divide(divide(B,B),X_9)) != divide(X_10,divide(divide(B,B),X_9))
| divide(divide(B,B),X_9) != inverse(X_9)
| divide(X_10,divide(divide(B,B),X_9)) = divide(X_10,inverse(X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_10,divide(divide(B,B),X_9)),divide(X_10,divide(divide(B,B),X_9))) ),[1,1],$fot(inverse(X_9))]]) ).
cnf(refute_0_44,plain,
( divide(divide(B,B),X_9) != inverse(X_9)
| divide(X_10,divide(divide(B,B),X_9)) = divide(X_10,inverse(X_9)) ),
inference(resolve,[$cnf( $equal(divide(X_10,divide(divide(B,B),X_9)),divide(X_10,divide(divide(B,B),X_9))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
divide(X_10,divide(divide(B,B),X_9)) = divide(X_10,inverse(X_9)),
inference(resolve,[$cnf( $equal(divide(divide(B,B),X_9),inverse(X_9)) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_47,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_3,refute_0_46]) ).
cnf(refute_0_48,plain,
( divide(X_10,divide(divide(B,B),X_9)) != divide(X_10,inverse(X_9))
| divide(X_10,inverse(X_9)) != multiply(X_10,X_9)
| divide(X_10,divide(divide(B,B),X_9)) = multiply(X_10,X_9) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(divide(X_10,divide(divide(B,B),X_9)))),bind(Y,$fot(divide(X_10,inverse(X_9)))),bind(Z,$fot(multiply(X_10,X_9)))]]) ).
cnf(refute_0_49,plain,
( divide(X_10,inverse(X_9)) != multiply(X_10,X_9)
| divide(X_10,divide(divide(B,B),X_9)) = multiply(X_10,X_9) ),
inference(resolve,[$cnf( $equal(divide(X_10,divide(divide(B,B),X_9)),divide(X_10,inverse(X_9))) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
divide(X_10,divide(divide(B,B),X_9)) = multiply(X_10,X_9),
inference(resolve,[$cnf( $equal(divide(X_10,inverse(X_9)),multiply(X_10,X_9)) )],[refute_0_40,refute_0_49]) ).
cnf(refute_0_51,plain,
divide(X_9,divide(X_10,divide(divide(B,B),X_9))) = divide(X_9,divide(X_10,divide(divide(B,B),X_9))),
introduced(tautology,[refl,[$fot(divide(X_9,divide(X_10,divide(divide(B,B),X_9))))]]) ).
cnf(refute_0_52,plain,
( divide(X_10,divide(divide(B,B),X_9)) != multiply(X_10,X_9)
| divide(X_9,divide(X_10,divide(divide(B,B),X_9))) != divide(X_9,divide(X_10,divide(divide(B,B),X_9)))
| divide(X_9,divide(X_10,divide(divide(B,B),X_9))) = divide(X_9,multiply(X_10,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_9,divide(X_10,divide(divide(B,B),X_9))),divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) ),[1,1],$fot(multiply(X_10,X_9))]]) ).
cnf(refute_0_53,plain,
( divide(X_10,divide(divide(B,B),X_9)) != multiply(X_10,X_9)
| divide(X_9,divide(X_10,divide(divide(B,B),X_9))) = divide(X_9,multiply(X_10,X_9)) ),
inference(resolve,[$cnf( $equal(divide(X_9,divide(X_10,divide(divide(B,B),X_9))),divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
divide(X_9,divide(X_10,divide(divide(B,B),X_9))) = divide(X_9,multiply(X_10,X_9)),
inference(resolve,[$cnf( $equal(divide(X_10,divide(divide(B,B),X_9)),multiply(X_10,X_9)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) = inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),
introduced(tautology,[refl,[$fot(inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))))]]) ).
cnf(refute_0_56,plain,
( divide(X_9,divide(X_10,divide(divide(B,B),X_9))) != divide(X_9,multiply(X_10,X_9))
| inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) != inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9))))
| inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) = inverse(divide(X_9,multiply(X_10,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9))))) ),[1,0],$fot(divide(X_9,multiply(X_10,X_9)))]]) ).
cnf(refute_0_57,plain,
( divide(X_9,divide(X_10,divide(divide(B,B),X_9))) != divide(X_9,multiply(X_10,X_9))
| inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) = inverse(divide(X_9,multiply(X_10,X_9))) ),
inference(resolve,[$cnf( $equal(inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9))))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) = inverse(divide(X_9,multiply(X_10,X_9))),
inference(resolve,[$cnf( $equal(divide(X_9,divide(X_10,divide(divide(B,B),X_9))),divide(X_9,multiply(X_10,X_9))) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
( inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) != X_10
| inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) != inverse(divide(X_9,multiply(X_10,X_9)))
| inverse(divide(X_9,multiply(X_10,X_9))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),X_10) ),[0],$fot(inverse(divide(X_9,multiply(X_10,X_9))))]]) ).
cnf(refute_0_60,plain,
( inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))) != X_10
| inverse(divide(X_9,multiply(X_10,X_9))) = X_10 ),
inference(resolve,[$cnf( $equal(inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),inverse(divide(X_9,multiply(X_10,X_9)))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
inverse(divide(X_9,multiply(X_10,X_9))) = X_10,
inference(resolve,[$cnf( $equal(inverse(divide(X_9,divide(X_10,divide(divide(B,B),X_9)))),X_10) )],[refute_0_37,refute_0_60]) ).
cnf(refute_0_62,plain,
inverse(divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12)))) = X_35,
inference(subst,[],[refute_0_61:[bind(X_10,$fot(X_35)),bind(X_9,$fot(multiply(inverse(X_12),X_12)))]]) ).
cnf(refute_0_63,plain,
inverse(A) = divide(divide(inverse(X_12),inverse(X_12)),A),
inference(subst,[],[inverse:[bind(B,$fot(inverse(X_12)))]]) ).
cnf(refute_0_64,plain,
multiply(inverse(X_12),X_12) = divide(inverse(X_12),inverse(X_12)),
inference(subst,[],[refute_0_13:[bind(A,$fot(inverse(X_12))),bind(B,$fot(X_12))]]) ).
cnf(refute_0_65,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_3:[bind(X,$fot(multiply(inverse(X_12),X_12))),bind(Y,$fot(divide(inverse(X_12),inverse(X_12))))]]) ).
cnf(refute_0_66,plain,
divide(inverse(X_12),inverse(X_12)) = multiply(inverse(X_12),X_12),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),X_12),divide(inverse(X_12),inverse(X_12))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( divide(inverse(X_12),inverse(X_12)) != multiply(inverse(X_12),X_12)
| inverse(A) != divide(divide(inverse(X_12),inverse(X_12)),A)
| inverse(A) = divide(multiply(inverse(X_12),X_12),A) ),
introduced(tautology,[equality,[$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_68,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( $equal(divide(inverse(X_12),inverse(X_12)),multiply(inverse(X_12),X_12)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
inverse(A) = divide(multiply(inverse(X_12),X_12),A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(inverse(X_12),inverse(X_12)),A)) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
inverse(multiply(X_35,multiply(inverse(X_12),X_12))) = divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12))),
inference(subst,[],[refute_0_69:[bind(A,$fot(multiply(X_35,multiply(inverse(X_12),X_12))))]]) ).
cnf(refute_0_71,plain,
( inverse(multiply(X_35,multiply(inverse(X_12),X_12))) != divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12)))
| divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12))) = inverse(multiply(X_35,multiply(inverse(X_12),X_12))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(multiply(X_35,multiply(inverse(X_12),X_12))))),bind(Y,$fot(divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12)))))]]) ).
cnf(refute_0_72,plain,
divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12))) = inverse(multiply(X_35,multiply(inverse(X_12),X_12))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_35,multiply(inverse(X_12),X_12))),divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12))) != inverse(multiply(X_35,multiply(inverse(X_12),X_12)))
| inverse(divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12)))) != X_35
| inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) = X_35 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12)))),X_35) ),[0,0],$fot(inverse(multiply(X_35,multiply(inverse(X_12),X_12))))]]) ).
cnf(refute_0_74,plain,
( inverse(divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12)))) != X_35
| inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) = X_35 ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12))),inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) = X_35,
inference(resolve,[$cnf( $equal(inverse(divide(multiply(inverse(X_12),X_12),multiply(X_35,multiply(inverse(X_12),X_12)))),X_35) )],[refute_0_62,refute_0_74]) ).
cnf(refute_0_76,plain,
divide(B,divide(B,divide(C,divide(B,B)))) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(B))]]) ).
cnf(refute_0_77,plain,
divide(A,divide(B,divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)))) = inverse(multiply(inverse(X_22),X_22)),
inference(subst,[],[single_axiom:[bind(C,$fot(inverse(multiply(inverse(X_22),X_22))))]]) ).
cnf(refute_0_78,plain,
inverse(A) = divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A),
inference(subst,[],[inverse:[bind(B,$fot(divide(X_1,X_1)))]]) ).
cnf(refute_0_79,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_80,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_3:[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_81,plain,
divide(divide(X_1,X_1),divide(X_1,X_1)) = inverse(divide(X_1,X_1)),
inference(resolve,[$cnf( $equal(inverse(divide(X_1,X_1)),divide(divide(X_1,X_1),divide(X_1,X_1))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( divide(divide(X_1,X_1),divide(X_1,X_1)) != inverse(divide(X_1,X_1))
| inverse(A) != divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)
| inverse(A) = divide(inverse(divide(X_1,X_1)),A) ),
introduced(tautology,[equality,[$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_83,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( $equal(divide(divide(X_1,X_1),divide(X_1,X_1)),inverse(divide(X_1,X_1))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
inverse(A) = divide(inverse(divide(X_1,X_1)),A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
inverse(A) = divide(inverse(divide(inverse(X_12),inverse(X_12))),A),
inference(subst,[],[refute_0_84:[bind(X_1,$fot(inverse(X_12)))]]) ).
cnf(refute_0_86,plain,
( divide(inverse(X_12),inverse(X_12)) != multiply(inverse(X_12),X_12)
| inverse(A) != divide(inverse(divide(inverse(X_12),inverse(X_12))),A)
| inverse(A) = divide(inverse(multiply(inverse(X_12),X_12)),A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(A),divide(inverse(divide(inverse(X_12),inverse(X_12))),A)) ),[1,0,0],$fot(multiply(inverse(X_12),X_12))]]) ).
cnf(refute_0_87,plain,
( inverse(A) != divide(inverse(divide(inverse(X_12),inverse(X_12))),A)
| inverse(A) = divide(inverse(multiply(inverse(X_12),X_12)),A) ),
inference(resolve,[$cnf( $equal(divide(inverse(X_12),inverse(X_12)),multiply(inverse(X_12),X_12)) )],[refute_0_66,refute_0_86]) ).
cnf(refute_0_88,plain,
inverse(A) = divide(inverse(multiply(inverse(X_12),X_12)),A),
inference(resolve,[$cnf( $equal(inverse(A),divide(inverse(divide(inverse(X_12),inverse(X_12))),A)) )],[refute_0_85,refute_0_87]) ).
cnf(refute_0_89,plain,
inverse(divide(A,B)) = divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)),
inference(subst,[],[refute_0_88:[bind(A,$fot(divide(A,B))),bind(X_12,$fot(X_22))]]) ).
cnf(refute_0_90,plain,
( inverse(divide(A,B)) != divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B))
| divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)) = inverse(divide(A,B)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(divide(A,B)))),bind(Y,$fot(divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B))))]]) ).
cnf(refute_0_91,plain,
divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)) = inverse(divide(A,B)),
inference(resolve,[$cnf( $equal(inverse(divide(A,B)),divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( divide(A,divide(B,divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)))) != inverse(multiply(inverse(X_22),X_22))
| divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)) != inverse(divide(A,B))
| divide(A,divide(B,inverse(divide(A,B)))) = inverse(multiply(inverse(X_22),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(B,divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)))),inverse(multiply(inverse(X_22),X_22))) ),[0,1,1],$fot(inverse(divide(A,B)))]]) ).
cnf(refute_0_93,plain,
( divide(A,divide(B,divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)))) != inverse(multiply(inverse(X_22),X_22))
| divide(A,divide(B,inverse(divide(A,B)))) = inverse(multiply(inverse(X_22),X_22)) ),
inference(resolve,[$cnf( $equal(divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)),inverse(divide(A,B))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
divide(A,divide(B,inverse(divide(A,B)))) = inverse(multiply(inverse(X_22),X_22)),
inference(resolve,[$cnf( $equal(divide(A,divide(B,divide(inverse(multiply(inverse(X_22),X_22)),divide(A,B)))),inverse(multiply(inverse(X_22),X_22))) )],[refute_0_77,refute_0_93]) ).
cnf(refute_0_95,plain,
divide(X_8,divide(X_9,divide(divide(B,B),divide(X_8,X_9)))) = divide(B,B),
inference(subst,[],[single_axiom:[bind(A,$fot(X_8)),bind(B,$fot(X_9)),bind(C,$fot(divide(B,B)))]]) ).
cnf(refute_0_96,plain,
inverse(divide(X_8,X_9)) = divide(divide(B,B),divide(X_8,X_9)),
inference(subst,[],[inverse:[bind(A,$fot(divide(X_8,X_9)))]]) ).
cnf(refute_0_97,plain,
( inverse(divide(X_8,X_9)) != divide(divide(B,B),divide(X_8,X_9))
| divide(divide(B,B),divide(X_8,X_9)) = inverse(divide(X_8,X_9)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(divide(X_8,X_9)))),bind(Y,$fot(divide(divide(B,B),divide(X_8,X_9))))]]) ).
cnf(refute_0_98,plain,
divide(divide(B,B),divide(X_8,X_9)) = inverse(divide(X_8,X_9)),
inference(resolve,[$cnf( $equal(inverse(divide(X_8,X_9)),divide(divide(B,B),divide(X_8,X_9))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( divide(X_8,divide(X_9,divide(divide(B,B),divide(X_8,X_9)))) != divide(B,B)
| divide(divide(B,B),divide(X_8,X_9)) != inverse(divide(X_8,X_9))
| divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) = divide(B,B) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_8,divide(X_9,divide(divide(B,B),divide(X_8,X_9)))),divide(B,B)) ),[0,1,1],$fot(inverse(divide(X_8,X_9)))]]) ).
cnf(refute_0_100,plain,
( divide(X_8,divide(X_9,divide(divide(B,B),divide(X_8,X_9)))) != divide(B,B)
| divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) = divide(B,B) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),divide(X_8,X_9)),inverse(divide(X_8,X_9))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) = divide(B,B),
inference(resolve,[$cnf( $equal(divide(X_8,divide(X_9,divide(divide(B,B),divide(X_8,X_9)))),divide(B,B)) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
divide(X_9,inverse(divide(X_8,X_9))) = multiply(X_9,divide(X_8,X_9)),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_9)),bind(B,$fot(divide(X_8,X_9)))]]) ).
cnf(refute_0_103,plain,
divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) = divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))),
introduced(tautology,[refl,[$fot(divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))))]]) ).
cnf(refute_0_104,plain,
( divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) != divide(X_8,divide(X_9,inverse(divide(X_8,X_9))))
| divide(X_9,inverse(divide(X_8,X_9))) != multiply(X_9,divide(X_8,X_9))
| divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) = divide(X_8,multiply(X_9,divide(X_8,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))),divide(X_8,divide(X_9,inverse(divide(X_8,X_9))))) ),[1,1],$fot(multiply(X_9,divide(X_8,X_9)))]]) ).
cnf(refute_0_105,plain,
( divide(X_9,inverse(divide(X_8,X_9))) != multiply(X_9,divide(X_8,X_9))
| divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) = divide(X_8,multiply(X_9,divide(X_8,X_9))) ),
inference(resolve,[$cnf( $equal(divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))),divide(X_8,divide(X_9,inverse(divide(X_8,X_9))))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) = divide(X_8,multiply(X_9,divide(X_8,X_9))),
inference(resolve,[$cnf( $equal(divide(X_9,inverse(divide(X_8,X_9))),multiply(X_9,divide(X_8,X_9))) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
( divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) != divide(B,B)
| divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) != divide(X_8,multiply(X_9,divide(X_8,X_9)))
| divide(X_8,multiply(X_9,divide(X_8,X_9))) = divide(B,B) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))),divide(B,B)) ),[0],$fot(divide(X_8,multiply(X_9,divide(X_8,X_9))))]]) ).
cnf(refute_0_108,plain,
( divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))) != divide(B,B)
| divide(X_8,multiply(X_9,divide(X_8,X_9))) = divide(B,B) ),
inference(resolve,[$cnf( $equal(divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))),divide(X_8,multiply(X_9,divide(X_8,X_9)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
divide(X_8,multiply(X_9,divide(X_8,X_9))) = divide(B,B),
inference(resolve,[$cnf( $equal(divide(X_8,divide(X_9,inverse(divide(X_8,X_9)))),divide(B,B)) )],[refute_0_101,refute_0_108]) ).
cnf(refute_0_110,plain,
divide(A,multiply(B,divide(A,B))) = divide(B,B),
inference(subst,[],[refute_0_109:[bind(X_8,$fot(A)),bind(X_9,$fot(B))]]) ).
cnf(refute_0_111,plain,
divide(B,inverse(divide(A,B))) = multiply(B,divide(A,B)),
inference(subst,[],[refute_0_39:[bind(A,$fot(B)),bind(B,$fot(divide(A,B)))]]) ).
cnf(refute_0_112,plain,
divide(A,divide(B,inverse(divide(A,B)))) = divide(A,divide(B,inverse(divide(A,B)))),
introduced(tautology,[refl,[$fot(divide(A,divide(B,inverse(divide(A,B)))))]]) ).
cnf(refute_0_113,plain,
( divide(A,divide(B,inverse(divide(A,B)))) != divide(A,divide(B,inverse(divide(A,B))))
| divide(B,inverse(divide(A,B))) != multiply(B,divide(A,B))
| divide(A,divide(B,inverse(divide(A,B)))) = divide(A,multiply(B,divide(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),divide(A,divide(B,inverse(divide(A,B))))) ),[1,1],$fot(multiply(B,divide(A,B)))]]) ).
cnf(refute_0_114,plain,
( divide(B,inverse(divide(A,B))) != multiply(B,divide(A,B))
| divide(A,divide(B,inverse(divide(A,B)))) = divide(A,multiply(B,divide(A,B))) ),
inference(resolve,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),divide(A,divide(B,inverse(divide(A,B))))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
divide(A,divide(B,inverse(divide(A,B)))) = divide(A,multiply(B,divide(A,B))),
inference(resolve,[$cnf( $equal(divide(B,inverse(divide(A,B))),multiply(B,divide(A,B))) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
( divide(A,multiply(B,divide(A,B))) != divide(B,B)
| divide(A,divide(B,inverse(divide(A,B)))) != divide(A,multiply(B,divide(A,B)))
| divide(A,divide(B,inverse(divide(A,B)))) = divide(B,B) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(divide(A,divide(B,inverse(divide(A,B)))))),bind(Y,$fot(divide(A,multiply(B,divide(A,B))))),bind(Z,$fot(divide(B,B)))]]) ).
cnf(refute_0_117,plain,
( divide(A,multiply(B,divide(A,B))) != divide(B,B)
| divide(A,divide(B,inverse(divide(A,B)))) = divide(B,B) ),
inference(resolve,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),divide(A,multiply(B,divide(A,B)))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
divide(A,divide(B,inverse(divide(A,B)))) = divide(B,B),
inference(resolve,[$cnf( $equal(divide(A,multiply(B,divide(A,B))),divide(B,B)) )],[refute_0_110,refute_0_117]) ).
cnf(refute_0_119,plain,
( divide(A,divide(B,inverse(divide(A,B)))) != divide(B,B)
| divide(A,divide(B,inverse(divide(A,B)))) != inverse(multiply(inverse(X_22),X_22))
| divide(B,B) = inverse(multiply(inverse(X_22),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),inverse(multiply(inverse(X_22),X_22))) ),[0],$fot(divide(B,B))]]) ).
cnf(refute_0_120,plain,
( divide(A,divide(B,inverse(divide(A,B)))) != inverse(multiply(inverse(X_22),X_22))
| divide(B,B) = inverse(multiply(inverse(X_22),X_22)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),divide(B,B)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
divide(B,B) = inverse(multiply(inverse(X_22),X_22)),
inference(resolve,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),inverse(multiply(inverse(X_22),X_22))) )],[refute_0_94,refute_0_120]) ).
cnf(refute_0_122,plain,
divide(B,B) = inverse(multiply(inverse(X_34),X_34)),
inference(subst,[],[refute_0_121:[bind(X_22,$fot(X_34))]]) ).
cnf(refute_0_123,plain,
( divide(B,B) != inverse(multiply(inverse(X_34),X_34))
| divide(B,divide(B,divide(C,divide(B,B)))) != C
| divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(B,divide(B,divide(C,divide(B,B)))),C) ),[0,1,1,1],$fot(inverse(multiply(inverse(X_34),X_34)))]]) ).
cnf(refute_0_124,plain,
( divide(B,divide(B,divide(C,divide(B,B)))) != C
| divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) = C ),
inference(resolve,[$cnf( $equal(divide(B,B),inverse(multiply(inverse(X_34),X_34))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) = C,
inference(resolve,[$cnf( $equal(divide(B,divide(B,divide(C,divide(B,B)))),C) )],[refute_0_76,refute_0_124]) ).
cnf(refute_0_126,plain,
divide(C,inverse(multiply(inverse(X_34),X_34))) = multiply(C,multiply(inverse(X_34),X_34)),
inference(subst,[],[refute_0_39:[bind(A,$fot(C)),bind(B,$fot(multiply(inverse(X_34),X_34)))]]) ).
cnf(refute_0_127,plain,
divide(A,divide(B,divide(multiply(inverse(X_16),X_16),divide(A,B)))) = multiply(inverse(X_16),X_16),
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(inverse(X_16),X_16)))]]) ).
cnf(refute_0_128,plain,
inverse(divide(A,B)) = divide(multiply(inverse(X_16),X_16),divide(A,B)),
inference(subst,[],[refute_0_69:[bind(A,$fot(divide(A,B))),bind(X_12,$fot(X_16))]]) ).
cnf(refute_0_129,plain,
( inverse(divide(A,B)) != divide(multiply(inverse(X_16),X_16),divide(A,B))
| divide(multiply(inverse(X_16),X_16),divide(A,B)) = inverse(divide(A,B)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(divide(A,B)))),bind(Y,$fot(divide(multiply(inverse(X_16),X_16),divide(A,B))))]]) ).
cnf(refute_0_130,plain,
divide(multiply(inverse(X_16),X_16),divide(A,B)) = inverse(divide(A,B)),
inference(resolve,[$cnf( $equal(inverse(divide(A,B)),divide(multiply(inverse(X_16),X_16),divide(A,B))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( divide(A,divide(B,divide(multiply(inverse(X_16),X_16),divide(A,B)))) != multiply(inverse(X_16),X_16)
| divide(multiply(inverse(X_16),X_16),divide(A,B)) != inverse(divide(A,B))
| divide(A,divide(B,inverse(divide(A,B)))) = multiply(inverse(X_16),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(B,divide(multiply(inverse(X_16),X_16),divide(A,B)))),multiply(inverse(X_16),X_16)) ),[0,1,1],$fot(inverse(divide(A,B)))]]) ).
cnf(refute_0_132,plain,
( divide(A,divide(B,divide(multiply(inverse(X_16),X_16),divide(A,B)))) != multiply(inverse(X_16),X_16)
| divide(A,divide(B,inverse(divide(A,B)))) = multiply(inverse(X_16),X_16) ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(X_16),X_16),divide(A,B)),inverse(divide(A,B))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
divide(A,divide(B,inverse(divide(A,B)))) = multiply(inverse(X_16),X_16),
inference(resolve,[$cnf( $equal(divide(A,divide(B,divide(multiply(inverse(X_16),X_16),divide(A,B)))),multiply(inverse(X_16),X_16)) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
( divide(A,divide(B,inverse(divide(A,B)))) != multiply(inverse(X_16),X_16)
| divide(A,divide(B,inverse(divide(A,B)))) != divide(B,B)
| divide(B,B) = multiply(inverse(X_16),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),multiply(inverse(X_16),X_16)) ),[0],$fot(divide(B,B))]]) ).
cnf(refute_0_135,plain,
( divide(A,divide(B,inverse(divide(A,B)))) != multiply(inverse(X_16),X_16)
| divide(B,B) = multiply(inverse(X_16),X_16) ),
inference(resolve,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),divide(B,B)) )],[refute_0_118,refute_0_134]) ).
cnf(refute_0_136,plain,
divide(B,B) = multiply(inverse(X_16),X_16),
inference(resolve,[$cnf( $equal(divide(A,divide(B,inverse(divide(A,B)))),multiply(inverse(X_16),X_16)) )],[refute_0_133,refute_0_135]) ).
cnf(refute_0_137,plain,
divide(B,B) = multiply(inverse(X_28),X_28),
inference(subst,[],[refute_0_136:[bind(X_16,$fot(X_28))]]) ).
cnf(refute_0_138,plain,
( divide(B,B) != multiply(inverse(X_28),X_28)
| divide(B,divide(B,divide(C,divide(B,B)))) != C
| divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(B,divide(B,divide(C,divide(B,B)))),C) ),[0,1,1,1],$fot(multiply(inverse(X_28),X_28))]]) ).
cnf(refute_0_139,plain,
( divide(B,divide(B,divide(C,divide(B,B)))) != C
| divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) = C ),
inference(resolve,[$cnf( $equal(divide(B,B),multiply(inverse(X_28),X_28)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) = C,
inference(resolve,[$cnf( $equal(divide(B,divide(B,divide(C,divide(B,B)))),C) )],[refute_0_76,refute_0_139]) ).
cnf(refute_0_141,plain,
divide(A,divide(B,divide(divide(A,B),divide(A,B)))) = divide(A,B),
inference(subst,[],[single_axiom:[bind(C,$fot(divide(A,B)))]]) ).
cnf(refute_0_142,plain,
divide(divide(A,B),divide(A,B)) = multiply(inverse(X_28),X_28),
inference(subst,[],[refute_0_136:[bind(B,$fot(divide(A,B))),bind(X_16,$fot(X_28))]]) ).
cnf(refute_0_143,plain,
( divide(A,divide(B,divide(divide(A,B),divide(A,B)))) != divide(A,B)
| divide(divide(A,B),divide(A,B)) != multiply(inverse(X_28),X_28)
| divide(A,divide(B,multiply(inverse(X_28),X_28))) = divide(A,B) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(B,divide(divide(A,B),divide(A,B)))),divide(A,B)) ),[0,1,1],$fot(multiply(inverse(X_28),X_28))]]) ).
cnf(refute_0_144,plain,
( divide(A,divide(B,divide(divide(A,B),divide(A,B)))) != divide(A,B)
| divide(A,divide(B,multiply(inverse(X_28),X_28))) = divide(A,B) ),
inference(resolve,[$cnf( $equal(divide(divide(A,B),divide(A,B)),multiply(inverse(X_28),X_28)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
divide(A,divide(B,multiply(inverse(X_28),X_28))) = divide(A,B),
inference(resolve,[$cnf( $equal(divide(A,divide(B,divide(divide(A,B),divide(A,B)))),divide(A,B)) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
divide(B,divide(C,multiply(inverse(X_28),X_28))) = divide(B,C),
inference(subst,[],[refute_0_145:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_147,plain,
divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) = divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))),
introduced(tautology,[refl,[$fot(divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))))]]) ).
cnf(refute_0_148,plain,
( divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) != divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28))))
| divide(B,divide(C,multiply(inverse(X_28),X_28))) != divide(B,C)
| divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) = divide(B,divide(B,C)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))),divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28))))) ),[1,1],$fot(divide(B,C))]]) ).
cnf(refute_0_149,plain,
( divide(B,divide(C,multiply(inverse(X_28),X_28))) != divide(B,C)
| divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) = divide(B,divide(B,C)) ),
inference(resolve,[$cnf( $equal(divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))),divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28))))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) = divide(B,divide(B,C)),
inference(resolve,[$cnf( $equal(divide(B,divide(C,multiply(inverse(X_28),X_28))),divide(B,C)) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) != C
| divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) != divide(B,divide(B,C))
| divide(B,divide(B,C)) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))),C) ),[0],$fot(divide(B,divide(B,C)))]]) ).
cnf(refute_0_152,plain,
( divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))) != C
| divide(B,divide(B,C)) = C ),
inference(resolve,[$cnf( $equal(divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))),divide(B,divide(B,C))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
divide(B,divide(B,C)) = C,
inference(resolve,[$cnf( $equal(divide(B,divide(B,divide(C,multiply(inverse(X_28),X_28)))),C) )],[refute_0_140,refute_0_152]) ).
cnf(refute_0_154,plain,
divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) = divide(C,inverse(multiply(inverse(X_34),X_34))),
inference(subst,[],[refute_0_153:[bind(C,$fot(divide(C,inverse(multiply(inverse(X_34),X_34)))))]]) ).
cnf(refute_0_155,plain,
( divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) != divide(C,inverse(multiply(inverse(X_34),X_34)))
| divide(C,inverse(multiply(inverse(X_34),X_34))) != multiply(C,multiply(inverse(X_34),X_34))
| divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) = multiply(C,multiply(inverse(X_34),X_34)) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))))),bind(Y,$fot(divide(C,inverse(multiply(inverse(X_34),X_34))))),bind(Z,$fot(multiply(C,multiply(inverse(X_34),X_34))))]]) ).
cnf(refute_0_156,plain,
( divide(C,inverse(multiply(inverse(X_34),X_34))) != multiply(C,multiply(inverse(X_34),X_34))
| divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) = multiply(C,multiply(inverse(X_34),X_34)) ),
inference(resolve,[$cnf( $equal(divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))),divide(C,inverse(multiply(inverse(X_34),X_34)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) = multiply(C,multiply(inverse(X_34),X_34)),
inference(resolve,[$cnf( $equal(divide(C,inverse(multiply(inverse(X_34),X_34))),multiply(C,multiply(inverse(X_34),X_34))) )],[refute_0_126,refute_0_156]) ).
cnf(refute_0_158,plain,
( divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) != C
| divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) != multiply(C,multiply(inverse(X_34),X_34))
| multiply(C,multiply(inverse(X_34),X_34)) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))),C) ),[0],$fot(multiply(C,multiply(inverse(X_34),X_34)))]]) ).
cnf(refute_0_159,plain,
( divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))) != C
| multiply(C,multiply(inverse(X_34),X_34)) = C ),
inference(resolve,[$cnf( $equal(divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))),multiply(C,multiply(inverse(X_34),X_34))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
multiply(C,multiply(inverse(X_34),X_34)) = C,
inference(resolve,[$cnf( $equal(divide(B,divide(B,divide(C,inverse(multiply(inverse(X_34),X_34))))),C) )],[refute_0_125,refute_0_159]) ).
cnf(refute_0_161,plain,
multiply(X_35,multiply(inverse(X_12),X_12)) = X_35,
inference(subst,[],[refute_0_160:[bind(C,$fot(X_35)),bind(X_34,$fot(X_12))]]) ).
cnf(refute_0_162,plain,
inverse(multiply(X_35,multiply(inverse(X_12),X_12))) = inverse(multiply(X_35,multiply(inverse(X_12),X_12))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_35,multiply(inverse(X_12),X_12))))]]) ).
cnf(refute_0_163,plain,
( multiply(X_35,multiply(inverse(X_12),X_12)) != X_35
| inverse(multiply(X_35,multiply(inverse(X_12),X_12))) != inverse(multiply(X_35,multiply(inverse(X_12),X_12)))
| inverse(multiply(X_35,multiply(inverse(X_12),X_12))) = inverse(X_35) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_35,multiply(inverse(X_12),X_12))),inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) ),[1,0],$fot(X_35)]]) ).
cnf(refute_0_164,plain,
( multiply(X_35,multiply(inverse(X_12),X_12)) != X_35
| inverse(multiply(X_35,multiply(inverse(X_12),X_12))) = inverse(X_35) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_35,multiply(inverse(X_12),X_12))),inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
inverse(multiply(X_35,multiply(inverse(X_12),X_12))) = inverse(X_35),
inference(resolve,[$cnf( $equal(multiply(X_35,multiply(inverse(X_12),X_12)),X_35) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) = inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))),
introduced(tautology,[refl,[$fot(inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))))]]) ).
cnf(refute_0_167,plain,
( inverse(multiply(X_35,multiply(inverse(X_12),X_12))) != inverse(X_35)
| inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) != inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12))))
| inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) = inverse(inverse(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))),inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12))))) ),[1,0],$fot(inverse(X_35))]]) ).
cnf(refute_0_168,plain,
( inverse(multiply(X_35,multiply(inverse(X_12),X_12))) != inverse(X_35)
| inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) = inverse(inverse(X_35)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))),inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12))))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) = inverse(inverse(X_35)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_35,multiply(inverse(X_12),X_12))),inverse(X_35)) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
( inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) != X_35
| inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) != inverse(inverse(X_35))
| inverse(inverse(X_35)) = X_35 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))),X_35) ),[0],$fot(inverse(inverse(X_35)))]]) ).
cnf(refute_0_171,plain,
( inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))) != X_35
| inverse(inverse(X_35)) = X_35 ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))),inverse(inverse(X_35))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
inverse(inverse(X_35)) = X_35,
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_35,multiply(inverse(X_12),X_12)))),X_35) )],[refute_0_75,refute_0_171]) ).
cnf(refute_0_173,plain,
inverse(inverse(a2)) = a2,
inference(subst,[],[refute_0_172:[bind(X_35,$fot(a2))]]) ).
cnf(refute_0_174,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_175,plain,
( a2 != a2
| inverse(inverse(a2)) = a2 ),
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_175,refute_0_32]) ).
cnf(refute_0_177,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_178,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_177,refute_0_176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 07:55:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.36/0.52
%------------------------------------------------------------------------------