TSTP Solution File: GRP557-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP557-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:42:20 EDT 2022
% Result : Unsatisfiable 0.22s 0.43s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 50
% Syntax : Number of clauses : 185 ( 96 unt; 0 nHn; 92 RR)
% Number of literals : 314 ( 313 equ; 132 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 : 366 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(A,inverse(divide(divide(B,C),divide(A,C)))) = B ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,inverse(B)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_4,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[multiply,refute_0_3]) ).
cnf(refute_0_5,plain,
divide(A,inverse(divide(divide(B,C),divide(A,C)))) = multiply(A,divide(divide(B,C),divide(A,C))),
inference(subst,[],[refute_0_4:[bind(B,$fot(divide(divide(B,C),divide(A,C))))]]) ).
cnf(refute_0_6,plain,
( divide(A,inverse(divide(divide(B,C),divide(A,C)))) != B
| divide(A,inverse(divide(divide(B,C),divide(A,C)))) != multiply(A,divide(divide(B,C),divide(A,C)))
| multiply(A,divide(divide(B,C),divide(A,C))) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,inverse(divide(divide(B,C),divide(A,C)))),B) ),[0],$fot(multiply(A,divide(divide(B,C),divide(A,C))))]]) ).
cnf(refute_0_7,plain,
( divide(A,inverse(divide(divide(B,C),divide(A,C)))) != B
| multiply(A,divide(divide(B,C),divide(A,C))) = B ),
inference(resolve,[$cnf( $equal(divide(A,inverse(divide(divide(B,C),divide(A,C)))),multiply(A,divide(divide(B,C),divide(A,C)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(A,divide(divide(B,C),divide(A,C))) = B,
inference(resolve,[$cnf( $equal(divide(A,inverse(divide(divide(B,C),divide(A,C)))),B) )],[single_axiom,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))) = X_3,
inference(subst,[],[refute_0_8:[bind(A,$fot(X_2)),bind(B,$fot(X_3)),bind(C,$fot(inverse(B)))]]) ).
cnf(refute_0_10,plain,
multiply(X_2,B) = divide(X_2,inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(X_2))]]) ).
cnf(refute_0_11,plain,
( multiply(X_2,B) != divide(X_2,inverse(B))
| divide(X_2,inverse(B)) = multiply(X_2,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_2,B))),bind(Y,$fot(divide(X_2,inverse(B))))]]) ).
cnf(refute_0_12,plain,
divide(X_2,inverse(B)) = multiply(X_2,B),
inference(resolve,[$cnf( $equal(multiply(X_2,B),divide(X_2,inverse(B))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))) != X_3
| divide(X_2,inverse(B)) != multiply(X_2,B)
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))),X_3) ),[0,1,1],$fot(multiply(X_2,B))]]) ).
cnf(refute_0_14,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))) != X_3
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = X_3 ),
inference(resolve,[$cnf( $equal(divide(X_2,inverse(B)),multiply(X_2,B)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))),X_3) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
divide(X_3,inverse(B)) = multiply(X_3,B),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_17,plain,
divide(divide(X_3,inverse(B)),multiply(X_2,B)) = divide(divide(X_3,inverse(B)),multiply(X_2,B)),
introduced(tautology,[refl,[$fot(divide(divide(X_3,inverse(B)),multiply(X_2,B)))]]) ).
cnf(refute_0_18,plain,
( divide(X_3,inverse(B)) != multiply(X_3,B)
| divide(divide(X_3,inverse(B)),multiply(X_2,B)) != divide(divide(X_3,inverse(B)),multiply(X_2,B))
| divide(divide(X_3,inverse(B)),multiply(X_2,B)) = divide(multiply(X_3,B),multiply(X_2,B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_3,inverse(B)),multiply(X_2,B)),divide(divide(X_3,inverse(B)),multiply(X_2,B))) ),[1,0],$fot(multiply(X_3,B))]]) ).
cnf(refute_0_19,plain,
( divide(X_3,inverse(B)) != multiply(X_3,B)
| divide(divide(X_3,inverse(B)),multiply(X_2,B)) = divide(multiply(X_3,B),multiply(X_2,B)) ),
inference(resolve,[$cnf( $equal(divide(divide(X_3,inverse(B)),multiply(X_2,B)),divide(divide(X_3,inverse(B)),multiply(X_2,B))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
divide(divide(X_3,inverse(B)),multiply(X_2,B)) = divide(multiply(X_3,B),multiply(X_2,B)),
inference(resolve,[$cnf( $equal(divide(X_3,inverse(B)),multiply(X_3,B)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),
introduced(tautology,[refl,[$fot(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))))]]) ).
cnf(refute_0_22,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) != multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B)))
| divide(divide(X_3,inverse(B)),multiply(X_2,B)) != divide(multiply(X_3,B),multiply(X_2,B))
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B)))) ),[1,1],$fot(divide(multiply(X_3,B),multiply(X_2,B)))]]) ).
cnf(refute_0_23,plain,
( divide(divide(X_3,inverse(B)),multiply(X_2,B)) != divide(multiply(X_3,B),multiply(X_2,B))
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))),
inference(resolve,[$cnf( $equal(divide(divide(X_3,inverse(B)),multiply(X_2,B)),divide(multiply(X_3,B),multiply(X_2,B))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) != X_3
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) != multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B)))
| multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),X_3) ),[0],$fot(multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))))]]) ).
cnf(refute_0_26,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) != X_3
| multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),X_3) )],[refute_0_15,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))) = X_3,
inference(subst,[],[refute_0_27:[bind(B,$fot(divide(X_20,X_20)))]]) ).
cnf(refute_0_29,plain,
multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) = X_3,
inference(subst,[],[refute_0_27:[bind(B,$fot(divide(multiply(X_7,X_5),multiply(X_3,X_5))))]]) ).
cnf(refute_0_30,plain,
multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))) = X_7,
inference(subst,[],[refute_0_27:[bind(B,$fot(X_5)),bind(X_2,$fot(X_3)),bind(X_3,$fot(X_7))]]) ).
cnf(refute_0_31,plain,
( multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) != X_3
| multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))) != X_7
| multiply(X_2,divide(X_7,multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))),X_3) ),[0,1,0],$fot(X_7)]]) ).
cnf(refute_0_32,plain,
( multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) != X_3
| multiply(X_2,divide(X_7,multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),X_7) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_2,divide(X_7,multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))),X_3) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))) = X_9,
inference(subst,[],[refute_0_33:[bind(X_2,$fot(X_9)),bind(X_3,$fot(X_9)),bind(X_5,$fot(X_10)),bind(X_7,$fot(X_11))]]) ).
cnf(refute_0_35,plain,
multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))) = X_11,
inference(subst,[],[refute_0_27:[bind(B,$fot(X_10)),bind(X_2,$fot(X_9)),bind(X_3,$fot(X_11))]]) ).
cnf(refute_0_36,plain,
( multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))) != X_9
| multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))) != X_11
| multiply(X_9,divide(X_11,X_11)) = X_9 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))),X_9) ),[0,1,1],$fot(X_11)]]) ).
cnf(refute_0_37,plain,
( multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))) != X_9
| multiply(X_9,divide(X_11,X_11)) = X_9 ),
inference(resolve,[$cnf( $equal(multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))),X_11) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(X_9,divide(X_11,X_11)) = X_9,
inference(resolve,[$cnf( $equal(multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))),X_9) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(X_3,divide(X_20,X_20)) = X_3,
inference(subst,[],[refute_0_38:[bind(X_11,$fot(X_20)),bind(X_9,$fot(X_3))]]) ).
cnf(refute_0_40,plain,
( multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))) != X_3
| multiply(X_3,divide(X_20,X_20)) != X_3
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))),X_3) ),[0,1,0],$fot(X_3)]]) ).
cnf(refute_0_41,plain,
( multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))) != X_3
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(X_3,divide(X_20,X_20)),X_3) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))),X_3) )],[refute_0_28,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(X_2,divide(X_20,X_20)) = X_2,
inference(subst,[],[refute_0_38:[bind(X_11,$fot(X_20)),bind(X_9,$fot(X_2))]]) ).
cnf(refute_0_44,plain,
divide(X_3,multiply(X_2,divide(X_20,X_20))) = divide(X_3,multiply(X_2,divide(X_20,X_20))),
introduced(tautology,[refl,[$fot(divide(X_3,multiply(X_2,divide(X_20,X_20))))]]) ).
cnf(refute_0_45,plain,
( multiply(X_2,divide(X_20,X_20)) != X_2
| divide(X_3,multiply(X_2,divide(X_20,X_20))) != divide(X_3,multiply(X_2,divide(X_20,X_20)))
| divide(X_3,multiply(X_2,divide(X_20,X_20))) = divide(X_3,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_3,multiply(X_2,divide(X_20,X_20))),divide(X_3,multiply(X_2,divide(X_20,X_20)))) ),[1,1],$fot(X_2)]]) ).
cnf(refute_0_46,plain,
( multiply(X_2,divide(X_20,X_20)) != X_2
| divide(X_3,multiply(X_2,divide(X_20,X_20))) = divide(X_3,X_2) ),
inference(resolve,[$cnf( $equal(divide(X_3,multiply(X_2,divide(X_20,X_20))),divide(X_3,multiply(X_2,divide(X_20,X_20)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
divide(X_3,multiply(X_2,divide(X_20,X_20))) = divide(X_3,X_2),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_20,X_20)),X_2) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),
introduced(tautology,[refl,[$fot(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))))]]) ).
cnf(refute_0_49,plain,
( multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) != multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20))))
| divide(X_3,multiply(X_2,divide(X_20,X_20))) != divide(X_3,X_2)
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = multiply(X_2,divide(X_3,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20))))) ),[1,1],$fot(divide(X_3,X_2))]]) ).
cnf(refute_0_50,plain,
( divide(X_3,multiply(X_2,divide(X_20,X_20))) != divide(X_3,X_2)
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = multiply(X_2,divide(X_3,X_2)) ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20))))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = multiply(X_2,divide(X_3,X_2)),
inference(resolve,[$cnf( $equal(divide(X_3,multiply(X_2,divide(X_20,X_20))),divide(X_3,X_2)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) != X_3
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) != multiply(X_2,divide(X_3,X_2))
| multiply(X_2,divide(X_3,X_2)) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),X_3) ),[0],$fot(multiply(X_2,divide(X_3,X_2)))]]) ).
cnf(refute_0_53,plain,
( multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) != X_3
| multiply(X_2,divide(X_3,X_2)) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),multiply(X_2,divide(X_3,X_2))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(X_2,divide(X_3,X_2)) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),X_3) )],[refute_0_42,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(X_2,divide(multiply(X_33,X_2),X_2)) = multiply(X_33,X_2),
inference(subst,[],[refute_0_54:[bind(X_3,$fot(multiply(X_33,X_2)))]]) ).
cnf(refute_0_56,plain,
multiply(inverse(multiply(inverse(X_31),X_31)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))) = X_3,
inference(subst,[],[refute_0_27:[bind(X_2,$fot(inverse(multiply(inverse(X_31),X_31))))]]) ).
cnf(refute_0_57,plain,
multiply(inverse(B),divide(X_23,inverse(B))) = X_23,
inference(subst,[],[refute_0_54:[bind(X_2,$fot(inverse(B))),bind(X_3,$fot(X_23))]]) ).
cnf(refute_0_58,plain,
multiply(X_23,B) = divide(X_23,inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_59,plain,
( multiply(X_23,B) != divide(X_23,inverse(B))
| divide(X_23,inverse(B)) = multiply(X_23,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_23,B))),bind(Y,$fot(divide(X_23,inverse(B))))]]) ).
cnf(refute_0_60,plain,
divide(X_23,inverse(B)) = multiply(X_23,B),
inference(resolve,[$cnf( $equal(multiply(X_23,B),divide(X_23,inverse(B))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(inverse(B),divide(X_23,inverse(B))) != X_23
| divide(X_23,inverse(B)) != multiply(X_23,B)
| multiply(inverse(B),multiply(X_23,B)) = X_23 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(B),divide(X_23,inverse(B))),X_23) ),[0,1],$fot(multiply(X_23,B))]]) ).
cnf(refute_0_62,plain,
( multiply(inverse(B),divide(X_23,inverse(B))) != X_23
| multiply(inverse(B),multiply(X_23,B)) = X_23 ),
inference(resolve,[$cnf( $equal(divide(X_23,inverse(B)),multiply(X_23,B)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(inverse(B),multiply(X_23,B)) = X_23,
inference(resolve,[$cnf( $equal(multiply(inverse(B),divide(X_23,inverse(B))),X_23) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(inverse(multiply(inverse(X_26),X_26)),multiply(X_23,multiply(inverse(X_26),X_26))) = X_23,
inference(subst,[],[refute_0_63:[bind(B,$fot(multiply(inverse(X_26),X_26)))]]) ).
cnf(refute_0_65,plain,
multiply(X_21,divide(inverse(B),inverse(B))) = X_21,
inference(subst,[],[refute_0_38:[bind(X_11,$fot(inverse(B))),bind(X_9,$fot(X_21))]]) ).
cnf(refute_0_66,plain,
multiply(inverse(B),B) = divide(inverse(B),inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(inverse(B)))]]) ).
cnf(refute_0_67,plain,
( multiply(inverse(B),B) != divide(inverse(B),inverse(B))
| divide(inverse(B),inverse(B)) = multiply(inverse(B),B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(inverse(B),B))),bind(Y,$fot(divide(inverse(B),inverse(B))))]]) ).
cnf(refute_0_68,plain,
divide(inverse(B),inverse(B)) = multiply(inverse(B),B),
inference(resolve,[$cnf( $equal(multiply(inverse(B),B),divide(inverse(B),inverse(B))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( multiply(X_21,divide(inverse(B),inverse(B))) != X_21
| divide(inverse(B),inverse(B)) != multiply(inverse(B),B)
| multiply(X_21,multiply(inverse(B),B)) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,divide(inverse(B),inverse(B))),X_21) ),[0,1],$fot(multiply(inverse(B),B))]]) ).
cnf(refute_0_70,plain,
( multiply(X_21,divide(inverse(B),inverse(B))) != X_21
| multiply(X_21,multiply(inverse(B),B)) = X_21 ),
inference(resolve,[$cnf( $equal(divide(inverse(B),inverse(B)),multiply(inverse(B),B)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_21,multiply(inverse(B),B)) = X_21,
inference(resolve,[$cnf( $equal(multiply(X_21,divide(inverse(B),inverse(B))),X_21) )],[refute_0_65,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(X_23,multiply(inverse(X_26),X_26)) = X_23,
inference(subst,[],[refute_0_71:[bind(B,$fot(X_26)),bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_73,plain,
( multiply(X_23,multiply(inverse(X_26),X_26)) != X_23
| multiply(inverse(multiply(inverse(X_26),X_26)),multiply(X_23,multiply(inverse(X_26),X_26))) != X_23
| multiply(inverse(multiply(inverse(X_26),X_26)),X_23) = X_23 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_26),X_26)),multiply(X_23,multiply(inverse(X_26),X_26))),X_23) ),[0,1],$fot(X_23)]]) ).
cnf(refute_0_74,plain,
( multiply(inverse(multiply(inverse(X_26),X_26)),multiply(X_23,multiply(inverse(X_26),X_26))) != X_23
| multiply(inverse(multiply(inverse(X_26),X_26)),X_23) = X_23 ),
inference(resolve,[$cnf( $equal(multiply(X_23,multiply(inverse(X_26),X_26)),X_23) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(inverse(multiply(inverse(X_26),X_26)),X_23) = X_23,
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_26),X_26)),multiply(X_23,multiply(inverse(X_26),X_26))),X_23) )],[refute_0_64,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(inverse(multiply(inverse(X_31),X_31)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))) = divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)),
inference(subst,[],[refute_0_75:[bind(X_23,$fot(divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)))),bind(X_26,$fot(X_31))]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(multiply(inverse(X_31),X_31)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))) != X_3
| multiply(inverse(multiply(inverse(X_31),X_31)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))) != divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))
| divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),X_31)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))),X_3) ),[0],$fot(divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)))]]) ).
cnf(refute_0_78,plain,
( multiply(inverse(multiply(inverse(X_31),X_31)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))) != X_3
| divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),X_31)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) = X_3,
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),X_31)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))),X_3) )],[refute_0_56,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(inverse(multiply(inverse(X_31),X_31)),B) = B,
inference(subst,[],[refute_0_75:[bind(X_23,$fot(B)),bind(X_26,$fot(X_31))]]) ).
cnf(refute_0_81,plain,
divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) = divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)),
introduced(tautology,[refl,[$fot(divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)))]]) ).
cnf(refute_0_82,plain,
( multiply(inverse(multiply(inverse(X_31),X_31)),B) != B
| divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) != divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))
| divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) = divide(multiply(X_3,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))) ),[1,1],$fot(B)]]) ).
cnf(refute_0_83,plain,
( multiply(inverse(multiply(inverse(X_31),X_31)),B) != B
| divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) = divide(multiply(X_3,B),B) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)),divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) = divide(multiply(X_3,B),B),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),X_31)),B),B) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
( divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) != X_3
| divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) != divide(multiply(X_3,B),B)
| divide(multiply(X_3,B),B) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)),X_3) ),[0],$fot(divide(multiply(X_3,B),B))]]) ).
cnf(refute_0_86,plain,
( divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)) != X_3
| divide(multiply(X_3,B),B) = X_3 ),
inference(resolve,[$cnf( $equal(divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)),divide(multiply(X_3,B),B)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
divide(multiply(X_3,B),B) = X_3,
inference(resolve,[$cnf( $equal(divide(multiply(X_3,B),multiply(inverse(multiply(inverse(X_31),X_31)),B)),X_3) )],[refute_0_79,refute_0_86]) ).
cnf(refute_0_88,plain,
divide(multiply(X_33,X_2),X_2) = X_33,
inference(subst,[],[refute_0_87:[bind(B,$fot(X_2)),bind(X_3,$fot(X_33))]]) ).
cnf(refute_0_89,plain,
( multiply(X_2,divide(multiply(X_33,X_2),X_2)) != multiply(X_33,X_2)
| divide(multiply(X_33,X_2),X_2) != X_33
| multiply(X_2,X_33) = multiply(X_33,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(multiply(X_33,X_2),X_2)),multiply(X_33,X_2)) ),[0,1],$fot(X_33)]]) ).
cnf(refute_0_90,plain,
( multiply(X_2,divide(multiply(X_33,X_2),X_2)) != multiply(X_33,X_2)
| multiply(X_2,X_33) = multiply(X_33,X_2) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_33,X_2),X_2),X_33) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(X_2,X_33) = multiply(X_33,X_2),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(multiply(X_33,X_2),X_2)),multiply(X_33,X_2)) )],[refute_0_55,refute_0_90]) ).
cnf(refute_0_92,plain,
( multiply(X_2,X_33) != multiply(X_33,X_2)
| multiply(X_33,X_2) = multiply(X_2,X_33) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_2,X_33))),bind(Y,$fot(multiply(X_33,X_2)))]]) ).
cnf(refute_0_93,plain,
multiply(X_33,X_2) = multiply(X_2,X_33),
inference(resolve,[$cnf( $equal(multiply(X_2,X_33),multiply(X_33,X_2)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(subst,[],[refute_0_93:[bind(X_2,$fot(a1)),bind(X_33,$fot(inverse(a1)))]]) ).
cnf(refute_0_95,plain,
( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) != multiply(a1,inverse(a1))
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a1),a1),multiply(a1,inverse(a1))) ),[1],$fot(multiply(inverse(b1),b1))]]) ).
cnf(refute_0_96,plain,
( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(a1,inverse(a1))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(inverse(b1),b1) = multiply(b1,inverse(b1)),
inference(subst,[],[refute_0_93:[bind(X_2,$fot(b1)),bind(X_33,$fot(inverse(b1)))]]) ).
cnf(refute_0_98,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(inverse(b1),b1) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a1,inverse(a1)),multiply(inverse(b1),b1)) ),[1],$fot(multiply(b1,inverse(b1)))]]) ).
cnf(refute_0_99,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b1),b1),multiply(b1,inverse(b1))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(inverse(b1),b1)) )],[refute_0_99,refute_0_96]) ).
cnf(refute_0_101,plain,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) )],[refute_0_100,prove_these_axioms_1]) ).
cnf(refute_0_102,plain,
multiply(A,inverse(X_36)) = divide(A,inverse(inverse(X_36))),
inference(subst,[],[multiply:[bind(B,$fot(inverse(X_36)))]]) ).
cnf(refute_0_103,plain,
multiply(inverse(inverse(X_23)),multiply(X_23,inverse(X_23))) = X_23,
inference(subst,[],[refute_0_63:[bind(B,$fot(inverse(X_23)))]]) ).
cnf(refute_0_104,plain,
multiply(inverse(multiply(inverse(X_31),X_31)),multiply(inverse(B),B)) = inverse(multiply(inverse(X_31),X_31)),
inference(subst,[],[refute_0_71:[bind(X_21,$fot(inverse(multiply(inverse(X_31),X_31))))]]) ).
cnf(refute_0_105,plain,
multiply(inverse(multiply(inverse(X_31),X_31)),multiply(inverse(B),B)) = multiply(inverse(B),B),
inference(subst,[],[refute_0_75:[bind(X_23,$fot(multiply(inverse(B),B))),bind(X_26,$fot(X_31))]]) ).
cnf(refute_0_106,plain,
( multiply(inverse(multiply(inverse(X_31),X_31)),multiply(inverse(B),B)) != multiply(inverse(B),B)
| multiply(inverse(multiply(inverse(X_31),X_31)),multiply(inverse(B),B)) != inverse(multiply(inverse(X_31),X_31))
| multiply(inverse(B),B) = inverse(multiply(inverse(X_31),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),X_31)),multiply(inverse(B),B)),inverse(multiply(inverse(X_31),X_31))) ),[0],$fot(multiply(inverse(B),B))]]) ).
cnf(refute_0_107,plain,
( multiply(inverse(multiply(inverse(X_31),X_31)),multiply(inverse(B),B)) != inverse(multiply(inverse(X_31),X_31))
| multiply(inverse(B),B) = inverse(multiply(inverse(X_31),X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),X_31)),multiply(inverse(B),B)),multiply(inverse(B),B)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(inverse(B),B) = inverse(multiply(inverse(X_31),X_31)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),X_31)),multiply(inverse(B),B)),inverse(multiply(inverse(X_31),X_31))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(inverse(B),B) = multiply(B,inverse(B)),
inference(subst,[],[refute_0_93:[bind(X_2,$fot(B)),bind(X_33,$fot(inverse(B)))]]) ).
cnf(refute_0_110,plain,
( multiply(inverse(B),B) != multiply(B,inverse(B))
| multiply(inverse(B),B) != inverse(multiply(inverse(X_31),X_31))
| multiply(B,inverse(B)) = inverse(multiply(inverse(X_31),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(B),B),inverse(multiply(inverse(X_31),X_31))) ),[0],$fot(multiply(B,inverse(B)))]]) ).
cnf(refute_0_111,plain,
( multiply(inverse(B),B) != inverse(multiply(inverse(X_31),X_31))
| multiply(B,inverse(B)) = inverse(multiply(inverse(X_31),X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(B),B),multiply(B,inverse(B))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(inverse(X_31),X_31) = multiply(X_31,inverse(X_31)),
inference(subst,[],[refute_0_93:[bind(X_2,$fot(X_31)),bind(X_33,$fot(inverse(X_31)))]]) ).
cnf(refute_0_113,plain,
inverse(multiply(inverse(X_31),X_31)) = inverse(multiply(inverse(X_31),X_31)),
introduced(tautology,[refl,[$fot(inverse(multiply(inverse(X_31),X_31)))]]) ).
cnf(refute_0_114,plain,
( multiply(inverse(X_31),X_31) != multiply(X_31,inverse(X_31))
| inverse(multiply(inverse(X_31),X_31)) != inverse(multiply(inverse(X_31),X_31))
| inverse(multiply(inverse(X_31),X_31)) = inverse(multiply(X_31,inverse(X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_31),X_31)),inverse(multiply(inverse(X_31),X_31))) ),[1,0],$fot(multiply(X_31,inverse(X_31)))]]) ).
cnf(refute_0_115,plain,
( multiply(inverse(X_31),X_31) != multiply(X_31,inverse(X_31))
| inverse(multiply(inverse(X_31),X_31)) = inverse(multiply(X_31,inverse(X_31))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_31),X_31)),inverse(multiply(inverse(X_31),X_31))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
inverse(multiply(inverse(X_31),X_31)) = inverse(multiply(X_31,inverse(X_31))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_31),X_31),multiply(X_31,inverse(X_31))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
( multiply(B,inverse(B)) != inverse(multiply(inverse(X_31),X_31))
| inverse(multiply(inverse(X_31),X_31)) != inverse(multiply(X_31,inverse(X_31)))
| multiply(B,inverse(B)) = inverse(multiply(X_31,inverse(X_31))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(B,inverse(B)),inverse(multiply(X_31,inverse(X_31)))) ),[0],$fot(inverse(multiply(inverse(X_31),X_31)))]]) ).
cnf(refute_0_118,plain,
( multiply(B,inverse(B)) != inverse(multiply(inverse(X_31),X_31))
| multiply(B,inverse(B)) = inverse(multiply(X_31,inverse(X_31))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_31),X_31)),inverse(multiply(X_31,inverse(X_31)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( multiply(inverse(B),B) != inverse(multiply(inverse(X_31),X_31))
| multiply(B,inverse(B)) = inverse(multiply(X_31,inverse(X_31))) ),
inference(resolve,[$cnf( $equal(multiply(B,inverse(B)),inverse(multiply(inverse(X_31),X_31))) )],[refute_0_111,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(B,inverse(B)) = inverse(multiply(X_31,inverse(X_31))),
inference(resolve,[$cnf( $equal(multiply(inverse(B),B),inverse(multiply(inverse(X_31),X_31))) )],[refute_0_108,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(X_23,inverse(X_23)) = inverse(multiply(X_35,inverse(X_35))),
inference(subst,[],[refute_0_120:[bind(B,$fot(X_23)),bind(X_31,$fot(X_35))]]) ).
cnf(refute_0_122,plain,
( multiply(X_23,inverse(X_23)) != inverse(multiply(X_35,inverse(X_35)))
| multiply(inverse(inverse(X_23)),multiply(X_23,inverse(X_23))) != X_23
| multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))) = X_23 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_23)),multiply(X_23,inverse(X_23))),X_23) ),[0,1],$fot(inverse(multiply(X_35,inverse(X_35))))]]) ).
cnf(refute_0_123,plain,
( multiply(inverse(inverse(X_23)),multiply(X_23,inverse(X_23))) != X_23
| multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))) = X_23 ),
inference(resolve,[$cnf( $equal(multiply(X_23,inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))) = X_23,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_23)),multiply(X_23,inverse(X_23))),X_23) )],[refute_0_103,refute_0_123]) ).
cnf(refute_0_125,plain,
multiply(X_21,multiply(inverse(multiply(inverse(X_26),X_26)),multiply(inverse(X_26),X_26))) = X_21,
inference(subst,[],[refute_0_71:[bind(B,$fot(multiply(inverse(X_26),X_26)))]]) ).
cnf(refute_0_126,plain,
multiply(inverse(multiply(inverse(X_26),X_26)),multiply(inverse(X_26),X_26)) = inverse(multiply(inverse(X_26),X_26)),
inference(subst,[],[refute_0_71:[bind(B,$fot(X_26)),bind(X_21,$fot(inverse(multiply(inverse(X_26),X_26))))]]) ).
cnf(refute_0_127,plain,
( multiply(X_21,multiply(inverse(multiply(inverse(X_26),X_26)),multiply(inverse(X_26),X_26))) != X_21
| multiply(inverse(multiply(inverse(X_26),X_26)),multiply(inverse(X_26),X_26)) != inverse(multiply(inverse(X_26),X_26))
| multiply(X_21,inverse(multiply(inverse(X_26),X_26))) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,multiply(inverse(multiply(inverse(X_26),X_26)),multiply(inverse(X_26),X_26))),X_21) ),[0,1],$fot(inverse(multiply(inverse(X_26),X_26)))]]) ).
cnf(refute_0_128,plain,
( multiply(X_21,multiply(inverse(multiply(inverse(X_26),X_26)),multiply(inverse(X_26),X_26))) != X_21
| multiply(X_21,inverse(multiply(inverse(X_26),X_26))) = X_21 ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_26),X_26)),multiply(inverse(X_26),X_26)),inverse(multiply(inverse(X_26),X_26))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
multiply(X_21,inverse(multiply(inverse(X_26),X_26))) = X_21,
inference(resolve,[$cnf( $equal(multiply(X_21,multiply(inverse(multiply(inverse(X_26),X_26)),multiply(inverse(X_26),X_26))),X_21) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(inverse(X_26),X_26) = multiply(X_26,inverse(X_26)),
inference(subst,[],[refute_0_93:[bind(X_2,$fot(X_26)),bind(X_33,$fot(inverse(X_26)))]]) ).
cnf(refute_0_131,plain,
inverse(multiply(inverse(X_26),X_26)) = inverse(multiply(inverse(X_26),X_26)),
introduced(tautology,[refl,[$fot(inverse(multiply(inverse(X_26),X_26)))]]) ).
cnf(refute_0_132,plain,
( multiply(inverse(X_26),X_26) != multiply(X_26,inverse(X_26))
| inverse(multiply(inverse(X_26),X_26)) != inverse(multiply(inverse(X_26),X_26))
| inverse(multiply(inverse(X_26),X_26)) = inverse(multiply(X_26,inverse(X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_26),X_26)),inverse(multiply(inverse(X_26),X_26))) ),[1,0],$fot(multiply(X_26,inverse(X_26)))]]) ).
cnf(refute_0_133,plain,
( multiply(inverse(X_26),X_26) != multiply(X_26,inverse(X_26))
| inverse(multiply(inverse(X_26),X_26)) = inverse(multiply(X_26,inverse(X_26))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_26),X_26)),inverse(multiply(inverse(X_26),X_26))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
inverse(multiply(inverse(X_26),X_26)) = inverse(multiply(X_26,inverse(X_26))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),X_26),multiply(X_26,inverse(X_26))) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(X_21,inverse(multiply(inverse(X_26),X_26))) = multiply(X_21,inverse(multiply(inverse(X_26),X_26))),
introduced(tautology,[refl,[$fot(multiply(X_21,inverse(multiply(inverse(X_26),X_26))))]]) ).
cnf(refute_0_136,plain,
( multiply(X_21,inverse(multiply(inverse(X_26),X_26))) != multiply(X_21,inverse(multiply(inverse(X_26),X_26)))
| inverse(multiply(inverse(X_26),X_26)) != inverse(multiply(X_26,inverse(X_26)))
| multiply(X_21,inverse(multiply(inverse(X_26),X_26))) = multiply(X_21,inverse(multiply(X_26,inverse(X_26)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,inverse(multiply(inverse(X_26),X_26))),multiply(X_21,inverse(multiply(inverse(X_26),X_26)))) ),[1,1],$fot(inverse(multiply(X_26,inverse(X_26))))]]) ).
cnf(refute_0_137,plain,
( inverse(multiply(inverse(X_26),X_26)) != inverse(multiply(X_26,inverse(X_26)))
| multiply(X_21,inverse(multiply(inverse(X_26),X_26))) = multiply(X_21,inverse(multiply(X_26,inverse(X_26)))) ),
inference(resolve,[$cnf( $equal(multiply(X_21,inverse(multiply(inverse(X_26),X_26))),multiply(X_21,inverse(multiply(inverse(X_26),X_26)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(X_21,inverse(multiply(inverse(X_26),X_26))) = multiply(X_21,inverse(multiply(X_26,inverse(X_26)))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_26),X_26)),inverse(multiply(X_26,inverse(X_26)))) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
( multiply(X_21,inverse(multiply(inverse(X_26),X_26))) != X_21
| multiply(X_21,inverse(multiply(inverse(X_26),X_26))) != multiply(X_21,inverse(multiply(X_26,inverse(X_26))))
| multiply(X_21,inverse(multiply(X_26,inverse(X_26)))) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,inverse(multiply(inverse(X_26),X_26))),X_21) ),[0],$fot(multiply(X_21,inverse(multiply(X_26,inverse(X_26)))))]]) ).
cnf(refute_0_140,plain,
( multiply(X_21,inverse(multiply(inverse(X_26),X_26))) != X_21
| multiply(X_21,inverse(multiply(X_26,inverse(X_26)))) = X_21 ),
inference(resolve,[$cnf( $equal(multiply(X_21,inverse(multiply(inverse(X_26),X_26))),multiply(X_21,inverse(multiply(X_26,inverse(X_26))))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(X_21,inverse(multiply(X_26,inverse(X_26)))) = X_21,
inference(resolve,[$cnf( $equal(multiply(X_21,inverse(multiply(inverse(X_26),X_26))),X_21) )],[refute_0_129,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))) = inverse(inverse(X_23)),
inference(subst,[],[refute_0_141:[bind(X_21,$fot(inverse(inverse(X_23)))),bind(X_26,$fot(X_35))]]) ).
cnf(refute_0_143,plain,
( multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))) != X_23
| multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))) != inverse(inverse(X_23))
| inverse(inverse(X_23)) = X_23 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))),X_23) ),[0],$fot(inverse(inverse(X_23)))]]) ).
cnf(refute_0_144,plain,
( multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))) != X_23
| inverse(inverse(X_23)) = X_23 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))),inverse(inverse(X_23))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
inverse(inverse(X_23)) = X_23,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_23)),inverse(multiply(X_35,inverse(X_35)))),X_23) )],[refute_0_124,refute_0_144]) ).
cnf(refute_0_146,plain,
inverse(inverse(X_36)) = X_36,
inference(subst,[],[refute_0_145:[bind(X_23,$fot(X_36))]]) ).
cnf(refute_0_147,plain,
( multiply(A,inverse(X_36)) != divide(A,inverse(inverse(X_36)))
| inverse(inverse(X_36)) != X_36
| multiply(A,inverse(X_36)) = divide(A,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,inverse(X_36)),divide(A,inverse(inverse(X_36)))) ),[1,1],$fot(X_36)]]) ).
cnf(refute_0_148,plain,
( multiply(A,inverse(X_36)) != divide(A,inverse(inverse(X_36)))
| multiply(A,inverse(X_36)) = divide(A,X_36) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_36)),X_36) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(A,inverse(X_36)) = divide(A,X_36),
inference(resolve,[$cnf( $equal(multiply(A,inverse(X_36)),divide(A,inverse(inverse(X_36)))) )],[refute_0_102,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(a1,inverse(a1)) = divide(a1,a1),
inference(subst,[],[refute_0_149:[bind(A,$fot(a1)),bind(X_36,$fot(a1))]]) ).
cnf(refute_0_151,plain,
( multiply(a1,inverse(a1)) != divide(a1,a1)
| divide(a1,a1) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(b1,inverse(b1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a1,inverse(a1)),multiply(b1,inverse(b1))) ),[0],$fot(divide(a1,a1))]]) ).
cnf(refute_0_152,plain,
( divide(a1,a1) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(b1,inverse(b1)) ),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),divide(a1,a1)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(b1,inverse(b1)) = divide(b1,b1),
inference(subst,[],[refute_0_149:[bind(A,$fot(b1)),bind(X_36,$fot(b1))]]) ).
cnf(refute_0_154,plain,
( multiply(b1,inverse(b1)) != divide(b1,b1)
| divide(a1,a1) != divide(b1,b1)
| divide(a1,a1) = multiply(b1,inverse(b1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(a1,a1),multiply(b1,inverse(b1))) ),[1],$fot(divide(b1,b1))]]) ).
cnf(refute_0_155,plain,
( divide(a1,a1) != divide(b1,b1)
| divide(a1,a1) = multiply(b1,inverse(b1)) ),
inference(resolve,[$cnf( $equal(multiply(b1,inverse(b1)),divide(b1,b1)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( divide(a1,a1) != divide(b1,b1)
| multiply(a1,inverse(a1)) = multiply(b1,inverse(b1)) ),
inference(resolve,[$cnf( $equal(divide(a1,a1),multiply(b1,inverse(b1))) )],[refute_0_155,refute_0_152]) ).
cnf(refute_0_157,plain,
divide(a1,a1) != divide(b1,b1),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(b1,inverse(b1))) )],[refute_0_156,refute_0_101]) ).
cnf(refute_0_158,plain,
inverse(inverse(multiply(X_31,inverse(X_31)))) = multiply(X_31,inverse(X_31)),
inference(subst,[],[refute_0_145:[bind(X_23,$fot(multiply(X_31,inverse(X_31))))]]) ).
cnf(refute_0_159,plain,
( multiply(B,inverse(B)) != inverse(multiply(X_31,inverse(X_31)))
| inverse(multiply(X_31,inverse(X_31))) = multiply(B,inverse(B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(B,inverse(B)))),bind(Y,$fot(inverse(multiply(X_31,inverse(X_31)))))]]) ).
cnf(refute_0_160,plain,
inverse(multiply(X_31,inverse(X_31))) = multiply(B,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(B,inverse(B)),inverse(multiply(X_31,inverse(X_31)))) )],[refute_0_120,refute_0_159]) ).
cnf(refute_0_161,plain,
( inverse(multiply(X_31,inverse(X_31))) != multiply(B,inverse(B))
| inverse(inverse(multiply(X_31,inverse(X_31)))) != multiply(X_31,inverse(X_31))
| inverse(multiply(B,inverse(B))) = multiply(X_31,inverse(X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_31,inverse(X_31)))),multiply(X_31,inverse(X_31))) ),[0,0],$fot(multiply(B,inverse(B)))]]) ).
cnf(refute_0_162,plain,
( inverse(inverse(multiply(X_31,inverse(X_31)))) != multiply(X_31,inverse(X_31))
| inverse(multiply(B,inverse(B))) = multiply(X_31,inverse(X_31)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_31,inverse(X_31))),multiply(B,inverse(B))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
inverse(multiply(B,inverse(B))) = multiply(X_31,inverse(X_31)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_31,inverse(X_31)))),multiply(X_31,inverse(X_31))) )],[refute_0_158,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(B,inverse(B)) = divide(B,B),
inference(subst,[],[refute_0_149:[bind(A,$fot(B)),bind(X_36,$fot(B))]]) ).
cnf(refute_0_165,plain,
inverse(multiply(B,inverse(B))) = multiply(B,inverse(B)),
inference(subst,[],[refute_0_160:[bind(X_31,$fot(B))]]) ).
cnf(refute_0_166,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_167,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_166]) ).
cnf(refute_0_168,plain,
( multiply(B,inverse(B)) != divide(B,B)
| inverse(multiply(B,inverse(B))) != multiply(B,inverse(B))
| inverse(multiply(B,inverse(B))) = divide(B,B) ),
inference(subst,[],[refute_0_167:[bind(X,$fot(inverse(multiply(B,inverse(B))))),bind(Y,$fot(multiply(B,inverse(B)))),bind(Z,$fot(divide(B,B)))]]) ).
cnf(refute_0_169,plain,
( multiply(B,inverse(B)) != divide(B,B)
| inverse(multiply(B,inverse(B))) = divide(B,B) ),
inference(resolve,[$cnf( $equal(inverse(multiply(B,inverse(B))),multiply(B,inverse(B))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
inverse(multiply(B,inverse(B))) = divide(B,B),
inference(resolve,[$cnf( $equal(multiply(B,inverse(B)),divide(B,B)) )],[refute_0_164,refute_0_169]) ).
cnf(refute_0_171,plain,
( inverse(multiply(B,inverse(B))) != multiply(X_31,inverse(X_31))
| inverse(multiply(B,inverse(B))) != divide(B,B)
| divide(B,B) = multiply(X_31,inverse(X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(B,inverse(B))),multiply(X_31,inverse(X_31))) ),[0],$fot(divide(B,B))]]) ).
cnf(refute_0_172,plain,
( inverse(multiply(B,inverse(B))) != multiply(X_31,inverse(X_31))
| divide(B,B) = multiply(X_31,inverse(X_31)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(B,inverse(B))),divide(B,B)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(X_31,inverse(X_31)) = divide(X_31,X_31),
inference(subst,[],[refute_0_149:[bind(A,$fot(X_31)),bind(X_36,$fot(X_31))]]) ).
cnf(refute_0_174,plain,
( multiply(X_31,inverse(X_31)) != divide(X_31,X_31)
| divide(B,B) != multiply(X_31,inverse(X_31))
| divide(B,B) = divide(X_31,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(divide(B,B),multiply(X_31,inverse(X_31))) ),[1],$fot(divide(X_31,X_31))]]) ).
cnf(refute_0_175,plain,
( divide(B,B) != multiply(X_31,inverse(X_31))
| divide(B,B) = divide(X_31,X_31) ),
inference(resolve,[$cnf( $equal(multiply(X_31,inverse(X_31)),divide(X_31,X_31)) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
( inverse(multiply(B,inverse(B))) != multiply(X_31,inverse(X_31))
| divide(B,B) = divide(X_31,X_31) ),
inference(resolve,[$cnf( $equal(divide(B,B),multiply(X_31,inverse(X_31))) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
divide(B,B) = divide(X_31,X_31),
inference(resolve,[$cnf( $equal(inverse(multiply(B,inverse(B))),multiply(X_31,inverse(X_31))) )],[refute_0_163,refute_0_176]) ).
cnf(refute_0_178,plain,
( divide(B,B) != divide(X_31,X_31)
| divide(X_31,X_31) = divide(B,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(divide(B,B))),bind(Y,$fot(divide(X_31,X_31)))]]) ).
cnf(refute_0_179,plain,
divide(X_31,X_31) = divide(B,B),
inference(resolve,[$cnf( $equal(divide(B,B),divide(X_31,X_31)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
divide(a1,a1) = divide(b1,b1),
inference(subst,[],[refute_0_179:[bind(B,$fot(b1)),bind(X_31,$fot(a1))]]) ).
cnf(refute_0_181,plain,
$false,
inference(resolve,[$cnf( $equal(divide(a1,a1),divide(b1,b1)) )],[refute_0_180,refute_0_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP557-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 23:54:23 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.43
% 0.22/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.47
%------------------------------------------------------------------------------