TSTP Solution File: GRP513-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP513-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 10:42:03 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 60
% Syntax : Number of clauses : 219 ( 115 unt; 0 nHn; 101 RR)
% Number of literals : 372 ( 371 equ; 156 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 624 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(refute_0_0,plain,
multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2))))))) = B,
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))))]]) ).
cnf(refute_0_1,plain,
multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))) = X_1,
inference(subst,[],[single_axiom:[bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_2,plain,
( multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2))))))) != B
| multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))) != X_1
| multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2))))))),B) ),[0,1,1,0],$fot(X_1)]]) ).
cnf(refute_0_3,plain,
( multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2))))))) != B
| multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))) = B ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),X_1) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2))))))),B) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(A,multiply(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))) = multiply(A,X_2),
inference(subst,[],[refute_0_4:[bind(B,$fot(multiply(A,X_2)))]]) ).
cnf(refute_0_6,plain,
multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B,
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(X_8,inverse(X_8))))]]) ).
cnf(refute_0_7,plain,
multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B,
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))))]]) ).
cnf(refute_0_8,plain,
multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) = X_1,
inference(subst,[],[single_axiom:[bind(A,$fot(B)),bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_9,plain,
( multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) != X_1
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) ),[0,1,0],$fot(X_1)]]) ).
cnf(refute_0_10,plain,
( multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B ),
inference(resolve,[$cnf( $equal(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),X_1) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))) = X_4,
inference(subst,[],[refute_0_11:[bind(A,$fot(X_4)),bind(B,$fot(X_4)),bind(X_1,$fot(X_5)),bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_13,plain,
multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6)))) = X_5,
inference(subst,[],[single_axiom:[bind(A,$fot(X_4)),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_14,plain,
( multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))) != X_4
| multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6)))) != X_5
| multiply(X_4,multiply(X_5,inverse(X_5))) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))),X_4) ),[0,1,1,0],$fot(X_5)]]) ).
cnf(refute_0_15,plain,
( multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))) != X_4
| multiply(X_4,multiply(X_5,inverse(X_5))) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6)))),X_5) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(X_4,multiply(X_5,inverse(X_5))) = X_4,
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))),X_4) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(B,multiply(X_8,inverse(X_8))) = B,
inference(subst,[],[refute_0_16:[bind(X_4,$fot(B)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_18,plain,
( multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(B,multiply(X_8,inverse(X_8))) != B
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) ),[0,1,0],$fot(B)]]) ).
cnf(refute_0_19,plain,
( multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B ),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_8,inverse(X_8))),B) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) )],[refute_0_6,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(A,multiply(X_8,inverse(X_8))) = A,
inference(subst,[],[refute_0_16:[bind(X_4,$fot(A)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_22,plain,
inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(multiply(A,multiply(X_8,inverse(X_8)))),
introduced(tautology,[refl,[$fot(inverse(multiply(A,multiply(X_8,inverse(X_8)))))]]) ).
cnf(refute_0_23,plain,
( multiply(A,multiply(X_8,inverse(X_8))) != A
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) != inverse(multiply(A,multiply(X_8,inverse(X_8))))
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(A,multiply(X_8,inverse(X_8)))),inverse(multiply(A,multiply(X_8,inverse(X_8))))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_24,plain,
( multiply(A,multiply(X_8,inverse(X_8))) != A
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(A) ),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_8,inverse(X_8)))),inverse(multiply(A,multiply(X_8,inverse(X_8))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(A),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_8,inverse(X_8))),A) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),
introduced(tautology,[refl,[$fot(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))]]) ).
cnf(refute_0_27,plain,
( multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) != multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) != inverse(A)
| multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) ),[1,1],$fot(inverse(A))]]) ).
cnf(refute_0_28,plain,
( inverse(multiply(A,multiply(X_8,inverse(X_8)))) != inverse(A)
| multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(A)) ),
inference(resolve,[$cnf( $equal(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(A)),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_8,inverse(X_8)))),inverse(A)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))))]]) ).
cnf(refute_0_31,plain,
( multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))
| multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) != multiply(B,inverse(A))
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))) ),[1,1],$fot(multiply(B,inverse(A)))]]) ).
cnf(refute_0_32,plain,
( multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) != multiply(B,inverse(A))
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(A))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(A))),
inference(resolve,[$cnf( $equal(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),multiply(B,inverse(A))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(B,inverse(A)))
| multiply(A,multiply(B,inverse(A))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) ),[0],$fot(multiply(A,multiply(B,inverse(A))))]]) ).
cnf(refute_0_35,plain,
( multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(A,multiply(B,inverse(A))) = B ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(B,inverse(A)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) )],[refute_0_20,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))) = multiply(X_1,X_2),
inference(subst,[],[refute_0_36:[bind(A,$fot(multiply(A,X_2))),bind(B,$fot(multiply(X_1,X_2)))]]) ).
cnf(refute_0_38,plain,
( multiply(A,multiply(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))) != multiply(A,X_2)
| multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))) != multiply(X_1,X_2)
| multiply(A,multiply(multiply(X_1,X_2),inverse(X_1))) = multiply(A,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))),multiply(A,X_2)) ),[0,1,0],$fot(multiply(X_1,X_2))]]) ).
cnf(refute_0_39,plain,
( multiply(A,multiply(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))) != multiply(A,X_2)
| multiply(A,multiply(multiply(X_1,X_2),inverse(X_1))) = multiply(A,X_2) ),
inference(resolve,[$cnf( $equal(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),multiply(X_1,X_2)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(A,multiply(multiply(X_1,X_2),inverse(X_1))) = multiply(A,X_2),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))),multiply(A,X_2)) )],[refute_0_5,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(A,multiply(multiply(X_1,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),inverse(X_1))) = multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),
inference(subst,[],[refute_0_40:[bind(X_2,$fot(multiply(X_39,inverse(multiply(X_39,inverse(X_1))))))]]) ).
cnf(refute_0_42,plain,
multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B,
inference(subst,[],[refute_0_11:[bind(A,$fot(multiply(B,X_2)))]]) ).
cnf(refute_0_43,plain,
multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) = multiply(X_1,X_2),
inference(subst,[],[refute_0_36:[bind(A,$fot(multiply(B,X_2))),bind(B,$fot(multiply(X_1,X_2)))]]) ).
cnf(refute_0_44,plain,
( multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) != multiply(X_1,X_2)
| multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(X_1,X_2)))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) ),[0,1,1,0],$fot(multiply(X_1,X_2))]]) ).
cnf(refute_0_45,plain,
( multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(X_1,X_2)))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),multiply(X_1,X_2)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(X_1,X_2)))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(multiply(multiply(X_18,X_20),multiply(X_19,inverse(multiply(X_19,X_20))))))) = B,
inference(subst,[],[refute_0_46:[bind(X_1,$fot(multiply(X_18,X_20))),bind(X_2,$fot(multiply(X_19,inverse(multiply(X_19,X_20)))))]]) ).
cnf(refute_0_48,plain,
multiply(multiply(X_18,X_20),multiply(X_19,inverse(multiply(X_19,X_20)))) = X_18,
inference(subst,[],[refute_0_46:[bind(B,$fot(X_18)),bind(X_1,$fot(X_19)),bind(X_2,$fot(X_20))]]) ).
cnf(refute_0_49,plain,
( multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(multiply(multiply(X_18,X_20),multiply(X_19,inverse(multiply(X_19,X_20))))))) != B
| multiply(multiply(X_18,X_20),multiply(X_19,inverse(multiply(X_19,X_20)))) != X_18
| multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(multiply(multiply(X_18,X_20),multiply(X_19,inverse(multiply(X_19,X_20))))))),B) ),[0,1,1,0],$fot(X_18)]]) ).
cnf(refute_0_50,plain,
( multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(multiply(multiply(X_18,X_20),multiply(X_19,inverse(multiply(X_19,X_20))))))) != B
| multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_18,X_20),multiply(X_19,inverse(multiply(X_19,X_20)))),X_18) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(multiply(multiply(X_18,X_20),multiply(X_19,inverse(multiply(X_19,X_20))))))),B) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))) = multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),X_20),
inference(subst,[],[refute_0_40:[bind(A,$fot(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))))),bind(X_1,$fot(X_18)),bind(X_2,$fot(X_20))]]) ).
cnf(refute_0_53,plain,
( multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))) != B
| multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))) != multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),X_20)
| multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),X_20) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))),B) ),[0],$fot(multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),X_20))]]) ).
cnf(refute_0_54,plain,
( multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))) != B
| multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),X_20) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))),multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),X_20)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),X_20) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_19,inverse(multiply(X_19,X_20)))),multiply(multiply(X_18,X_20),inverse(X_18))),B) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(multiply(X_1,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),inverse(X_1)) = X_1,
inference(subst,[],[refute_0_55:[bind(B,$fot(X_1)),bind(X_19,$fot(X_39)),bind(X_20,$fot(inverse(X_1)))]]) ).
cnf(refute_0_57,plain,
( multiply(A,multiply(multiply(X_1,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),inverse(X_1))) != multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1)))))
| multiply(multiply(X_1,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),inverse(X_1)) != X_1
| multiply(A,X_1) = multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(X_1,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),inverse(X_1))),multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1)))))) ),[0,1],$fot(X_1)]]) ).
cnf(refute_0_58,plain,
( multiply(A,multiply(multiply(X_1,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),inverse(X_1))) != multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1)))))
| multiply(A,X_1) = multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_1,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),inverse(X_1)),X_1) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(A,X_1) = multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(X_1,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),inverse(X_1))),multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1)))))) )],[refute_0_41,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(A,multiply(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),inverse(A))) = multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),
inference(subst,[],[refute_0_36:[bind(B,$fot(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A)))))))]]) ).
cnf(refute_0_61,plain,
multiply(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),inverse(A)) = X_38,
inference(subst,[],[refute_0_55:[bind(B,$fot(X_38)),bind(X_19,$fot(X_39)),bind(X_20,$fot(inverse(A)))]]) ).
cnf(refute_0_62,plain,
( multiply(A,multiply(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),inverse(A))) != multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A)))))
| multiply(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),inverse(A)) != X_38
| multiply(A,X_38) = multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),inverse(A))),multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A)))))) ),[0,1],$fot(X_38)]]) ).
cnf(refute_0_63,plain,
( multiply(A,multiply(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),inverse(A))) != multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A)))))
| multiply(A,X_38) = multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),inverse(A)),X_38) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(A,X_38) = multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))),inverse(A))),multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A)))))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_66,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_67,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( multiply(A,X_38) != multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A)))))
| multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))) = multiply(A,X_38) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(multiply(A,X_38))),bind(Y,$fot(multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A)))))))]]) ).
cnf(refute_0_69,plain,
multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A))))) = multiply(A,X_38),
inference(resolve,[$cnf( $equal(multiply(A,X_38),multiply(X_38,multiply(X_39,inverse(multiply(X_39,inverse(A)))))) )],[refute_0_64,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))) = multiply(X_1,A),
inference(subst,[],[refute_0_69:[bind(A,$fot(X_1)),bind(X_38,$fot(A))]]) ).
cnf(refute_0_71,plain,
( multiply(A,X_1) != multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1)))))
| multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))) != multiply(X_1,A)
| multiply(A,X_1) = multiply(X_1,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,X_1),multiply(X_1,A)) ),[0],$fot(multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))))]]) ).
cnf(refute_0_72,plain,
( multiply(A,X_1) != multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1)))))
| multiply(A,X_1) = multiply(X_1,A) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1))))),multiply(X_1,A)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(A,X_1) = multiply(X_1,A),
inference(resolve,[$cnf( $equal(multiply(A,X_1),multiply(A,multiply(X_39,inverse(multiply(X_39,inverse(X_1)))))) )],[refute_0_59,refute_0_72]) ).
cnf(refute_0_74,plain,
( multiply(A,X_1) != multiply(X_1,A)
| multiply(X_1,A) = multiply(A,X_1) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(multiply(A,X_1))),bind(Y,$fot(multiply(X_1,A)))]]) ).
cnf(refute_0_75,plain,
multiply(X_1,A) = multiply(A,X_1),
inference(resolve,[$cnf( $equal(multiply(A,X_1),multiply(X_1,A)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(subst,[],[refute_0_75:[bind(A,$fot(a1)),bind(X_1,$fot(inverse(a1)))]]) ).
cnf(refute_0_77,plain,
( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) != multiply(a1,inverse(a1))
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a1),a1),multiply(a1,inverse(a1))) ),[1],$fot(multiply(inverse(b1),b1))]]) ).
cnf(refute_0_78,plain,
( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(a1,inverse(a1))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(b1),b1) = multiply(b1,inverse(b1)),
inference(subst,[],[refute_0_75:[bind(A,$fot(b1)),bind(X_1,$fot(inverse(b1)))]]) ).
cnf(refute_0_80,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(inverse(b1),b1) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a1,inverse(a1)),multiply(inverse(b1),b1)) ),[1],$fot(multiply(b1,inverse(b1)))]]) ).
cnf(refute_0_81,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b1),b1),multiply(b1,inverse(b1))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(inverse(b1),b1)) )],[refute_0_81,refute_0_78]) ).
cnf(refute_0_83,plain,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) )],[refute_0_82,prove_these_axioms_1]) ).
cnf(refute_0_84,plain,
multiply(multiply(X_44,inverse(X_44)),multiply(X_5,inverse(X_5))) = multiply(X_44,inverse(X_44)),
inference(subst,[],[refute_0_16:[bind(X_4,$fot(multiply(X_44,inverse(X_44))))]]) ).
cnf(refute_0_85,plain,
multiply(X_4,multiply(X_5,inverse(X_5))) = multiply(multiply(X_5,inverse(X_5)),X_4),
inference(subst,[],[refute_0_73:[bind(A,$fot(X_4)),bind(X_1,$fot(multiply(X_5,inverse(X_5))))]]) ).
cnf(refute_0_86,plain,
( multiply(X_4,multiply(X_5,inverse(X_5))) != X_4
| multiply(X_4,multiply(X_5,inverse(X_5))) != multiply(multiply(X_5,inverse(X_5)),X_4)
| multiply(multiply(X_5,inverse(X_5)),X_4) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_4,multiply(X_5,inverse(X_5))),X_4) ),[0],$fot(multiply(multiply(X_5,inverse(X_5)),X_4))]]) ).
cnf(refute_0_87,plain,
( multiply(X_4,multiply(X_5,inverse(X_5))) != X_4
| multiply(multiply(X_5,inverse(X_5)),X_4) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(X_5,inverse(X_5))),multiply(multiply(X_5,inverse(X_5)),X_4)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(multiply(X_5,inverse(X_5)),X_4) = X_4,
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(X_5,inverse(X_5))),X_4) )],[refute_0_16,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(multiply(X_44,inverse(X_44)),multiply(X_5,inverse(X_5))) = multiply(X_5,inverse(X_5)),
inference(subst,[],[refute_0_88:[bind(X_4,$fot(multiply(X_5,inverse(X_5)))),bind(X_5,$fot(X_44))]]) ).
cnf(refute_0_90,plain,
( multiply(multiply(X_44,inverse(X_44)),multiply(X_5,inverse(X_5))) != multiply(X_44,inverse(X_44))
| multiply(multiply(X_44,inverse(X_44)),multiply(X_5,inverse(X_5))) != multiply(X_5,inverse(X_5))
| multiply(X_5,inverse(X_5)) = multiply(X_44,inverse(X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_5,inverse(X_5))),multiply(X_44,inverse(X_44))) ),[0],$fot(multiply(X_5,inverse(X_5)))]]) ).
cnf(refute_0_91,plain,
( multiply(multiply(X_44,inverse(X_44)),multiply(X_5,inverse(X_5))) != multiply(X_44,inverse(X_44))
| multiply(X_5,inverse(X_5)) = multiply(X_44,inverse(X_44)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_5,inverse(X_5))),multiply(X_5,inverse(X_5))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(X_5,inverse(X_5)) = multiply(X_44,inverse(X_44)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_5,inverse(X_5))),multiply(X_44,inverse(X_44))) )],[refute_0_84,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(a1,inverse(a1)) = multiply(X_48,inverse(X_48)),
inference(subst,[],[refute_0_92:[bind(X_44,$fot(X_48)),bind(X_5,$fot(a1))]]) ).
cnf(refute_0_94,plain,
( multiply(X_48,inverse(X_48)) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) != multiply(X_48,inverse(X_48))
| multiply(a1,inverse(a1)) = multiply(b1,inverse(b1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(X_48,inverse(X_48))) ),[1],$fot(multiply(b1,inverse(b1)))]]) ).
cnf(refute_0_95,plain,
( multiply(X_48,inverse(X_48)) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(b1,inverse(b1)) ),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(X_48,inverse(X_48))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(X_48,inverse(X_48)) != multiply(b1,inverse(b1)),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(b1,inverse(b1))) )],[refute_0_95,refute_0_83]) ).
cnf(refute_0_97,plain,
multiply(multiply(B,X_2),multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))) = B,
inference(subst,[],[refute_0_46:[bind(X_1,$fot(multiply(X_44,inverse(X_44))))]]) ).
cnf(refute_0_98,plain,
multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = inverse(multiply(multiply(X_44,inverse(X_44)),X_2)),
inference(subst,[],[refute_0_88:[bind(X_4,$fot(inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))),bind(X_5,$fot(X_44))]]) ).
cnf(refute_0_99,plain,
( multiply(multiply(B,X_2),multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))) != B
| multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != inverse(multiply(multiply(X_44,inverse(X_44)),X_2))
| multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,X_2),multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))),B) ),[0,1],$fot(inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))]]) ).
cnf(refute_0_100,plain,
( multiply(multiply(B,X_2),multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))) != B
| multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))),B) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(multiply(B,X_2),inverse(X_2)) = multiply(inverse(X_2),multiply(B,X_2)),
inference(subst,[],[refute_0_75:[bind(A,$fot(inverse(X_2))),bind(X_1,$fot(multiply(B,X_2)))]]) ).
cnf(refute_0_103,plain,
multiply(multiply(X_44,inverse(X_44)),X_2) = X_2,
inference(subst,[],[refute_0_88:[bind(X_4,$fot(X_2)),bind(X_5,$fot(X_44))]]) ).
cnf(refute_0_104,plain,
inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) = inverse(multiply(multiply(X_44,inverse(X_44)),X_2)),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))]]) ).
cnf(refute_0_105,plain,
( multiply(multiply(X_44,inverse(X_44)),X_2) != X_2
| inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) != inverse(multiply(multiply(X_44,inverse(X_44)),X_2))
| inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) = inverse(X_2) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(X_44,inverse(X_44)),X_2)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) ),[1,0],$fot(X_2)]]) ).
cnf(refute_0_106,plain,
( multiply(multiply(X_44,inverse(X_44)),X_2) != X_2
| inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) = inverse(X_2) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_44,inverse(X_44)),X_2)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) = inverse(X_2),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),X_2),X_2) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),
introduced(tautology,[refl,[$fot(multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))))]]) ).
cnf(refute_0_109,plain,
( multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))
| inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) != inverse(X_2)
| multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(multiply(B,X_2),inverse(X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))) ),[1,1],$fot(inverse(X_2))]]) ).
cnf(refute_0_110,plain,
( inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) != inverse(X_2)
| multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(multiply(B,X_2),inverse(X_2)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(multiply(B,X_2),inverse(X_2)),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_44,inverse(X_44)),X_2)),inverse(X_2)) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_113,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_67,refute_0_112]) ).
cnf(refute_0_114,plain,
( multiply(multiply(B,X_2),inverse(X_2)) != multiply(inverse(X_2),multiply(B,X_2))
| multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != multiply(multiply(B,X_2),inverse(X_2))
| multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(inverse(X_2),multiply(B,X_2)) ),
inference(subst,[],[refute_0_113:[bind(X,$fot(multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))))),bind(Y,$fot(multiply(multiply(B,X_2),inverse(X_2)))),bind(Z,$fot(multiply(inverse(X_2),multiply(B,X_2))))]]) ).
cnf(refute_0_115,plain,
( multiply(multiply(B,X_2),inverse(X_2)) != multiply(inverse(X_2),multiply(B,X_2))
| multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(inverse(X_2),multiply(B,X_2)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),multiply(multiply(B,X_2),inverse(X_2))) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(inverse(X_2),multiply(B,X_2)),
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),inverse(X_2)),multiply(inverse(X_2),multiply(B,X_2))) )],[refute_0_102,refute_0_115]) ).
cnf(refute_0_117,plain,
( multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != B
| multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != multiply(inverse(X_2),multiply(B,X_2))
| multiply(inverse(X_2),multiply(B,X_2)) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),B) ),[0],$fot(multiply(inverse(X_2),multiply(B,X_2)))]]) ).
cnf(refute_0_118,plain,
( multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != B
| multiply(inverse(X_2),multiply(B,X_2)) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),multiply(inverse(X_2),multiply(B,X_2))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
multiply(inverse(X_2),multiply(B,X_2)) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),B) )],[refute_0_101,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(inverse(X_47),multiply(multiply(X_5,inverse(X_5)),X_47)) = multiply(X_5,inverse(X_5)),
inference(subst,[],[refute_0_119:[bind(B,$fot(multiply(X_5,inverse(X_5)))),bind(X_2,$fot(X_47))]]) ).
cnf(refute_0_121,plain,
multiply(multiply(X_5,inverse(X_5)),X_47) = X_47,
inference(subst,[],[refute_0_88:[bind(X_4,$fot(X_47))]]) ).
cnf(refute_0_122,plain,
( multiply(multiply(X_5,inverse(X_5)),X_47) != X_47
| multiply(inverse(X_47),multiply(multiply(X_5,inverse(X_5)),X_47)) != multiply(X_5,inverse(X_5))
| multiply(inverse(X_47),X_47) = multiply(X_5,inverse(X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_47),multiply(multiply(X_5,inverse(X_5)),X_47)),multiply(X_5,inverse(X_5))) ),[0,1],$fot(X_47)]]) ).
cnf(refute_0_123,plain,
( multiply(inverse(X_47),multiply(multiply(X_5,inverse(X_5)),X_47)) != multiply(X_5,inverse(X_5))
| multiply(inverse(X_47),X_47) = multiply(X_5,inverse(X_5)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_5,inverse(X_5)),X_47),X_47) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(inverse(X_47),X_47) = multiply(X_5,inverse(X_5)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),multiply(multiply(X_5,inverse(X_5)),X_47)),multiply(X_5,inverse(X_5))) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
multiply(A,multiply(multiply(X_1,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))),inverse(X_1))) = multiply(A,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))),
inference(subst,[],[refute_0_40:[bind(X_2,$fot(multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))))]]) ).
cnf(refute_0_126,plain,
multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(multiply(X_9,multiply(X_5,inverse(X_5)))))),inverse(X_11))) = X_10,
inference(subst,[],[refute_0_4:[bind(A,$fot(X_9)),bind(B,$fot(X_10)),bind(X_1,$fot(X_11)),bind(X_2,$fot(multiply(X_5,inverse(X_5))))]]) ).
cnf(refute_0_127,plain,
multiply(X_9,multiply(X_5,inverse(X_5))) = X_9,
inference(subst,[],[refute_0_16:[bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_128,plain,
( multiply(X_9,multiply(X_5,inverse(X_5))) != X_9
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(multiply(X_9,multiply(X_5,inverse(X_5)))))),inverse(X_11))) != X_10
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(multiply(X_9,multiply(X_5,inverse(X_5)))))),inverse(X_11))),X_10) ),[0,1,0,1,1,0],$fot(X_9)]]) ).
cnf(refute_0_129,plain,
( multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(multiply(X_9,multiply(X_5,inverse(X_5)))))),inverse(X_11))) != X_10
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = X_10 ),
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(X_5,inverse(X_5))),X_9) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = X_10,
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(multiply(X_9,multiply(X_5,inverse(X_5)))))),inverse(X_11))),X_10) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(X_11,multiply(X_5,inverse(X_5))) = X_11,
inference(subst,[],[refute_0_16:[bind(X_4,$fot(X_11))]]) ).
cnf(refute_0_132,plain,
multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) = multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)),
introduced(tautology,[refl,[$fot(multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)))]]) ).
cnf(refute_0_133,plain,
( multiply(X_11,multiply(X_5,inverse(X_5))) != X_11
| multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) != multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))
| multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) = multiply(X_11,inverse(X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)),multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) ),[1,0],$fot(X_11)]]) ).
cnf(refute_0_134,plain,
( multiply(X_11,multiply(X_5,inverse(X_5))) != X_11
| multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) = multiply(X_11,inverse(X_9)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)),multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) = multiply(X_11,inverse(X_9)),
inference(resolve,[$cnf( $equal(multiply(X_11,multiply(X_5,inverse(X_5))),X_11) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) = multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),
introduced(tautology,[refl,[$fot(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))))]]) ).
cnf(refute_0_137,plain,
( multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) != multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)))
| multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) != multiply(X_11,inverse(X_9))
| multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) = multiply(X_10,multiply(X_11,inverse(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)))) ),[1,1],$fot(multiply(X_11,inverse(X_9)))]]) ).
cnf(refute_0_138,plain,
( multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) != multiply(X_11,inverse(X_9))
| multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) = multiply(X_10,multiply(X_11,inverse(X_9))) ),
inference(resolve,[$cnf( $equal(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) = multiply(X_10,multiply(X_11,inverse(X_9))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)),multiply(X_11,inverse(X_9))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) = multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)),
introduced(tautology,[refl,[$fot(multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)))]]) ).
cnf(refute_0_141,plain,
( multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) != multiply(X_10,multiply(X_11,inverse(X_9)))
| multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) != multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))
| multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) = multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)),multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) ),[1,0],$fot(multiply(X_10,multiply(X_11,inverse(X_9))))]]) ).
cnf(refute_0_142,plain,
( multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) != multiply(X_10,multiply(X_11,inverse(X_9)))
| multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) = multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)),multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) = multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)),
inference(resolve,[$cnf( $equal(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),multiply(X_10,multiply(X_11,inverse(X_9)))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),
introduced(tautology,[refl,[$fot(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))))]]) ).
cnf(refute_0_145,plain,
( multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) != multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)))
| multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) != multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)))) ),[1,1],$fot(multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)))]]) ).
cnf(refute_0_146,plain,
( multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) != multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) ),
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)),multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
( multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) != X_10
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) != multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)))
| multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),X_10) ),[0],$fot(multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))))]]) ).
cnf(refute_0_149,plain,
( multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) != X_10
| multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) = X_10 ),
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) = X_10,
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),X_10) )],[refute_0_130,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_15,multiply(X_9,inverse(X_10))),inverse(X_9))),inverse(multiply(X_15,multiply(X_9,inverse(X_10)))))) = X_10,
inference(subst,[],[refute_0_150:[bind(X_11,$fot(multiply(X_15,multiply(X_9,inverse(X_10)))))]]) ).
cnf(refute_0_152,plain,
multiply(X_10,multiply(multiply(X_15,multiply(X_9,inverse(X_10))),inverse(X_9))) = X_15,
inference(subst,[],[refute_0_150:[bind(X_10,$fot(X_15)),bind(X_11,$fot(X_9)),bind(X_9,$fot(X_10))]]) ).
cnf(refute_0_153,plain,
( multiply(X_10,multiply(multiply(X_15,multiply(X_9,inverse(X_10))),inverse(X_9))) != X_15
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_15,multiply(X_9,inverse(X_10))),inverse(X_9))),inverse(multiply(X_15,multiply(X_9,inverse(X_10)))))) != X_10
| multiply(X_9,multiply(X_15,inverse(multiply(X_15,multiply(X_9,inverse(X_10)))))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_15,multiply(X_9,inverse(X_10))),inverse(X_9))),inverse(multiply(X_15,multiply(X_9,inverse(X_10)))))),X_10) ),[0,1,0],$fot(X_15)]]) ).
cnf(refute_0_154,plain,
( multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_15,multiply(X_9,inverse(X_10))),inverse(X_9))),inverse(multiply(X_15,multiply(X_9,inverse(X_10)))))) != X_10
| multiply(X_9,multiply(X_15,inverse(multiply(X_15,multiply(X_9,inverse(X_10)))))) = X_10 ),
inference(resolve,[$cnf( $equal(multiply(X_10,multiply(multiply(X_15,multiply(X_9,inverse(X_10))),inverse(X_9))),X_15) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
multiply(X_9,multiply(X_15,inverse(multiply(X_15,multiply(X_9,inverse(X_10)))))) = X_10,
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_15,multiply(X_9,inverse(X_10))),inverse(X_9))),inverse(multiply(X_15,multiply(X_9,inverse(X_10)))))),X_10) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(X_1,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))) = X_27,
inference(subst,[],[refute_0_155:[bind(X_10,$fot(X_27)),bind(X_15,$fot(X_28)),bind(X_9,$fot(X_1))]]) ).
cnf(refute_0_157,plain,
( multiply(A,multiply(multiply(X_1,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))),inverse(X_1))) != multiply(A,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27))))))
| multiply(X_1,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))) != X_27
| multiply(A,multiply(X_27,inverse(X_1))) = multiply(A,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(X_1,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))),inverse(X_1))),multiply(A,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27))))))) ),[0,1,0],$fot(X_27)]]) ).
cnf(refute_0_158,plain,
( multiply(A,multiply(multiply(X_1,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))),inverse(X_1))) != multiply(A,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27))))))
| multiply(A,multiply(X_27,inverse(X_1))) = multiply(A,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))) ),
inference(resolve,[$cnf( $equal(multiply(X_1,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))),X_27) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(A,multiply(X_27,inverse(X_1))) = multiply(A,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(X_1,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27)))))),inverse(X_1))),multiply(A,multiply(X_28,inverse(multiply(X_28,multiply(X_1,inverse(X_27))))))) )],[refute_0_125,refute_0_158]) ).
cnf(refute_0_160,plain,
multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,multiply(X_33,inverse(multiply(X_33,multiply(multiply(X_32,X_2),inverse(X_32)))))),
inference(subst,[],[refute_0_159:[bind(A,$fot(X_30)),bind(X_1,$fot(multiply(X_32,X_2))),bind(X_27,$fot(X_32)),bind(X_28,$fot(X_33))]]) ).
cnf(refute_0_161,plain,
multiply(X_33,multiply(multiply(X_32,X_2),inverse(X_32))) = multiply(X_33,X_2),
inference(subst,[],[refute_0_40:[bind(A,$fot(X_33)),bind(X_1,$fot(X_32))]]) ).
cnf(refute_0_162,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,multiply(X_33,inverse(multiply(X_33,multiply(multiply(X_32,X_2),inverse(X_32))))))
| multiply(X_33,multiply(multiply(X_32,X_2),inverse(X_32))) != multiply(X_33,X_2)
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_30,multiply(X_33,inverse(multiply(X_33,multiply(multiply(X_32,X_2),inverse(X_32))))))) ),[1,1,1,0],$fot(multiply(X_33,X_2))]]) ).
cnf(refute_0_163,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,multiply(X_33,inverse(multiply(X_33,multiply(multiply(X_32,X_2),inverse(X_32))))))
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2)))) ),
inference(resolve,[$cnf( $equal(multiply(X_33,multiply(multiply(X_32,X_2),inverse(X_32))),multiply(X_33,X_2)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2)))),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_30,multiply(X_33,inverse(multiply(X_33,multiply(multiply(X_32,X_2),inverse(X_32))))))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2)))) = multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30),
inference(subst,[],[refute_0_73:[bind(A,$fot(X_30)),bind(X_1,$fot(multiply(X_33,inverse(multiply(X_33,X_2)))))]]) ).
cnf(refute_0_166,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2))))
| multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2)))) != multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)) ),[0],$fot(multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2)))))]]) ).
cnf(refute_0_167,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2))))
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) ),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2)))),multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_30,multiply(X_33,inverse(multiply(X_33,X_2))))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))),
inference(subst,[],[refute_0_164:[bind(X_33,$fot(multiply(X_44,inverse(X_44))))]]) ).
cnf(refute_0_170,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))))
| multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != inverse(multiply(multiply(X_44,inverse(X_44)),X_2))
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_30,multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))))) ),[1,1],$fot(inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))]]) ).
cnf(refute_0_171,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))))
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) )],[refute_0_98,refute_0_170]) ).
cnf(refute_0_172,plain,
multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_30,multiply(multiply(X_44,inverse(X_44)),inverse(multiply(multiply(X_44,inverse(X_44)),X_2))))) )],[refute_0_169,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),
introduced(tautology,[refl,[$fot(multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))))]]) ).
cnf(refute_0_174,plain,
( multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))
| inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) != inverse(X_2)
| multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(X_30,inverse(X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))) ),[1,1],$fot(inverse(X_2))]]) ).
cnf(refute_0_175,plain,
( inverse(multiply(multiply(X_44,inverse(X_44)),X_2)) != inverse(X_2)
| multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(X_30,inverse(X_2)) ),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) = multiply(X_30,inverse(X_2)),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_44,inverse(X_44)),X_2)),inverse(X_2)) )],[refute_0_107,refute_0_175]) ).
cnf(refute_0_177,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))
| multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))) != multiply(X_30,inverse(X_2))
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,inverse(X_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_30,inverse(X_2))) ),[0],$fot(multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))))]]) ).
cnf(refute_0_178,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,inverse(X_2)) ),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2))),multiply(X_30,inverse(X_2))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_30,inverse(X_2)),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_30,inverse(multiply(multiply(X_44,inverse(X_44)),X_2)))) )],[refute_0_172,refute_0_178]) ).
cnf(refute_0_180,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_30,inverse(X_2))
| multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)
| multiply(X_30,inverse(X_2)) = multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)) ),[0],$fot(multiply(X_30,inverse(X_2)))]]) ).
cnf(refute_0_181,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)
| multiply(X_30,inverse(X_2)) = multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) ),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_30,inverse(X_2))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))) = multiply(X_33,inverse(multiply(X_33,X_2))),
inference(subst,[],[refute_0_88:[bind(X_4,$fot(multiply(X_33,inverse(multiply(X_33,X_2))))),bind(X_5,$fot(X_44))]]) ).
cnf(refute_0_183,plain,
multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))),
inference(subst,[],[refute_0_164:[bind(X_30,$fot(multiply(X_44,inverse(X_44))))]]) ).
cnf(refute_0_184,plain,
( multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2))))
| multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))) = multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))))),bind(Y,$fot(multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2))))))]]) ).
cnf(refute_0_185,plain,
multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))) = multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2))))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
( multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))) != multiply(X_33,inverse(multiply(X_33,X_2)))
| multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))) != multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2))))
| multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_33,inverse(multiply(X_33,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))),multiply(X_33,inverse(multiply(X_33,X_2)))) ),[0],$fot(multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))))]]) ).
cnf(refute_0_187,plain,
( multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))) != multiply(X_33,inverse(multiply(X_33,X_2)))
| multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_33,inverse(multiply(X_33,X_2))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))),multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2))))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(X_33,inverse(multiply(X_33,X_2))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_33,inverse(multiply(X_33,X_2)))),multiply(X_33,inverse(multiply(X_33,X_2)))) )],[refute_0_182,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(multiply(X_44,inverse(X_44)),inverse(X_2)) = inverse(X_2),
inference(subst,[],[refute_0_88:[bind(X_4,$fot(inverse(X_2))),bind(X_5,$fot(X_44))]]) ).
cnf(refute_0_190,plain,
multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) = multiply(multiply(X_44,inverse(X_44)),inverse(X_2)),
inference(subst,[],[refute_0_179:[bind(X_30,$fot(multiply(X_44,inverse(X_44))))]]) ).
cnf(refute_0_191,plain,
( multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(multiply(X_44,inverse(X_44)),inverse(X_2))
| multiply(multiply(X_44,inverse(X_44)),inverse(X_2)) != inverse(X_2)
| multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) = inverse(X_2) ),
inference(subst,[],[refute_0_113:[bind(X,$fot(multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))))),bind(Y,$fot(multiply(multiply(X_44,inverse(X_44)),inverse(X_2)))),bind(Z,$fot(inverse(X_2)))]]) ).
cnf(refute_0_192,plain,
( multiply(multiply(X_44,inverse(X_44)),inverse(X_2)) != inverse(X_2)
| multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) = inverse(X_2) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(multiply(X_44,inverse(X_44)),inverse(X_2))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) = inverse(X_2),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),inverse(X_2)),inverse(X_2)) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
( multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_33,inverse(multiply(X_33,X_2)))
| multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) != inverse(X_2)
| inverse(X_2) = multiply(X_33,inverse(multiply(X_33,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_33,inverse(multiply(X_33,X_2)))) ),[0],$fot(inverse(X_2))]]) ).
cnf(refute_0_195,plain,
( multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(X_33,inverse(multiply(X_33,X_2)))
| inverse(X_2) = multiply(X_33,inverse(multiply(X_33,X_2))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))),inverse(X_2)) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
inverse(X_2) = multiply(X_33,inverse(multiply(X_33,X_2))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(X_33,inverse(multiply(X_33,X_2)))) )],[refute_0_188,refute_0_195]) ).
cnf(refute_0_197,plain,
( inverse(X_2) != multiply(X_33,inverse(multiply(X_33,X_2)))
| multiply(X_33,inverse(multiply(X_33,X_2))) = inverse(X_2) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(inverse(X_2))),bind(Y,$fot(multiply(X_33,inverse(multiply(X_33,X_2)))))]]) ).
cnf(refute_0_198,plain,
multiply(X_33,inverse(multiply(X_33,X_2))) = inverse(X_2),
inference(resolve,[$cnf( $equal(inverse(X_2),multiply(X_33,inverse(multiply(X_33,X_2)))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) = multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30),
introduced(tautology,[refl,[$fot(multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30))]]) ).
cnf(refute_0_200,plain,
( multiply(X_33,inverse(multiply(X_33,X_2))) != inverse(X_2)
| multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) != multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)
| multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) = multiply(inverse(X_2),X_30) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30),multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)) ),[1,0],$fot(inverse(X_2))]]) ).
cnf(refute_0_201,plain,
( multiply(X_33,inverse(multiply(X_33,X_2))) != inverse(X_2)
| multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) = multiply(inverse(X_2),X_30) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30),multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) = multiply(inverse(X_2),X_30),
inference(resolve,[$cnf( $equal(multiply(X_33,inverse(multiply(X_33,X_2))),inverse(X_2)) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
( multiply(X_30,inverse(X_2)) != multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)
| multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30) != multiply(inverse(X_2),X_30)
| multiply(X_30,inverse(X_2)) = multiply(inverse(X_2),X_30) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_30,inverse(X_2)),multiply(inverse(X_2),X_30)) ),[0],$fot(multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30))]]) ).
cnf(refute_0_204,plain,
( multiply(X_30,inverse(X_2)) != multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)
| multiply(X_30,inverse(X_2)) = multiply(inverse(X_2),X_30) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30),multiply(inverse(X_2),X_30)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
( multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))) != multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)
| multiply(X_30,inverse(X_2)) = multiply(inverse(X_2),X_30) ),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(X_2)),multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)) )],[refute_0_181,refute_0_204]) ).
cnf(refute_0_206,plain,
multiply(X_30,inverse(X_2)) = multiply(inverse(X_2),X_30),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_32,inverse(multiply(X_32,X_2)))),multiply(multiply(X_33,inverse(multiply(X_33,X_2))),X_30)) )],[refute_0_168,refute_0_205]) ).
cnf(refute_0_207,plain,
( multiply(X_30,inverse(X_2)) != multiply(inverse(X_2),X_30)
| multiply(inverse(X_2),X_30) = multiply(X_30,inverse(X_2)) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(multiply(X_30,inverse(X_2)))),bind(Y,$fot(multiply(inverse(X_2),X_30)))]]) ).
cnf(refute_0_208,plain,
multiply(inverse(X_2),X_30) = multiply(X_30,inverse(X_2)),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(X_2)),multiply(inverse(X_2),X_30)) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
multiply(inverse(X_47),X_47) = multiply(X_47,inverse(X_47)),
inference(subst,[],[refute_0_208:[bind(X_2,$fot(X_47)),bind(X_30,$fot(X_47))]]) ).
cnf(refute_0_210,plain,
( multiply(inverse(X_47),X_47) != multiply(X_47,inverse(X_47))
| multiply(inverse(X_47),X_47) != multiply(X_5,inverse(X_5))
| multiply(X_47,inverse(X_47)) = multiply(X_5,inverse(X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_47),X_47),multiply(X_5,inverse(X_5))) ),[0],$fot(multiply(X_47,inverse(X_47)))]]) ).
cnf(refute_0_211,plain,
( multiply(inverse(X_47),X_47) != multiply(X_5,inverse(X_5))
| multiply(X_47,inverse(X_47)) = multiply(X_5,inverse(X_5)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),X_47),multiply(X_47,inverse(X_47))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
multiply(X_47,inverse(X_47)) = multiply(X_5,inverse(X_5)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),X_47),multiply(X_5,inverse(X_5))) )],[refute_0_124,refute_0_211]) ).
cnf(refute_0_213,plain,
( multiply(X_47,inverse(X_47)) != multiply(X_5,inverse(X_5))
| multiply(X_5,inverse(X_5)) = multiply(X_47,inverse(X_47)) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(multiply(X_47,inverse(X_47)))),bind(Y,$fot(multiply(X_5,inverse(X_5))))]]) ).
cnf(refute_0_214,plain,
multiply(X_5,inverse(X_5)) = multiply(X_47,inverse(X_47)),
inference(resolve,[$cnf( $equal(multiply(X_47,inverse(X_47)),multiply(X_5,inverse(X_5))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(X_48,inverse(X_48)) = multiply(b1,inverse(b1)),
inference(subst,[],[refute_0_214:[bind(X_47,$fot(b1)),bind(X_5,$fot(X_48))]]) ).
cnf(refute_0_216,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(X_48,inverse(X_48)),multiply(b1,inverse(b1))) )],[refute_0_215,refute_0_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP513-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 16:16:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44
% 0.18/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.48
%------------------------------------------------------------------------------