TSTP Solution File: GRP516-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP516-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 10:42:04 EDT 2022
% Result : Unsatisfiable 0.17s 0.40s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 56
% Syntax : Number of clauses : 160 ( 87 unt; 0 nHn; 72 RR)
% Number of literals : 269 ( 268 equ; 111 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 3 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 : 485 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
cnf(refute_0_0,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,$fot(multiply(X_8,inverse(X_8))))]]) ).
cnf(refute_0_1,plain,
multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B,
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))))]]) ).
cnf(refute_0_2,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,$fot(X_2))]]) ).
cnf(refute_0_3,plain,
( multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) != X_1
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B ),
introduced(tautology,[equality,[$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_4,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( $equal(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),X_1) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))) = X_4,
inference(subst,[],[refute_0_5:[bind(A,$fot(X_4)),bind(B,$fot(X_4)),bind(X_1,$fot(X_5)),bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_7,plain,
multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6)))) = X_5,
inference(subst,[],[single_axiom:[bind(A,$fot(X_4)),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_8,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_9,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( $equal(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6)))),X_5) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(X_4,multiply(X_5,inverse(X_5))) = X_4,
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))),X_4) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
multiply(B,multiply(X_8,inverse(X_8))) = B,
inference(subst,[],[refute_0_10:[bind(X_4,$fot(B)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_12,plain,
( multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(B,multiply(X_8,inverse(X_8))) != B
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B ),
introduced(tautology,[equality,[$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_13,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( $equal(multiply(B,multiply(X_8,inverse(X_8))),B) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) )],[refute_0_0,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(A,multiply(X_8,inverse(X_8))) = A,
inference(subst,[],[refute_0_10:[bind(X_4,$fot(A)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_16,plain,
inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(multiply(A,multiply(X_8,inverse(X_8)))),
introduced(tautology,[refl,[$fot(inverse(multiply(A,multiply(X_8,inverse(X_8)))))]]) ).
cnf(refute_0_17,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_18,plain,
( multiply(A,multiply(X_8,inverse(X_8))) != A
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(A) ),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_8,inverse(X_8)))),inverse(multiply(A,multiply(X_8,inverse(X_8))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(A),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_8,inverse(X_8))),A) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),
introduced(tautology,[refl,[$fot(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))]]) ).
cnf(refute_0_21,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_22,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( $equal(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(A)),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_8,inverse(X_8)))),inverse(A)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))))]]) ).
cnf(refute_0_25,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_26,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( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(A))),
inference(resolve,[$cnf( $equal(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),multiply(B,inverse(A))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(B,inverse(A)))
| multiply(A,multiply(B,inverse(A))) = B ),
introduced(tautology,[equality,[$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_29,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( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(B,inverse(A)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) )],[refute_0_14,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(A,multiply(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),inverse(A))) = multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),
inference(subst,[],[refute_0_30:[bind(B,$fot(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))))]]) ).
cnf(refute_0_32,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_5:[bind(A,$fot(multiply(B,X_2)))]]) ).
cnf(refute_0_33,plain,
multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) = multiply(X_1,X_2),
inference(subst,[],[refute_0_30:[bind(A,$fot(multiply(B,X_2))),bind(B,$fot(multiply(X_1,X_2)))]]) ).
cnf(refute_0_34,plain,
( multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) != multiply(X_1,X_2)
| multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(X_1,X_2)))) = B ),
introduced(tautology,[equality,[$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_35,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( $equal(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),multiply(X_1,X_2)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(X_1,X_2)))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(multiply(multiply(X_24,X_26),multiply(X_25,inverse(multiply(X_25,X_26))))))) = B,
inference(subst,[],[refute_0_36:[bind(X_1,$fot(multiply(X_24,X_26))),bind(X_2,$fot(multiply(X_25,inverse(multiply(X_25,X_26)))))]]) ).
cnf(refute_0_38,plain,
multiply(multiply(X_24,X_26),multiply(X_25,inverse(multiply(X_25,X_26)))) = X_24,
inference(subst,[],[refute_0_36:[bind(B,$fot(X_24)),bind(X_1,$fot(X_25)),bind(X_2,$fot(X_26))]]) ).
cnf(refute_0_39,plain,
( multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(multiply(multiply(X_24,X_26),multiply(X_25,inverse(multiply(X_25,X_26))))))) != B
| multiply(multiply(X_24,X_26),multiply(X_25,inverse(multiply(X_25,X_26)))) != X_24
| multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(multiply(multiply(X_24,X_26),multiply(X_25,inverse(multiply(X_25,X_26))))))),B) ),[0,1,1,0],$fot(X_24)]]) ).
cnf(refute_0_40,plain,
( multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(multiply(multiply(X_24,X_26),multiply(X_25,inverse(multiply(X_25,X_26))))))) != B
| multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_24,X_26),multiply(X_25,inverse(multiply(X_25,X_26)))),X_24) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(multiply(multiply(X_24,X_26),multiply(X_25,inverse(multiply(X_25,X_26))))))),B) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2))))))) = B,
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))))]]) ).
cnf(refute_0_43,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_44,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_45,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( $equal(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),X_1) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(A,X_2))))))),B) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(A,multiply(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))) = multiply(A,X_2),
inference(subst,[],[refute_0_46:[bind(B,$fot(multiply(A,X_2)))]]) ).
cnf(refute_0_48,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_30:[bind(A,$fot(multiply(A,X_2))),bind(B,$fot(multiply(X_1,X_2)))]]) ).
cnf(refute_0_49,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_50,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( $equal(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),multiply(X_1,X_2)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(A,multiply(multiply(X_1,X_2),inverse(X_1))) = multiply(A,X_2),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))),multiply(A,X_2)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))) = multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),X_26),
inference(subst,[],[refute_0_51:[bind(A,$fot(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))))),bind(X_1,$fot(X_24)),bind(X_2,$fot(X_26))]]) ).
cnf(refute_0_53,plain,
( multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))) != B
| multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))) != multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),X_26)
| multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),X_26) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))),B) ),[0],$fot(multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),X_26))]]) ).
cnf(refute_0_54,plain,
( multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))) != B
| multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),X_26) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))),multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),X_26)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),X_26) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_25,inverse(multiply(X_25,X_26)))),multiply(multiply(X_24,X_26),inverse(X_24))),B) )],[refute_0_41,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),inverse(A)) = X_27,
inference(subst,[],[refute_0_55:[bind(B,$fot(X_27)),bind(X_25,$fot(X_28)),bind(X_26,$fot(inverse(A)))]]) ).
cnf(refute_0_57,plain,
( multiply(A,multiply(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),inverse(A))) != multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))
| multiply(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),inverse(A)) != X_27
| multiply(A,X_27) = multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),inverse(A))),multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))) ),[0,1],$fot(X_27)]]) ).
cnf(refute_0_58,plain,
( multiply(A,multiply(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),inverse(A))) != multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))
| multiply(A,X_27) = multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),inverse(A)),X_27) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(A,X_27) = multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),inverse(A))),multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))) )],[refute_0_31,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B,
inference(subst,[],[refute_0_5:[bind(X_2,$fot(multiply(X_8,inverse(X_8))))]]) ).
cnf(refute_0_61,plain,
multiply(X_1,multiply(X_8,inverse(X_8))) = X_1,
inference(subst,[],[refute_0_10:[bind(X_4,$fot(X_1)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_62,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(X_1,multiply(X_8,inverse(X_8))) != X_1
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) ),[0,1,1,0,1,0],$fot(X_1)]]) ).
cnf(refute_0_63,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B ),
inference(resolve,[$cnf( $equal(multiply(X_1,multiply(X_8,inverse(X_8))),X_1) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(multiply(B,multiply(X_8,inverse(X_8)))),
introduced(tautology,[refl,[$fot(inverse(multiply(B,multiply(X_8,inverse(X_8)))))]]) ).
cnf(refute_0_66,plain,
( multiply(B,multiply(X_8,inverse(X_8))) != B
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) != inverse(multiply(B,multiply(X_8,inverse(X_8))))
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(B) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(B,multiply(X_8,inverse(X_8)))),inverse(multiply(B,multiply(X_8,inverse(X_8))))) ),[1,0],$fot(B)]]) ).
cnf(refute_0_67,plain,
( multiply(B,multiply(X_8,inverse(X_8))) != B
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(B) ),
inference(resolve,[$cnf( $equal(inverse(multiply(B,multiply(X_8,inverse(X_8)))),inverse(multiply(B,multiply(X_8,inverse(X_8))))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(B),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_8,inverse(X_8))),B) )],[refute_0_11,refute_0_67]) ).
cnf(refute_0_69,plain,
multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),
introduced(tautology,[refl,[$fot(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))]]) ).
cnf(refute_0_70,plain,
( multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) != multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) != inverse(B)
| multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_71,plain,
( inverse(multiply(B,multiply(X_8,inverse(X_8)))) != inverse(B)
| multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(B)) ),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(B)),
inference(resolve,[$cnf( $equal(inverse(multiply(B,multiply(X_8,inverse(X_8)))),inverse(B)) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))]]) ).
cnf(refute_0_74,plain,
( multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))
| multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) != multiply(X_1,inverse(B))
| multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) ),[1,1],$fot(multiply(X_1,inverse(B)))]]) ).
cnf(refute_0_75,plain,
( multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) != multiply(X_1,inverse(B))
| multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(B))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(B))),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),multiply(X_1,inverse(B))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),
introduced(tautology,[refl,[$fot(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))]]) ).
cnf(refute_0_78,plain,
( multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(X_1,inverse(B)))
| inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) != inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))
| inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) ),[1,0],$fot(multiply(A,multiply(X_1,inverse(B))))]]) ).
cnf(refute_0_79,plain,
( multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(X_1,inverse(B)))
| inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(B)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(B)))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(X_1,inverse(B)))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),
introduced(tautology,[refl,[$fot(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))]]) ).
cnf(refute_0_82,plain,
( multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) != multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))
| inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) != inverse(multiply(A,multiply(X_1,inverse(B))))
| multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) ),[1,1],$fot(inverse(multiply(A,multiply(X_1,inverse(B)))))]]) ).
cnf(refute_0_83,plain,
( inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) != inverse(multiply(A,multiply(X_1,inverse(B))))
| multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))) ),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),inverse(multiply(A,multiply(X_1,inverse(B))))) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))))]]) ).
cnf(refute_0_86,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))
| multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) != multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))) ),[1,1],$fot(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))))]]) ).
cnf(refute_0_87,plain,
( multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) != multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))))
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) ),[0],$fot(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))))]]) ).
cnf(refute_0_90,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) = B ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) )],[refute_0_64,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))) = B,
inference(subst,[],[refute_0_91:[bind(A,$fot(multiply(X_31,inverse(X_31))))]]) ).
cnf(refute_0_93,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_46:[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_94,plain,
multiply(X_9,multiply(X_5,inverse(X_5))) = X_9,
inference(subst,[],[refute_0_10:[bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_95,plain,
( multiply(X_9,multiply(X_5,inverse(X_5))) != X_9
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(multiply(X_9,multiply(X_5,inverse(X_5)))))),inverse(X_11))) != X_10
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = X_10 ),
introduced(tautology,[equality,[$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_96,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( $equal(multiply(X_9,multiply(X_5,inverse(X_5))),X_9) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = X_10,
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(multiply(X_9,multiply(X_5,inverse(X_5)))))),inverse(X_11))),X_10) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(X_11,multiply(X_5,inverse(X_5))) = X_11,
inference(subst,[],[refute_0_10:[bind(X_4,$fot(X_11))]]) ).
cnf(refute_0_99,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,[$fot(multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)))]]) ).
cnf(refute_0_100,plain,
( multiply(X_11,multiply(X_5,inverse(X_5))) != X_11
| multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) != multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))
| multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) = multiply(X_11,inverse(X_9)) ),
introduced(tautology,[equality,[$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_101,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( $equal(multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)),multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)) = multiply(X_11,inverse(X_9)),
inference(resolve,[$cnf( $equal(multiply(X_11,multiply(X_5,inverse(X_5))),X_11) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) = multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),
introduced(tautology,[refl,[$fot(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))))]]) ).
cnf(refute_0_104,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_105,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( $equal(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))) = multiply(X_10,multiply(X_11,inverse(X_9))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9)),multiply(X_11,inverse(X_9))) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) = multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)),
introduced(tautology,[refl,[$fot(multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)))]]) ).
cnf(refute_0_108,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_109,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( $equal(multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)),multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)) = multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)),
inference(resolve,[$cnf( $equal(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),multiply(X_10,multiply(X_11,inverse(X_9)))) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),
introduced(tautology,[refl,[$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_112,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_113,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( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) = multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11)),multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) != X_10
| multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))) != multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)))
| multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) = X_10 ),
introduced(tautology,[equality,[$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_116,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( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(X_9,multiply(multiply(X_10,multiply(X_11,inverse(X_9))),inverse(X_11))) = X_10,
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(X_10,multiply(multiply(X_11,multiply(X_5,inverse(X_5))),inverse(X_9))),inverse(X_11))),X_10) )],[refute_0_97,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(multiply(X_11,inverse(X_11)),multiply(multiply(X_10,multiply(X_11,inverse(multiply(X_11,inverse(X_11))))),inverse(X_11))) = X_10,
inference(subst,[],[refute_0_117:[bind(X_9,$fot(multiply(X_11,inverse(X_11))))]]) ).
cnf(refute_0_119,plain,
multiply(multiply(X_10,multiply(X_11,inverse(multiply(X_11,inverse(X_11))))),inverse(X_11)) = X_10,
inference(subst,[],[refute_0_55:[bind(B,$fot(X_10)),bind(X_25,$fot(X_11)),bind(X_26,$fot(inverse(X_11)))]]) ).
cnf(refute_0_120,plain,
( multiply(multiply(X_10,multiply(X_11,inverse(multiply(X_11,inverse(X_11))))),inverse(X_11)) != X_10
| multiply(multiply(X_11,inverse(X_11)),multiply(multiply(X_10,multiply(X_11,inverse(multiply(X_11,inverse(X_11))))),inverse(X_11))) != X_10
| multiply(multiply(X_11,inverse(X_11)),X_10) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,inverse(X_11)),multiply(multiply(X_10,multiply(X_11,inverse(multiply(X_11,inverse(X_11))))),inverse(X_11))),X_10) ),[0,1],$fot(X_10)]]) ).
cnf(refute_0_121,plain,
( multiply(multiply(X_11,inverse(X_11)),multiply(multiply(X_10,multiply(X_11,inverse(multiply(X_11,inverse(X_11))))),inverse(X_11))) != X_10
| multiply(multiply(X_11,inverse(X_11)),X_10) = X_10 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_10,multiply(X_11,inverse(multiply(X_11,inverse(X_11))))),inverse(X_11)),X_10) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(multiply(X_11,inverse(X_11)),X_10) = X_10,
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,inverse(X_11)),multiply(multiply(X_10,multiply(X_11,inverse(multiply(X_11,inverse(X_11))))),inverse(X_11))),X_10) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))) = multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))),
inference(subst,[],[refute_0_122:[bind(X_10,$fot(multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))))),bind(X_11,$fot(X_31))]]) ).
cnf(refute_0_124,plain,
( multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))) != B
| multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))) != multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))
| multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))),B) ),[0],$fot(multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))))]]) ).
cnf(refute_0_125,plain,
( multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))) != B
| multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))),B) )],[refute_0_92,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))) = multiply(X_1,inverse(B)),
inference(subst,[],[refute_0_122:[bind(X_10,$fot(multiply(X_1,inverse(B)))),bind(X_11,$fot(X_31))]]) ).
cnf(refute_0_128,plain,
inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))) = inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))]]) ).
cnf(refute_0_129,plain,
( multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))) != multiply(X_1,inverse(B))
| inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))) != inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))
| inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))) = inverse(multiply(X_1,inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))),inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) ),[1,0],$fot(multiply(X_1,inverse(B)))]]) ).
cnf(refute_0_130,plain,
( multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))) != multiply(X_1,inverse(B))
| inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))) = inverse(multiply(X_1,inverse(B))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))),inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))) = inverse(multiply(X_1,inverse(B))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))),multiply(X_1,inverse(B))) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) = multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))),
introduced(tautology,[refl,[$fot(multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))))]]) ).
cnf(refute_0_133,plain,
( multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) != multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))
| inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))) != inverse(multiply(X_1,inverse(B)))
| multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) = multiply(X_1,inverse(multiply(X_1,inverse(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))) ),[1,1],$fot(inverse(multiply(X_1,inverse(B))))]]) ).
cnf(refute_0_134,plain,
( inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))) != inverse(multiply(X_1,inverse(B)))
| multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) = multiply(X_1,inverse(multiply(X_1,inverse(B)))) ),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))),multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) = multiply(X_1,inverse(multiply(X_1,inverse(B)))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B)))),inverse(multiply(X_1,inverse(B)))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) != B
| multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) != multiply(X_1,inverse(multiply(X_1,inverse(B))))
| multiply(X_1,inverse(multiply(X_1,inverse(B)))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))),B) ),[0],$fot(multiply(X_1,inverse(multiply(X_1,inverse(B)))))]]) ).
cnf(refute_0_137,plain,
( multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))) != B
| multiply(X_1,inverse(multiply(X_1,inverse(B)))) = B ),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))),multiply(X_1,inverse(multiply(X_1,inverse(B))))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(X_1,inverse(multiply(X_1,inverse(B)))) = B,
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_31,inverse(X_31)),multiply(X_1,inverse(B))))),B) )],[refute_0_126,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(X_28,inverse(multiply(X_28,inverse(A)))) = A,
inference(subst,[],[refute_0_138:[bind(B,$fot(A)),bind(X_1,$fot(X_28))]]) ).
cnf(refute_0_140,plain,
multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))) = multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),
introduced(tautology,[refl,[$fot(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))))]]) ).
cnf(refute_0_141,plain,
( multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))) != multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))
| multiply(X_28,inverse(multiply(X_28,inverse(A)))) != A
| multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))) = multiply(X_27,A) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_142,plain,
( multiply(X_28,inverse(multiply(X_28,inverse(A)))) != A
| multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))) = multiply(X_27,A) ),
inference(resolve,[$cnf( $equal(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))) = multiply(X_27,A),
inference(resolve,[$cnf( $equal(multiply(X_28,inverse(multiply(X_28,inverse(A)))),A) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
( multiply(A,X_27) != multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))
| multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))) != multiply(X_27,A)
| multiply(A,X_27) = multiply(X_27,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,X_27),multiply(X_27,A)) ),[0],$fot(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))))]]) ).
cnf(refute_0_145,plain,
( multiply(A,X_27) != multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))
| multiply(A,X_27) = multiply(X_27,A) ),
inference(resolve,[$cnf( $equal(multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A))))),multiply(X_27,A)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(A,X_27) = multiply(X_27,A),
inference(resolve,[$cnf( $equal(multiply(A,X_27),multiply(X_27,multiply(X_28,inverse(multiply(X_28,inverse(A)))))) )],[refute_0_59,refute_0_145]) ).
cnf(refute_0_147,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_148,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_149,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
( multiply(A,X_27) != multiply(X_27,A)
| multiply(X_27,A) = multiply(A,X_27) ),
inference(subst,[],[refute_0_149:[bind(X,$fot(multiply(A,X_27))),bind(Y,$fot(multiply(X_27,A)))]]) ).
cnf(refute_0_151,plain,
multiply(X_27,A) = multiply(A,X_27),
inference(resolve,[$cnf( $equal(multiply(A,X_27),multiply(X_27,A)) )],[refute_0_146,refute_0_150]) ).
cnf(refute_0_152,plain,
multiply(b,a) = multiply(a,b),
inference(subst,[],[refute_0_151:[bind(A,$fot(a)),bind(X_27,$fot(b))]]) ).
cnf(refute_0_153,plain,
( multiply(a,b) != multiply(a,b)
| multiply(b,a) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,b),multiply(b,a)) ),[1],$fot(multiply(a,b))]]) ).
cnf(refute_0_154,plain,
( multiply(a,b) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
multiply(a,b) != multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(b,a)) )],[refute_0_154,prove_these_axioms_4]) ).
cnf(refute_0_156,plain,
multiply(a,b) = multiply(a,b),
introduced(tautology,[refl,[$fot(multiply(a,b))]]) ).
cnf(refute_0_157,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(a,b)) )],[refute_0_156,refute_0_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP516-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 13:12:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.40
% 0.17/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.17/0.44
%------------------------------------------------------------------------------