TSTP Solution File: GRP515-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP515-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 0.21s 0.53s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 50
% Syntax : Number of clauses : 162 ( 87 unt; 0 nHn; 79 RR)
% Number of literals : 274 ( 273 equ; 115 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 433 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
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( $equal(multiply(A,multiply(multiply(multiply(A,X_2),multiply(multiply(X_1,X_2),inverse(multiply(A,X_2)))),inverse(X_1))),multiply(A,X_2)) )],[refute_0_5,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(A,multiply(multiply(X_1,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),inverse(X_1))) = multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),
inference(subst,[],[refute_0_40:[bind(X_2,$fot(multiply(X_35,inverse(multiply(X_35,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( $equal(multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(multiply(multiply(X_21,X_23),multiply(X_22,inverse(multiply(X_22,X_23))))))) = B,
inference(subst,[],[refute_0_46:[bind(X_1,$fot(multiply(X_21,X_23))),bind(X_2,$fot(multiply(X_22,inverse(multiply(X_22,X_23)))))]]) ).
cnf(refute_0_48,plain,
multiply(multiply(X_21,X_23),multiply(X_22,inverse(multiply(X_22,X_23)))) = X_21,
inference(subst,[],[refute_0_46:[bind(B,$fot(X_21)),bind(X_1,$fot(X_22)),bind(X_2,$fot(X_23))]]) ).
cnf(refute_0_49,plain,
( multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(multiply(multiply(X_21,X_23),multiply(X_22,inverse(multiply(X_22,X_23))))))) != B
| multiply(multiply(X_21,X_23),multiply(X_22,inverse(multiply(X_22,X_23)))) != X_21
| multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(multiply(multiply(X_21,X_23),multiply(X_22,inverse(multiply(X_22,X_23))))))),B) ),[0,1,1,0],$fot(X_21)]]) ).
cnf(refute_0_50,plain,
( multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(multiply(multiply(X_21,X_23),multiply(X_22,inverse(multiply(X_22,X_23))))))) != B
| multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,X_23),multiply(X_22,inverse(multiply(X_22,X_23)))),X_21) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(multiply(multiply(X_21,X_23),multiply(X_22,inverse(multiply(X_22,X_23))))))),B) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))) = multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),X_23),
inference(subst,[],[refute_0_40:[bind(A,$fot(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))))),bind(X_1,$fot(X_21)),bind(X_2,$fot(X_23))]]) ).
cnf(refute_0_53,plain,
( multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))) != B
| multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))) != multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),X_23)
| multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),X_23) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))),B) ),[0],$fot(multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),X_23))]]) ).
cnf(refute_0_54,plain,
( multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))) != B
| multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),X_23) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))),multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),X_23)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),X_23) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_22,inverse(multiply(X_22,X_23)))),multiply(multiply(X_21,X_23),inverse(X_21))),B) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(multiply(X_1,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),inverse(X_1)) = X_1,
inference(subst,[],[refute_0_55:[bind(B,$fot(X_1)),bind(X_22,$fot(X_35)),bind(X_23,$fot(inverse(X_1)))]]) ).
cnf(refute_0_57,plain,
( multiply(A,multiply(multiply(X_1,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),inverse(X_1))) != multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1)))))
| multiply(multiply(X_1,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),inverse(X_1)) != X_1
| multiply(A,X_1) = multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(X_1,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),inverse(X_1))),multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1)))))) ),[0,1],$fot(X_1)]]) ).
cnf(refute_0_58,plain,
( multiply(A,multiply(multiply(X_1,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),inverse(X_1))) != multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1)))))
| multiply(A,X_1) = multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_1,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),inverse(X_1)),X_1) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(A,X_1) = multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(X_1,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),inverse(X_1))),multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1)))))) )],[refute_0_41,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(A,multiply(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),inverse(A))) = multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),
inference(subst,[],[refute_0_36:[bind(B,$fot(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A)))))))]]) ).
cnf(refute_0_61,plain,
multiply(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),inverse(A)) = X_34,
inference(subst,[],[refute_0_55:[bind(B,$fot(X_34)),bind(X_22,$fot(X_35)),bind(X_23,$fot(inverse(A)))]]) ).
cnf(refute_0_62,plain,
( multiply(A,multiply(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),inverse(A))) != multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A)))))
| multiply(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),inverse(A)) != X_34
| multiply(A,X_34) = multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),inverse(A))),multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A)))))) ),[0,1],$fot(X_34)]]) ).
cnf(refute_0_63,plain,
( multiply(A,multiply(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),inverse(A))) != multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A)))))
| multiply(A,X_34) = multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),inverse(A)),X_34) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(A,X_34) = multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))),inverse(A))),multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A)))))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( multiply(A,X_34) != multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A)))))
| multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))) = multiply(A,X_34) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(multiply(A,X_34))),bind(Y,$fot(multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A)))))))]]) ).
cnf(refute_0_69,plain,
multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A))))) = multiply(A,X_34),
inference(resolve,[$cnf( $equal(multiply(A,X_34),multiply(X_34,multiply(X_35,inverse(multiply(X_35,inverse(A)))))) )],[refute_0_64,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))) = multiply(X_1,A),
inference(subst,[],[refute_0_69:[bind(A,$fot(X_1)),bind(X_34,$fot(A))]]) ).
cnf(refute_0_71,plain,
( multiply(A,X_1) != multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1)))))
| multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))) != multiply(X_1,A)
| multiply(A,X_1) = multiply(X_1,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,X_1),multiply(X_1,A)) ),[0],$fot(multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))))]]) ).
cnf(refute_0_72,plain,
( multiply(A,X_1) != multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1)))))
| multiply(A,X_1) = multiply(X_1,A) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1))))),multiply(X_1,A)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(A,X_1) = multiply(X_1,A),
inference(resolve,[$cnf( $equal(multiply(A,X_1),multiply(A,multiply(X_35,inverse(multiply(X_35,inverse(X_1)))))) )],[refute_0_59,refute_0_72]) ).
cnf(refute_0_74,plain,
( multiply(A,X_1) != multiply(X_1,A)
| multiply(X_1,A) = multiply(A,X_1) ),
inference(subst,[],[refute_0_67:[bind(X,$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( $equal(multiply(A,X_1),multiply(X_1,A)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(multiply(a3,b3),c3) = multiply(c3,multiply(a3,b3)),
inference(subst,[],[refute_0_75:[bind(A,$fot(c3)),bind(X_1,$fot(multiply(a3,b3)))]]) ).
cnf(refute_0_77,plain,
( multiply(multiply(a3,b3),c3) != multiply(c3,multiply(a3,b3))
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),[0],$fot(multiply(c3,multiply(a3,b3)))]]) ).
cnf(refute_0_78,plain,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(c3,multiply(a3,b3))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_78,prove_these_axioms_3]) ).
cnf(refute_0_80,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B,
inference(subst,[],[refute_0_11:[bind(X_2,$fot(multiply(X_8,inverse(X_8))))]]) ).
cnf(refute_0_81,plain,
multiply(X_1,multiply(X_8,inverse(X_8))) = X_1,
inference(subst,[],[refute_0_16:[bind(X_4,$fot(X_1)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_82,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_83,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( $equal(multiply(X_1,multiply(X_8,inverse(X_8))),X_1) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(multiply(B,multiply(X_8,inverse(X_8)))),
introduced(tautology,[refl,[$fot(inverse(multiply(B,multiply(X_8,inverse(X_8)))))]]) ).
cnf(refute_0_86,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_87,plain,
( multiply(B,multiply(X_8,inverse(X_8))) != B
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(B) ),
inference(resolve,[$cnf( $equal(inverse(multiply(B,multiply(X_8,inverse(X_8)))),inverse(multiply(B,multiply(X_8,inverse(X_8))))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(B),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_8,inverse(X_8))),B) )],[refute_0_17,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),
introduced(tautology,[refl,[$fot(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))]]) ).
cnf(refute_0_90,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_91,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( $equal(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(B)),
inference(resolve,[$cnf( $equal(inverse(multiply(B,multiply(X_8,inverse(X_8)))),inverse(B)) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))]]) ).
cnf(refute_0_94,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_95,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( $equal(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(B))),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),multiply(X_1,inverse(B))) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),
introduced(tautology,[refl,[$fot(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))]]) ).
cnf(refute_0_98,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_99,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( $equal(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(B)))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(X_1,inverse(B)))) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),
introduced(tautology,[refl,[$fot(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))]]) ).
cnf(refute_0_102,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_103,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( $equal(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),inverse(multiply(A,multiply(X_1,inverse(B))))) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))))]]) ).
cnf(refute_0_106,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_107,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( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))))
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) = B ),
introduced(tautology,[equality,[$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_110,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( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) )],[refute_0_84,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(X_1,X_23))))))) = multiply(X_1,X_23),
inference(subst,[],[refute_0_111:[bind(A,$fot(multiply(X_21,X_23))),bind(B,$fot(multiply(X_1,X_23)))]]) ).
cnf(refute_0_113,plain,
multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(X_1,X_23)))) = X_21,
inference(subst,[],[refute_0_46:[bind(B,$fot(X_21)),bind(X_2,$fot(X_23))]]) ).
cnf(refute_0_114,plain,
( multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(X_1,X_23)))) != X_21
| multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(X_1,X_23))))))) != multiply(X_1,X_23)
| multiply(multiply(X_21,X_23),multiply(X_1,inverse(X_21))) = multiply(X_1,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(X_1,X_23))))))),multiply(X_1,X_23)) ),[0,1,1,0],$fot(X_21)]]) ).
cnf(refute_0_115,plain,
( multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(X_1,X_23))))))) != multiply(X_1,X_23)
| multiply(multiply(X_21,X_23),multiply(X_1,inverse(X_21))) = multiply(X_1,X_23) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(X_1,X_23)))),X_21) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(multiply(X_21,X_23),multiply(X_1,inverse(X_21))) = multiply(X_1,X_23),
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(multiply(X_21,X_23),multiply(X_1,inverse(multiply(X_1,X_23))))))),multiply(X_1,X_23)) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(multiply(inverse(X_47),multiply(X_47,B)),multiply(X_62,inverse(inverse(X_47)))) = multiply(X_62,multiply(X_47,B)),
inference(subst,[],[refute_0_116:[bind(X_1,$fot(X_62)),bind(X_21,$fot(inverse(X_47))),bind(X_23,$fot(multiply(X_47,B)))]]) ).
cnf(refute_0_118,plain,
multiply(B,inverse(A)) = multiply(inverse(A),B),
inference(subst,[],[refute_0_73:[bind(A,$fot(B)),bind(X_1,$fot(inverse(A)))]]) ).
cnf(refute_0_119,plain,
( multiply(A,multiply(B,inverse(A))) != B
| multiply(B,inverse(A)) != multiply(inverse(A),B)
| multiply(A,multiply(inverse(A),B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(B,inverse(A))),B) ),[0,1],$fot(multiply(inverse(A),B))]]) ).
cnf(refute_0_120,plain,
( multiply(A,multiply(B,inverse(A))) != B
| multiply(A,multiply(inverse(A),B)) = B ),
inference(resolve,[$cnf( $equal(multiply(B,inverse(A)),multiply(inverse(A),B)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(B,inverse(A))),B) )],[refute_0_36,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(inverse(X_47),multiply(inverse(inverse(X_47)),B)) = B,
inference(subst,[],[refute_0_121:[bind(A,$fot(inverse(X_47)))]]) ).
cnf(refute_0_123,plain,
multiply(X_4,multiply(inverse(X_4),inverse(inverse(X_4)))) = X_4,
inference(subst,[],[refute_0_16:[bind(X_5,$fot(inverse(X_4)))]]) ).
cnf(refute_0_124,plain,
multiply(X_4,multiply(inverse(X_4),inverse(inverse(X_4)))) = inverse(inverse(X_4)),
inference(subst,[],[refute_0_121:[bind(A,$fot(X_4)),bind(B,$fot(inverse(inverse(X_4))))]]) ).
cnf(refute_0_125,plain,
( multiply(X_4,multiply(inverse(X_4),inverse(inverse(X_4)))) != X_4
| multiply(X_4,multiply(inverse(X_4),inverse(inverse(X_4)))) != inverse(inverse(X_4))
| inverse(inverse(X_4)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_4,multiply(inverse(X_4),inverse(inverse(X_4)))),X_4) ),[0],$fot(inverse(inverse(X_4)))]]) ).
cnf(refute_0_126,plain,
( multiply(X_4,multiply(inverse(X_4),inverse(inverse(X_4)))) != X_4
| inverse(inverse(X_4)) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(inverse(X_4),inverse(inverse(X_4)))),inverse(inverse(X_4))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
inverse(inverse(X_4)) = X_4,
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(inverse(X_4),inverse(inverse(X_4)))),X_4) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
inverse(inverse(X_47)) = X_47,
inference(subst,[],[refute_0_127:[bind(X_4,$fot(X_47))]]) ).
cnf(refute_0_129,plain,
( multiply(inverse(X_47),multiply(inverse(inverse(X_47)),B)) != B
| inverse(inverse(X_47)) != X_47
| multiply(inverse(X_47),multiply(X_47,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_47),multiply(inverse(inverse(X_47)),B)),B) ),[0,1,0],$fot(X_47)]]) ).
cnf(refute_0_130,plain,
( multiply(inverse(X_47),multiply(inverse(inverse(X_47)),B)) != B
| multiply(inverse(X_47),multiply(X_47,B)) = B ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_47)),X_47) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(inverse(X_47),multiply(X_47,B)) = B,
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),multiply(inverse(inverse(X_47)),B)),B) )],[refute_0_122,refute_0_130]) ).
cnf(refute_0_132,plain,
( multiply(multiply(inverse(X_47),multiply(X_47,B)),multiply(X_62,inverse(inverse(X_47)))) != multiply(X_62,multiply(X_47,B))
| multiply(inverse(X_47),multiply(X_47,B)) != B
| multiply(B,multiply(X_62,inverse(inverse(X_47)))) = multiply(X_62,multiply(X_47,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_47),multiply(X_47,B)),multiply(X_62,inverse(inverse(X_47)))),multiply(X_62,multiply(X_47,B))) ),[0,0],$fot(B)]]) ).
cnf(refute_0_133,plain,
( multiply(multiply(inverse(X_47),multiply(X_47,B)),multiply(X_62,inverse(inverse(X_47)))) != multiply(X_62,multiply(X_47,B))
| multiply(B,multiply(X_62,inverse(inverse(X_47)))) = multiply(X_62,multiply(X_47,B)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),multiply(X_47,B)),B) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(B,multiply(X_62,inverse(inverse(X_47)))) = multiply(X_62,multiply(X_47,B)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_47),multiply(X_47,B)),multiply(X_62,inverse(inverse(X_47)))),multiply(X_62,multiply(X_47,B))) )],[refute_0_117,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(X_62,inverse(inverse(X_47))) = multiply(X_62,inverse(inverse(X_47))),
introduced(tautology,[refl,[$fot(multiply(X_62,inverse(inverse(X_47))))]]) ).
cnf(refute_0_136,plain,
( multiply(X_62,inverse(inverse(X_47))) != multiply(X_62,inverse(inverse(X_47)))
| inverse(inverse(X_47)) != X_47
| multiply(X_62,inverse(inverse(X_47))) = multiply(X_62,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_62,inverse(inverse(X_47))),multiply(X_62,inverse(inverse(X_47)))) ),[1,1],$fot(X_47)]]) ).
cnf(refute_0_137,plain,
( inverse(inverse(X_47)) != X_47
| multiply(X_62,inverse(inverse(X_47))) = multiply(X_62,X_47) ),
inference(resolve,[$cnf( $equal(multiply(X_62,inverse(inverse(X_47))),multiply(X_62,inverse(inverse(X_47)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(X_62,inverse(inverse(X_47))) = multiply(X_62,X_47),
inference(resolve,[$cnf( $equal(inverse(inverse(X_47)),X_47) )],[refute_0_128,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(B,multiply(X_62,inverse(inverse(X_47)))) = multiply(B,multiply(X_62,inverse(inverse(X_47)))),
introduced(tautology,[refl,[$fot(multiply(B,multiply(X_62,inverse(inverse(X_47)))))]]) ).
cnf(refute_0_140,plain,
( multiply(B,multiply(X_62,inverse(inverse(X_47)))) != multiply(B,multiply(X_62,inverse(inverse(X_47))))
| multiply(X_62,inverse(inverse(X_47))) != multiply(X_62,X_47)
| multiply(B,multiply(X_62,inverse(inverse(X_47)))) = multiply(B,multiply(X_62,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(B,multiply(X_62,inverse(inverse(X_47)))),multiply(B,multiply(X_62,inverse(inverse(X_47))))) ),[1,1],$fot(multiply(X_62,X_47))]]) ).
cnf(refute_0_141,plain,
( multiply(X_62,inverse(inverse(X_47))) != multiply(X_62,X_47)
| multiply(B,multiply(X_62,inverse(inverse(X_47)))) = multiply(B,multiply(X_62,X_47)) ),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_62,inverse(inverse(X_47)))),multiply(B,multiply(X_62,inverse(inverse(X_47))))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(B,multiply(X_62,inverse(inverse(X_47)))) = multiply(B,multiply(X_62,X_47)),
inference(resolve,[$cnf( $equal(multiply(X_62,inverse(inverse(X_47))),multiply(X_62,X_47)) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
( multiply(B,multiply(X_62,inverse(inverse(X_47)))) != multiply(B,multiply(X_62,X_47))
| multiply(B,multiply(X_62,inverse(inverse(X_47)))) != multiply(X_62,multiply(X_47,B))
| multiply(B,multiply(X_62,X_47)) = multiply(X_62,multiply(X_47,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(B,multiply(X_62,inverse(inverse(X_47)))),multiply(X_62,multiply(X_47,B))) ),[0],$fot(multiply(B,multiply(X_62,X_47)))]]) ).
cnf(refute_0_144,plain,
( multiply(B,multiply(X_62,inverse(inverse(X_47)))) != multiply(X_62,multiply(X_47,B))
| multiply(B,multiply(X_62,X_47)) = multiply(X_62,multiply(X_47,B)) ),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_62,inverse(inverse(X_47)))),multiply(B,multiply(X_62,X_47))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
multiply(B,multiply(X_62,X_47)) = multiply(X_62,multiply(X_47,B)),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_62,inverse(inverse(X_47)))),multiply(X_62,multiply(X_47,B))) )],[refute_0_134,refute_0_144]) ).
cnf(refute_0_146,plain,
( multiply(B,multiply(X_62,X_47)) != multiply(X_62,multiply(X_47,B))
| multiply(X_62,multiply(X_47,B)) = multiply(B,multiply(X_62,X_47)) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(multiply(B,multiply(X_62,X_47)))),bind(Y,$fot(multiply(X_62,multiply(X_47,B))))]]) ).
cnf(refute_0_147,plain,
multiply(X_62,multiply(X_47,B)) = multiply(B,multiply(X_62,X_47)),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_62,X_47)),multiply(X_62,multiply(X_47,B))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(b3,multiply(c3,a3)) = multiply(a3,multiply(b3,c3)),
inference(subst,[],[refute_0_147:[bind(B,$fot(a3)),bind(X_47,$fot(c3)),bind(X_62,$fot(b3))]]) ).
cnf(refute_0_149,plain,
multiply(c3,multiply(a3,b3)) = multiply(b3,multiply(c3,a3)),
inference(subst,[],[refute_0_147:[bind(B,$fot(b3)),bind(X_47,$fot(a3)),bind(X_62,$fot(c3))]]) ).
cnf(refute_0_150,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_151,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_67,refute_0_150]) ).
cnf(refute_0_152,plain,
( multiply(b3,multiply(c3,a3)) != multiply(a3,multiply(b3,c3))
| multiply(c3,multiply(a3,b3)) != multiply(b3,multiply(c3,a3))
| multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(b3,c3)) ),
inference(subst,[],[refute_0_151:[bind(X,$fot(multiply(c3,multiply(a3,b3)))),bind(Y,$fot(multiply(b3,multiply(c3,a3)))),bind(Z,$fot(multiply(a3,multiply(b3,c3))))]]) ).
cnf(refute_0_153,plain,
( multiply(b3,multiply(c3,a3)) != multiply(a3,multiply(b3,c3))
| multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(c3,multiply(a3,b3)),multiply(b3,multiply(c3,a3))) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(b3,c3))) )],[refute_0_148,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(b3,c3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),[1],$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_156,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) )],[refute_0_156,refute_0_79]) ).
cnf(refute_0_158,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_159,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_158,refute_0_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP515-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 22:06:18 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.53
% 0.21/0.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.56
%------------------------------------------------------------------------------