TSTP Solution File: GRP517-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP517-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 10:42:05 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 56
% Syntax : Number of clauses : 258 ( 137 unt; 0 nHn; 122 RR)
% Number of literals : 436 ( 435 equ; 181 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 714 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(refute_0_0,plain,
multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) = X_2,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(multiply(A,B)))),bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_2,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)) != multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)
| multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) != X_2
| multiply(A,multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) ),[0,1,0],$fot(X_2)]]) ).
cnf(refute_0_3,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)) != multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)
| multiply(A,multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),X_2) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(A,multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C,
inference(subst,[],[single_axiom:[bind(B,$fot(multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)))]]) ).
cnf(refute_0_6,plain,
multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)) = X_2,
inference(subst,[],[single_axiom:[bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_7,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)) != X_2
| multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) != C
| multiply(A,multiply(multiply(inverse(X_2),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C) ),[0,1,0,0,0],$fot(X_2)]]) ).
cnf(refute_0_8,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) != C
| multiply(A,multiply(multiply(inverse(X_2),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)),X_2) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(A,multiply(multiply(inverse(X_2),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))) = X_4,
inference(subst,[],[refute_0_9:[bind(A,$fot(multiply(inverse(X_6),X_4))),bind(C,$fot(X_4)),bind(X_1,$fot(X_5)),bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5)) = X_6,
inference(subst,[],[single_axiom:[bind(A,$fot(multiply(inverse(X_6),X_4))),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_12,plain,
( multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))) != X_4
| multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5)) != X_6
| multiply(multiply(inverse(X_6),X_4),X_6) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))),X_4) ),[0,1],$fot(X_6)]]) ).
cnf(refute_0_13,plain,
( multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))) != X_4
| multiply(multiply(inverse(X_6),X_4),X_6) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5)),X_6) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(multiply(inverse(X_6),X_4),X_6) = X_4,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))),X_4) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B),
inference(subst,[],[refute_0_14:[bind(X_4,$fot(multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B))),bind(X_6,$fot(X_8))]]) ).
cnf(refute_0_16,plain,
multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(X_8)))]]) ).
cnf(refute_0_17,plain,
( multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8) != multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)
| multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) != C
| multiply(C,X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) ),[0,0],$fot(C)]]) ).
cnf(refute_0_18,plain,
( multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8) != multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)
| multiply(C,X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),C) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(C,X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_21,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_22,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(C,X_8) != multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)
| multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) = multiply(C,X_8) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(C,X_8))),bind(Y,$fot(multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)))]]) ).
cnf(refute_0_24,plain,
multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) = multiply(C,X_8),
inference(resolve,[$cnf( $equal(multiply(C,X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) = multiply(X_2,multiply(A,B)),
inference(subst,[],[refute_0_24:[bind(B,$fot(X_1)),bind(C,$fot(X_2)),bind(X_8,$fot(multiply(A,B)))]]) ).
cnf(refute_0_26,plain,
( multiply(A,multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)
| multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) != multiply(X_2,multiply(A,B))
| multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,multiply(X_2,B)),multiply(X_2,multiply(A,B))) ),[0],$fot(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1))]]) ).
cnf(refute_0_27,plain,
( multiply(A,multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)
| multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),multiply(X_2,multiply(A,B))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(A,B)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_2,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) )],[refute_0_4,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)) = multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_9)),bind(B,$fot(X_10)),bind(X_2,$fot(multiply(inverse(X_10),X_4)))]]) ).
cnf(refute_0_30,plain,
multiply(multiply(inverse(X_10),X_4),X_10) = X_4,
inference(subst,[],[refute_0_14:[bind(X_6,$fot(X_10))]]) ).
cnf(refute_0_31,plain,
( multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)) != multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))
| multiply(multiply(inverse(X_10),X_4),X_10) != X_4
| multiply(X_9,X_4) = multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)),multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))) ),[0,1],$fot(X_4)]]) ).
cnf(refute_0_32,plain,
( multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)) != multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))
| multiply(X_9,X_4) = multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_10),X_4),X_10),X_4) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_9,X_4) = multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)),
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)),multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6) = multiply(X_11,X_10),
inference(subst,[],[refute_0_14:[bind(X_4,$fot(multiply(X_11,X_10)))]]) ).
cnf(refute_0_35,plain,
multiply(inverse(X_6),multiply(X_11,X_10)) = multiply(X_11,multiply(inverse(X_6),X_10)),
inference(subst,[],[refute_0_28:[bind(A,$fot(inverse(X_6))),bind(B,$fot(X_10)),bind(X_2,$fot(X_11))]]) ).
cnf(refute_0_36,plain,
( multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6) != multiply(X_11,X_10)
| multiply(inverse(X_6),multiply(X_11,X_10)) != multiply(X_11,multiply(inverse(X_6),X_10))
| multiply(multiply(X_11,multiply(inverse(X_6),X_10)),X_6) = multiply(X_11,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6),multiply(X_11,X_10)) ),[0,0],$fot(multiply(X_11,multiply(inverse(X_6),X_10)))]]) ).
cnf(refute_0_37,plain,
( multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6) != multiply(X_11,X_10)
| multiply(multiply(X_11,multiply(inverse(X_6),X_10)),X_6) = multiply(X_11,X_10) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_6),multiply(X_11,X_10)),multiply(X_11,multiply(inverse(X_6),X_10))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(multiply(X_11,multiply(inverse(X_6),X_10)),X_6) = multiply(X_11,X_10),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6),multiply(X_11,X_10)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(multiply(X_13,multiply(inverse(X_14),X_12)),X_14) = multiply(X_13,X_12),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(X_12)),bind(X_11,$fot(X_13)),bind(X_6,$fot(X_14))]]) ).
cnf(refute_0_40,plain,
multiply(inverse(X_14),multiply(X_13,X_12)) = multiply(X_13,multiply(inverse(X_14),X_12)),
inference(subst,[],[refute_0_28:[bind(A,$fot(inverse(X_14))),bind(B,$fot(X_12)),bind(X_2,$fot(X_13))]]) ).
cnf(refute_0_41,plain,
( multiply(inverse(X_14),multiply(X_13,X_12)) != multiply(X_13,multiply(inverse(X_14),X_12))
| multiply(X_13,multiply(inverse(X_14),X_12)) = multiply(inverse(X_14),multiply(X_13,X_12)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(inverse(X_14),multiply(X_13,X_12)))),bind(Y,$fot(multiply(X_13,multiply(inverse(X_14),X_12))))]]) ).
cnf(refute_0_42,plain,
multiply(X_13,multiply(inverse(X_14),X_12)) = multiply(inverse(X_14),multiply(X_13,X_12)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(X_13,X_12)),multiply(X_13,multiply(inverse(X_14),X_12))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( multiply(X_13,multiply(inverse(X_14),X_12)) != multiply(inverse(X_14),multiply(X_13,X_12))
| multiply(multiply(X_13,multiply(inverse(X_14),X_12)),X_14) != multiply(X_13,X_12)
| multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) = multiply(X_13,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(X_14),X_12)),X_14),multiply(X_13,X_12)) ),[0,0],$fot(multiply(inverse(X_14),multiply(X_13,X_12)))]]) ).
cnf(refute_0_44,plain,
( multiply(multiply(X_13,multiply(inverse(X_14),X_12)),X_14) != multiply(X_13,X_12)
| multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) = multiply(X_13,X_12) ),
inference(resolve,[$cnf( $equal(multiply(X_13,multiply(inverse(X_14),X_12)),multiply(inverse(X_14),multiply(X_13,X_12))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) = multiply(X_13,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(X_14),X_12)),X_14),multiply(X_13,X_12)) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(multiply(X_13,multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))),X_14) = multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))),bind(X_11,$fot(X_13)),bind(X_6,$fot(X_14))]]) ).
cnf(refute_0_47,plain,
multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(X_14)))]]) ).
cnf(refute_0_48,plain,
( multiply(multiply(X_13,multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))),X_14) != multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))
| multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) != C
| multiply(multiply(X_13,C),X_14) = multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))),X_14),multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))) ),[0,0,1],$fot(C)]]) ).
cnf(refute_0_49,plain,
( multiply(multiply(X_13,multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))),X_14) != multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))
| multiply(multiply(X_13,C),X_14) = multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),C) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(multiply(X_13,C),X_14) = multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))),X_14),multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B) = multiply(C,X_14),
inference(subst,[],[refute_0_24:[bind(X_8,$fot(X_14))]]) ).
cnf(refute_0_52,plain,
multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) = multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),
introduced(tautology,[refl,[$fot(multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)))]]) ).
cnf(refute_0_53,plain,
( multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) != multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))
| multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B) != multiply(C,X_14)
| multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) = multiply(X_13,multiply(C,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))) ),[1,1],$fot(multiply(C,X_14))]]) ).
cnf(refute_0_54,plain,
( multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B) != multiply(C,X_14)
| multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) = multiply(X_13,multiply(C,X_14)) ),
inference(resolve,[$cnf( $equal(multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) = multiply(X_13,multiply(C,X_14)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B),multiply(C,X_14)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) != multiply(X_13,multiply(C,X_14))
| multiply(multiply(X_13,C),X_14) != multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))
| multiply(multiply(X_13,C),X_14) = multiply(X_13,multiply(C,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_13,C),X_14),multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))) ),[1],$fot(multiply(X_13,multiply(C,X_14)))]]) ).
cnf(refute_0_57,plain,
( multiply(multiply(X_13,C),X_14) != multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))
| multiply(multiply(X_13,C),X_14) = multiply(X_13,multiply(C,X_14)) ),
inference(resolve,[$cnf( $equal(multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),multiply(X_13,multiply(C,X_14))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(multiply(X_13,C),X_14) = multiply(X_13,multiply(C,X_14)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,C),X_14),multiply(X_13,multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B))) )],[refute_0_50,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(multiply(X_13,X_12),X_14) = multiply(X_13,multiply(X_12,X_14)),
inference(subst,[],[refute_0_58:[bind(C,$fot(X_12))]]) ).
cnf(refute_0_60,plain,
multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)) = multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)),
introduced(tautology,[refl,[$fot(multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)))]]) ).
cnf(refute_0_61,plain,
( multiply(multiply(X_13,X_12),X_14) != multiply(X_13,multiply(X_12,X_14))
| multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)) != multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14))
| multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)) = multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)),multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14))) ),[1,1],$fot(multiply(X_13,multiply(X_12,X_14)))]]) ).
cnf(refute_0_62,plain,
( multiply(multiply(X_13,X_12),X_14) != multiply(X_13,multiply(X_12,X_14))
| multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)) = multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)),multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)) = multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,X_12),X_14),multiply(X_13,multiply(X_12,X_14))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) = multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)),
inference(subst,[],[refute_0_58:[bind(C,$fot(multiply(X_13,X_12))),bind(X_13,$fot(inverse(X_14)))]]) ).
cnf(refute_0_65,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_66,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_22,refute_0_65]) ).
cnf(refute_0_67,plain,
( multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) != multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14))
| multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)) != multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14)))
| multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) = multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14))),bind(Y,$fot(multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)))),bind(Z,$fot(multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14)))))]]) ).
cnf(refute_0_68,plain,
( multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)) != multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14)))
| multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) = multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14),multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) = multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(X_13,X_12),X_14)),multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14)))) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
( multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) != multiply(X_13,X_12)
| multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) != multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14)))
| multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))) = multiply(X_13,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14),multiply(X_13,X_12)) ),[0],$fot(multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))))]]) ).
cnf(refute_0_71,plain,
( multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14) != multiply(X_13,X_12)
| multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))) = multiply(X_13,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14),multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(inverse(X_14),multiply(X_13,multiply(X_12,X_14))) = multiply(X_13,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_14),multiply(X_13,X_12)),X_14),multiply(X_13,X_12)) )],[refute_0_45,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))) = multiply(X_4,X_9),
inference(subst,[],[refute_0_72:[bind(X_12,$fot(X_9)),bind(X_13,$fot(X_4)),bind(X_14,$fot(X_10))]]) ).
cnf(refute_0_74,plain,
multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) = multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))),
inference(subst,[],[refute_0_58:[bind(C,$fot(X_4)),bind(X_13,$fot(inverse(X_10))),bind(X_14,$fot(multiply(X_9,X_10)))]]) ).
cnf(refute_0_75,plain,
( multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) != multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10)))
| multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))) != multiply(X_4,X_9)
| multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) = multiply(X_4,X_9) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)))),bind(Y,$fot(multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))))),bind(Z,$fot(multiply(X_4,X_9)))]]) ).
cnf(refute_0_76,plain,
( multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))) != multiply(X_4,X_9)
| multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) = multiply(X_4,X_9) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)),multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) = multiply(X_4,X_9),
inference(resolve,[$cnf( $equal(multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))),multiply(X_4,X_9)) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
( multiply(X_9,X_4) != multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))
| multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) != multiply(X_4,X_9)
| multiply(X_9,X_4) = multiply(X_4,X_9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_9,X_4),multiply(X_4,X_9)) ),[0],$fot(multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)))]]) ).
cnf(refute_0_79,plain,
( multiply(X_9,X_4) != multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))
| multiply(X_9,X_4) = multiply(X_4,X_9) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)),multiply(X_4,X_9)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(X_9,X_4) = multiply(X_4,X_9),
inference(resolve,[$cnf( $equal(multiply(X_9,X_4),multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))) )],[refute_0_33,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(X_9,X_4) != multiply(X_4,X_9)
| multiply(X_4,X_9) = multiply(X_9,X_4) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(X_9,X_4))),bind(Y,$fot(multiply(X_4,X_9)))]]) ).
cnf(refute_0_82,plain,
multiply(X_4,X_9) = multiply(X_9,X_4),
inference(resolve,[$cnf( $equal(multiply(X_9,X_4),multiply(X_4,X_9)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(subst,[],[refute_0_82:[bind(X_4,$fot(inverse(a1))),bind(X_9,$fot(a1))]]) ).
cnf(refute_0_84,plain,
( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) != multiply(a1,inverse(a1))
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a1),a1),multiply(a1,inverse(a1))) ),[1],$fot(multiply(inverse(b1),b1))]]) ).
cnf(refute_0_85,plain,
( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(a1,inverse(a1))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(inverse(b1),b1) = multiply(b1,inverse(b1)),
inference(subst,[],[refute_0_82:[bind(X_4,$fot(inverse(b1))),bind(X_9,$fot(b1))]]) ).
cnf(refute_0_87,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(inverse(b1),b1) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a1,inverse(a1)),multiply(inverse(b1),b1)) ),[1],$fot(multiply(b1,inverse(b1)))]]) ).
cnf(refute_0_88,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b1),b1),multiply(b1,inverse(b1))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(inverse(b1),b1)) )],[refute_0_88,refute_0_85]) ).
cnf(refute_0_90,plain,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) )],[refute_0_89,prove_these_axioms_1]) ).
cnf(refute_0_91,plain,
multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) = multiply(X_2,multiply(multiply(X_13,multiply(inverse(B),X_12)),B)),
inference(subst,[],[refute_0_28:[bind(A,$fot(multiply(X_13,multiply(inverse(B),X_12))))]]) ).
cnf(refute_0_92,plain,
multiply(multiply(X_13,multiply(inverse(B),X_12)),B) = multiply(X_13,X_12),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(X_12)),bind(X_11,$fot(X_13)),bind(X_6,$fot(B))]]) ).
cnf(refute_0_93,plain,
( multiply(multiply(X_13,multiply(inverse(B),X_12)),B) != multiply(X_13,X_12)
| multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) != multiply(X_2,multiply(multiply(X_13,multiply(inverse(B),X_12)),B))
| multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) = multiply(X_2,multiply(X_13,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)),multiply(X_2,multiply(multiply(X_13,multiply(inverse(B),X_12)),B))) ),[1,1],$fot(multiply(X_13,X_12))]]) ).
cnf(refute_0_94,plain,
( multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) != multiply(X_2,multiply(multiply(X_13,multiply(inverse(B),X_12)),B))
| multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) = multiply(X_2,multiply(X_13,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(B),X_12)),B),multiply(X_13,X_12)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) = multiply(X_2,multiply(X_13,X_12)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)),multiply(X_2,multiply(multiply(X_13,multiply(inverse(B),X_12)),B))) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(inverse(B),multiply(X_12,multiply(X_2,B))) = multiply(X_12,X_2),
inference(subst,[],[refute_0_72:[bind(X_12,$fot(X_2)),bind(X_13,$fot(X_12)),bind(X_14,$fot(B))]]) ).
cnf(refute_0_97,plain,
multiply(multiply(inverse(B),X_12),multiply(X_2,B)) = multiply(inverse(B),multiply(X_12,multiply(X_2,B))),
inference(subst,[],[refute_0_58:[bind(C,$fot(X_12)),bind(X_13,$fot(inverse(B))),bind(X_14,$fot(multiply(X_2,B)))]]) ).
cnf(refute_0_98,plain,
( multiply(multiply(inverse(B),X_12),multiply(X_2,B)) != multiply(inverse(B),multiply(X_12,multiply(X_2,B)))
| multiply(inverse(B),multiply(X_12,multiply(X_2,B))) != multiply(X_12,X_2)
| multiply(multiply(inverse(B),X_12),multiply(X_2,B)) = multiply(X_12,X_2) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(inverse(B),X_12),multiply(X_2,B)))),bind(Y,$fot(multiply(inverse(B),multiply(X_12,multiply(X_2,B))))),bind(Z,$fot(multiply(X_12,X_2)))]]) ).
cnf(refute_0_99,plain,
( multiply(inverse(B),multiply(X_12,multiply(X_2,B))) != multiply(X_12,X_2)
| multiply(multiply(inverse(B),X_12),multiply(X_2,B)) = multiply(X_12,X_2) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_12),multiply(X_2,B)),multiply(inverse(B),multiply(X_12,multiply(X_2,B)))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
multiply(multiply(inverse(B),X_12),multiply(X_2,B)) = multiply(X_12,X_2),
inference(resolve,[$cnf( $equal(multiply(inverse(B),multiply(X_12,multiply(X_2,B))),multiply(X_12,X_2)) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))) = multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))),
introduced(tautology,[refl,[$fot(multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))))]]) ).
cnf(refute_0_102,plain,
( multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))) != multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B)))
| multiply(multiply(inverse(B),X_12),multiply(X_2,B)) != multiply(X_12,X_2)
| multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))) = multiply(X_13,multiply(X_12,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))),multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B)))) ),[1,1],$fot(multiply(X_12,X_2))]]) ).
cnf(refute_0_103,plain,
( multiply(multiply(inverse(B),X_12),multiply(X_2,B)) != multiply(X_12,X_2)
| multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))) = multiply(X_13,multiply(X_12,X_2)) ),
inference(resolve,[$cnf( $equal(multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))),multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))) = multiply(X_13,multiply(X_12,X_2)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_12),multiply(X_2,B)),multiply(X_12,X_2)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) = multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))),
inference(subst,[],[refute_0_58:[bind(C,$fot(multiply(inverse(B),X_12))),bind(X_14,$fot(multiply(X_2,B)))]]) ).
cnf(refute_0_106,plain,
( multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))) != multiply(X_13,multiply(X_12,X_2))
| multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) != multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B)))
| multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) = multiply(X_13,multiply(X_12,X_2)) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)))),bind(Y,$fot(multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))))),bind(Z,$fot(multiply(X_13,multiply(X_12,X_2))))]]) ).
cnf(refute_0_107,plain,
( multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))) != multiply(X_13,multiply(X_12,X_2))
| multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) = multiply(X_13,multiply(X_12,X_2)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)),multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B)))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) = multiply(X_13,multiply(X_12,X_2)),
inference(resolve,[$cnf( $equal(multiply(X_13,multiply(multiply(inverse(B),X_12),multiply(X_2,B))),multiply(X_13,multiply(X_12,X_2))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) != multiply(X_13,multiply(X_12,X_2))
| multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) != multiply(X_2,multiply(X_13,X_12))
| multiply(X_13,multiply(X_12,X_2)) = multiply(X_2,multiply(X_13,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)),multiply(X_2,multiply(X_13,X_12))) ),[0],$fot(multiply(X_13,multiply(X_12,X_2)))]]) ).
cnf(refute_0_110,plain,
( multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)) != multiply(X_2,multiply(X_13,X_12))
| multiply(X_13,multiply(X_12,X_2)) = multiply(X_2,multiply(X_13,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)),multiply(X_13,multiply(X_12,X_2))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(X_13,multiply(X_12,X_2)) = multiply(X_2,multiply(X_13,X_12)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(B),X_12)),multiply(X_2,B)),multiply(X_2,multiply(X_13,X_12))) )],[refute_0_95,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(inverse(multiply(A,B)),multiply(C,B)) = multiply(B,multiply(inverse(multiply(A,B)),C)),
inference(subst,[],[refute_0_111:[bind(X_12,$fot(C)),bind(X_13,$fot(inverse(multiply(A,B)))),bind(X_2,$fot(B))]]) ).
cnf(refute_0_113,plain,
multiply(multiply(inverse(multiply(A,B)),C),B) = multiply(inverse(multiply(A,B)),multiply(C,B)),
inference(subst,[],[refute_0_58:[bind(X_13,$fot(inverse(multiply(A,B)))),bind(X_14,$fot(B))]]) ).
cnf(refute_0_114,plain,
( multiply(multiply(inverse(multiply(A,B)),C),B) != multiply(inverse(multiply(A,B)),multiply(C,B))
| multiply(inverse(multiply(A,B)),multiply(C,B)) != multiply(B,multiply(inverse(multiply(A,B)),C))
| multiply(multiply(inverse(multiply(A,B)),C),B) = multiply(B,multiply(inverse(multiply(A,B)),C)) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(inverse(multiply(A,B)),C),B))),bind(Y,$fot(multiply(inverse(multiply(A,B)),multiply(C,B)))),bind(Z,$fot(multiply(B,multiply(inverse(multiply(A,B)),C))))]]) ).
cnf(refute_0_115,plain,
( multiply(inverse(multiply(A,B)),multiply(C,B)) != multiply(B,multiply(inverse(multiply(A,B)),C))
| multiply(multiply(inverse(multiply(A,B)),C),B) = multiply(B,multiply(inverse(multiply(A,B)),C)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(A,B)),C),B),multiply(inverse(multiply(A,B)),multiply(C,B))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(multiply(inverse(multiply(A,B)),C),B) = multiply(B,multiply(inverse(multiply(A,B)),C)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(A,B)),multiply(C,B)),multiply(B,multiply(inverse(multiply(A,B)),C))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)),
introduced(tautology,[refl,[$fot(multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)))]]) ).
cnf(refute_0_118,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) != multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))
| multiply(multiply(inverse(multiply(A,B)),C),B) != multiply(B,multiply(inverse(multiply(A,B)),C))
| multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)),multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))) ),[1,1],$fot(multiply(B,multiply(inverse(multiply(A,B)),C)))]]) ).
cnf(refute_0_119,plain,
( multiply(multiply(inverse(multiply(A,B)),C),B) != multiply(B,multiply(inverse(multiply(A,B)),C))
| multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)),multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(A,B)),C),B),multiply(B,multiply(inverse(multiply(A,B)),C))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) != C
| multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) != multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C)))
| multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)),C) ),[0],$fot(multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))))]]) ).
cnf(refute_0_122,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) != C
| multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))) = C ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)),multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C)))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))) = C,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)),C) )],[single_axiom,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(X_24,multiply(X_25,multiply(inverse(multiply(X_24,X_25)),inverse(X_25)))) = inverse(X_25),
inference(subst,[],[refute_0_123:[bind(A,$fot(X_24)),bind(B,$fot(X_25)),bind(C,$fot(inverse(X_25)))]]) ).
cnf(refute_0_125,plain,
multiply(inverse(X_2),multiply(X_2,B)) = multiply(X_2,multiply(inverse(X_2),B)),
inference(subst,[],[refute_0_28:[bind(A,$fot(inverse(X_2)))]]) ).
cnf(refute_0_126,plain,
multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = multiply(multiply(inverse(X_12),X_4),X_12),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(X_12)),bind(X_11,$fot(multiply(inverse(X_12),X_4))),bind(X_6,$fot(X_14))]]) ).
cnf(refute_0_127,plain,
multiply(multiply(inverse(X_12),X_4),X_12) = X_4,
inference(subst,[],[refute_0_14:[bind(X_6,$fot(X_12))]]) ).
cnf(refute_0_128,plain,
( multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) != multiply(multiply(inverse(X_12),X_4),X_12)
| multiply(multiply(inverse(X_12),X_4),X_12) != X_4
| multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = X_4 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14),X_4) ),[0],$fot(multiply(multiply(inverse(X_12),X_4),X_12))]]) ).
cnf(refute_0_129,plain,
( multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) != multiply(multiply(inverse(X_12),X_4),X_12)
| multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_12),X_4),X_12),X_4) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = X_4,
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14),multiply(multiply(inverse(X_12),X_4),X_12)) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(multiply(X_13,multiply(inverse(X_14),multiply(A,B))),X_14) = multiply(X_13,multiply(A,B)),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(multiply(A,B))),bind(X_11,$fot(X_13)),bind(X_6,$fot(X_14))]]) ).
cnf(refute_0_132,plain,
multiply(A,multiply(inverse(X_14),B)) = multiply(inverse(X_14),multiply(A,B)),
inference(subst,[],[refute_0_28:[bind(X_2,$fot(inverse(X_14)))]]) ).
cnf(refute_0_133,plain,
( multiply(A,multiply(inverse(X_14),B)) != multiply(inverse(X_14),multiply(A,B))
| multiply(inverse(X_14),multiply(A,B)) = multiply(A,multiply(inverse(X_14),B)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(A,multiply(inverse(X_14),B)))),bind(Y,$fot(multiply(inverse(X_14),multiply(A,B))))]]) ).
cnf(refute_0_134,plain,
multiply(inverse(X_14),multiply(A,B)) = multiply(A,multiply(inverse(X_14),B)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(inverse(X_14),B)),multiply(inverse(X_14),multiply(A,B))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( multiply(multiply(X_13,multiply(inverse(X_14),multiply(A,B))),X_14) != multiply(X_13,multiply(A,B))
| multiply(inverse(X_14),multiply(A,B)) != multiply(A,multiply(inverse(X_14),B))
| multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) = multiply(X_13,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(X_14),multiply(A,B))),X_14),multiply(X_13,multiply(A,B))) ),[0,0,1],$fot(multiply(A,multiply(inverse(X_14),B)))]]) ).
cnf(refute_0_136,plain,
( multiply(multiply(X_13,multiply(inverse(X_14),multiply(A,B))),X_14) != multiply(X_13,multiply(A,B))
| multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) = multiply(X_13,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(A,B)),multiply(A,multiply(inverse(X_14),B))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) = multiply(X_13,multiply(A,B)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(inverse(X_14),multiply(A,B))),X_14),multiply(X_13,multiply(A,B))) )],[refute_0_131,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(multiply(inverse(X_14),B),X_14) = multiply(inverse(X_14),multiply(B,X_14)),
inference(subst,[],[refute_0_58:[bind(C,$fot(B)),bind(X_13,$fot(inverse(X_14)))]]) ).
cnf(refute_0_139,plain,
multiply(A,multiply(multiply(inverse(X_14),B),X_14)) = multiply(A,multiply(multiply(inverse(X_14),B),X_14)),
introduced(tautology,[refl,[$fot(multiply(A,multiply(multiply(inverse(X_14),B),X_14)))]]) ).
cnf(refute_0_140,plain,
( multiply(A,multiply(multiply(inverse(X_14),B),X_14)) != multiply(A,multiply(multiply(inverse(X_14),B),X_14))
| multiply(multiply(inverse(X_14),B),X_14) != multiply(inverse(X_14),multiply(B,X_14))
| multiply(A,multiply(multiply(inverse(X_14),B),X_14)) = multiply(A,multiply(inverse(X_14),multiply(B,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(X_14),B),X_14)),multiply(A,multiply(multiply(inverse(X_14),B),X_14))) ),[1,1],$fot(multiply(inverse(X_14),multiply(B,X_14)))]]) ).
cnf(refute_0_141,plain,
( multiply(multiply(inverse(X_14),B),X_14) != multiply(inverse(X_14),multiply(B,X_14))
| multiply(A,multiply(multiply(inverse(X_14),B),X_14)) = multiply(A,multiply(inverse(X_14),multiply(B,X_14))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(X_14),B),X_14)),multiply(A,multiply(multiply(inverse(X_14),B),X_14))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(A,multiply(multiply(inverse(X_14),B),X_14)) = multiply(A,multiply(inverse(X_14),multiply(B,X_14))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_14),B),X_14),multiply(inverse(X_14),multiply(B,X_14))) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(multiply(A,multiply(inverse(X_14),B)),X_14) = multiply(A,multiply(multiply(inverse(X_14),B),X_14)),
inference(subst,[],[refute_0_58:[bind(C,$fot(multiply(inverse(X_14),B))),bind(X_13,$fot(A))]]) ).
cnf(refute_0_144,plain,
( multiply(A,multiply(multiply(inverse(X_14),B),X_14)) != multiply(A,multiply(inverse(X_14),multiply(B,X_14)))
| multiply(multiply(A,multiply(inverse(X_14),B)),X_14) != multiply(A,multiply(multiply(inverse(X_14),B),X_14))
| multiply(multiply(A,multiply(inverse(X_14),B)),X_14) = multiply(A,multiply(inverse(X_14),multiply(B,X_14))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(A,multiply(inverse(X_14),B)),X_14))),bind(Y,$fot(multiply(A,multiply(multiply(inverse(X_14),B),X_14)))),bind(Z,$fot(multiply(A,multiply(inverse(X_14),multiply(B,X_14)))))]]) ).
cnf(refute_0_145,plain,
( multiply(A,multiply(multiply(inverse(X_14),B),X_14)) != multiply(A,multiply(inverse(X_14),multiply(B,X_14)))
| multiply(multiply(A,multiply(inverse(X_14),B)),X_14) = multiply(A,multiply(inverse(X_14),multiply(B,X_14))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(A,multiply(inverse(X_14),B)),X_14),multiply(A,multiply(multiply(inverse(X_14),B),X_14))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(multiply(A,multiply(inverse(X_14),B)),X_14) = multiply(A,multiply(inverse(X_14),multiply(B,X_14))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(X_14),B),X_14)),multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)) = multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)),
introduced(tautology,[refl,[$fot(multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)))]]) ).
cnf(refute_0_148,plain,
( multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)) != multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14))
| multiply(multiply(A,multiply(inverse(X_14),B)),X_14) != multiply(A,multiply(inverse(X_14),multiply(B,X_14)))
| multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)) = multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)),multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14))) ),[1,1],$fot(multiply(A,multiply(inverse(X_14),multiply(B,X_14))))]]) ).
cnf(refute_0_149,plain,
( multiply(multiply(A,multiply(inverse(X_14),B)),X_14) != multiply(A,multiply(inverse(X_14),multiply(B,X_14)))
| multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)) = multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) ),
inference(resolve,[$cnf( $equal(multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)),multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)) = multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))),
inference(resolve,[$cnf( $equal(multiply(multiply(A,multiply(inverse(X_14),B)),X_14),multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) = multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)),
inference(subst,[],[refute_0_58:[bind(C,$fot(multiply(A,multiply(inverse(X_14),B))))]]) ).
cnf(refute_0_152,plain,
( multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)) != multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14))))
| multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) != multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14))
| multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) = multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14))),bind(Y,$fot(multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)))),bind(Z,$fot(multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14))))))]]) ).
cnf(refute_0_153,plain,
( multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)) != multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14))))
| multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) = multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14),multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) = multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))),
inference(resolve,[$cnf( $equal(multiply(X_13,multiply(multiply(A,multiply(inverse(X_14),B)),X_14)),multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14))))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) != multiply(X_13,multiply(A,B))
| multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) != multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14))))
| multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) = multiply(X_13,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14),multiply(X_13,multiply(A,B))) ),[0],$fot(multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))))]]) ).
cnf(refute_0_156,plain,
( multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14) != multiply(X_13,multiply(A,B))
| multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) = multiply(X_13,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14),multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14))))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(X_13,multiply(A,multiply(inverse(X_14),multiply(B,X_14)))) = multiply(X_13,multiply(A,B)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_13,multiply(A,multiply(inverse(X_14),B))),X_14),multiply(X_13,multiply(A,B))) )],[refute_0_137,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))) = multiply(inverse(X_12),multiply(X_4,X_12)),
inference(subst,[],[refute_0_157:[bind(A,$fot(X_4)),bind(B,$fot(X_12)),bind(X_13,$fot(inverse(X_12)))]]) ).
cnf(refute_0_159,plain,
multiply(multiply(inverse(X_14),X_12),X_14) = multiply(inverse(X_14),multiply(X_12,X_14)),
inference(subst,[],[refute_0_58:[bind(C,$fot(X_12)),bind(X_13,$fot(inverse(X_14)))]]) ).
cnf(refute_0_160,plain,
multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)) = multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)),
introduced(tautology,[refl,[$fot(multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))]]) ).
cnf(refute_0_161,plain,
( multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)) != multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))
| multiply(multiply(inverse(X_14),X_12),X_14) != multiply(inverse(X_14),multiply(X_12,X_14))
| multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)) = multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) ),[1,1],$fot(multiply(inverse(X_14),multiply(X_12,X_14)))]]) ).
cnf(refute_0_162,plain,
( multiply(multiply(inverse(X_14),X_12),X_14) != multiply(inverse(X_14),multiply(X_12,X_14))
| multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)) = multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)) = multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_14),X_12),X_14),multiply(inverse(X_14),multiply(X_12,X_14))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) = multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))))]]) ).
cnf(refute_0_165,plain,
( multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)) != multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))
| multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) != multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))
| multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) = multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))),multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))) ),[1,1],$fot(multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14))))]]) ).
cnf(refute_0_166,plain,
( multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)) != multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))
| multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) = multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))),multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) = multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))),
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
( multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) != multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14))))
| multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))) != multiply(inverse(X_12),multiply(X_4,X_12))
| multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) = multiply(inverse(X_12),multiply(X_4,X_12)) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))))),bind(Y,$fot(multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))))),bind(Z,$fot(multiply(inverse(X_12),multiply(X_4,X_12))))]]) ).
cnf(refute_0_169,plain,
( multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))) != multiply(inverse(X_12),multiply(X_4,X_12))
| multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) = multiply(inverse(X_12),multiply(X_4,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))),multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14))))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) = multiply(inverse(X_12),multiply(X_4,X_12)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(X_4,multiply(inverse(X_14),multiply(X_12,X_14)))),multiply(inverse(X_12),multiply(X_4,X_12))) )],[refute_0_158,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(multiply(inverse(X_12),X_4),multiply(multiply(inverse(X_14),X_12),X_14)) = multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))),
inference(subst,[],[refute_0_58:[bind(C,$fot(X_4)),bind(X_13,$fot(inverse(X_12))),bind(X_14,$fot(multiply(multiply(inverse(X_14),X_12),X_14)))]]) ).
cnf(refute_0_172,plain,
multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = multiply(multiply(inverse(X_12),X_4),multiply(multiply(inverse(X_14),X_12),X_14)),
inference(subst,[],[refute_0_58:[bind(C,$fot(multiply(inverse(X_14),X_12))),bind(X_13,$fot(multiply(inverse(X_12),X_4)))]]) ).
cnf(refute_0_173,plain,
( multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) != multiply(multiply(inverse(X_12),X_4),multiply(multiply(inverse(X_14),X_12),X_14))
| multiply(multiply(inverse(X_12),X_4),multiply(multiply(inverse(X_14),X_12),X_14)) != multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))
| multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14))),bind(Y,$fot(multiply(multiply(inverse(X_12),X_4),multiply(multiply(inverse(X_14),X_12),X_14)))),bind(Z,$fot(multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))))]]) ).
cnf(refute_0_174,plain,
( multiply(multiply(inverse(X_12),X_4),multiply(multiply(inverse(X_14),X_12),X_14)) != multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))
| multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14),multiply(multiply(inverse(X_12),X_4),multiply(multiply(inverse(X_14),X_12),X_14))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_12),X_4),multiply(multiply(inverse(X_14),X_12),X_14)),multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
( multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) != multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))
| multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) != multiply(inverse(X_12),multiply(X_4,X_12))
| multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = multiply(inverse(X_12),multiply(X_4,X_12)) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14))),bind(Y,$fot(multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))))),bind(Z,$fot(multiply(inverse(X_12),multiply(X_4,X_12))))]]) ).
cnf(refute_0_177,plain,
( multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))) != multiply(inverse(X_12),multiply(X_4,X_12))
| multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = multiply(inverse(X_12),multiply(X_4,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14),multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14)))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) = multiply(inverse(X_12),multiply(X_4,X_12)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(X_4,multiply(multiply(inverse(X_14),X_12),X_14))),multiply(inverse(X_12),multiply(X_4,X_12))) )],[refute_0_170,refute_0_177]) ).
cnf(refute_0_179,plain,
( multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) != X_4
| multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) != multiply(inverse(X_12),multiply(X_4,X_12))
| multiply(inverse(X_12),multiply(X_4,X_12)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14),X_4) ),[0],$fot(multiply(inverse(X_12),multiply(X_4,X_12)))]]) ).
cnf(refute_0_180,plain,
( multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14) != X_4
| multiply(inverse(X_12),multiply(X_4,X_12)) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14),multiply(inverse(X_12),multiply(X_4,X_12))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
multiply(inverse(X_12),multiply(X_4,X_12)) = X_4,
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(inverse(X_12),X_4),multiply(inverse(X_14),X_12)),X_14),X_4) )],[refute_0_130,refute_0_180]) ).
cnf(refute_0_182,plain,
multiply(inverse(X_12),multiply(X_4,X_12)) = multiply(X_12,multiply(inverse(X_12),X_4)),
inference(subst,[],[refute_0_111:[bind(X_12,$fot(X_4)),bind(X_13,$fot(inverse(X_12))),bind(X_2,$fot(X_12))]]) ).
cnf(refute_0_183,plain,
( multiply(inverse(X_12),multiply(X_4,X_12)) != X_4
| multiply(inverse(X_12),multiply(X_4,X_12)) != multiply(X_12,multiply(inverse(X_12),X_4))
| multiply(X_12,multiply(inverse(X_12),X_4)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_12),multiply(X_4,X_12)),X_4) ),[0],$fot(multiply(X_12,multiply(inverse(X_12),X_4)))]]) ).
cnf(refute_0_184,plain,
( multiply(inverse(X_12),multiply(X_4,X_12)) != X_4
| multiply(X_12,multiply(inverse(X_12),X_4)) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(X_4,X_12)),multiply(X_12,multiply(inverse(X_12),X_4))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
multiply(X_12,multiply(inverse(X_12),X_4)) = X_4,
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),multiply(X_4,X_12)),X_4) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(X_2,multiply(inverse(X_2),B)) = B,
inference(subst,[],[refute_0_185:[bind(X_12,$fot(X_2)),bind(X_4,$fot(B))]]) ).
cnf(refute_0_187,plain,
( multiply(X_2,multiply(inverse(X_2),B)) != B
| multiply(inverse(X_2),multiply(X_2,B)) != multiply(X_2,multiply(inverse(X_2),B))
| multiply(inverse(X_2),multiply(X_2,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_2),multiply(X_2,B)),multiply(X_2,multiply(inverse(X_2),B))) ),[1],$fot(B)]]) ).
cnf(refute_0_188,plain,
( multiply(inverse(X_2),multiply(X_2,B)) != multiply(X_2,multiply(inverse(X_2),B))
| multiply(inverse(X_2),multiply(X_2,B)) = B ),
inference(resolve,[$cnf( $equal(multiply(X_2,multiply(inverse(X_2),B)),B) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(inverse(X_2),multiply(X_2,B)) = B,
inference(resolve,[$cnf( $equal(multiply(inverse(X_2),multiply(X_2,B)),multiply(X_2,multiply(inverse(X_2),B))) )],[refute_0_125,refute_0_188]) ).
cnf(refute_0_190,plain,
multiply(A,B) = multiply(B,A),
inference(subst,[],[refute_0_80:[bind(X_4,$fot(B)),bind(X_9,$fot(A))]]) ).
cnf(refute_0_191,plain,
( multiply(A,B) != multiply(B,A)
| multiply(A,multiply(X_2,B)) != multiply(X_2,multiply(A,B))
| multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(B,A)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_2,B)),multiply(X_2,multiply(A,B))) ),[1,1],$fot(multiply(B,A))]]) ).
cnf(refute_0_192,plain,
( multiply(A,multiply(X_2,B)) != multiply(X_2,multiply(A,B))
| multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(B,A)) ),
inference(resolve,[$cnf( $equal(multiply(A,B),multiply(B,A)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_2,B)),multiply(X_2,multiply(A,B))) )],[refute_0_28,refute_0_192]) ).
cnf(refute_0_194,plain,
multiply(inverse(X_2),multiply(X_2,B)) = multiply(X_2,multiply(B,inverse(X_2))),
inference(subst,[],[refute_0_193:[bind(A,$fot(inverse(X_2)))]]) ).
cnf(refute_0_195,plain,
( multiply(inverse(X_2),multiply(X_2,B)) != B
| multiply(inverse(X_2),multiply(X_2,B)) != multiply(X_2,multiply(B,inverse(X_2)))
| multiply(X_2,multiply(B,inverse(X_2))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_2),multiply(X_2,B)),B) ),[0],$fot(multiply(X_2,multiply(B,inverse(X_2))))]]) ).
cnf(refute_0_196,plain,
( multiply(inverse(X_2),multiply(X_2,B)) != B
| multiply(X_2,multiply(B,inverse(X_2))) = B ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_2),multiply(X_2,B)),multiply(X_2,multiply(B,inverse(X_2)))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
multiply(X_2,multiply(B,inverse(X_2))) = B,
inference(resolve,[$cnf( $equal(multiply(inverse(X_2),multiply(X_2,B)),B) )],[refute_0_189,refute_0_196]) ).
cnf(refute_0_198,plain,
multiply(X_25,multiply(inverse(multiply(X_24,X_25)),inverse(X_25))) = inverse(multiply(X_24,X_25)),
inference(subst,[],[refute_0_197:[bind(B,$fot(inverse(multiply(X_24,X_25)))),bind(X_2,$fot(X_25))]]) ).
cnf(refute_0_199,plain,
( multiply(X_24,multiply(X_25,multiply(inverse(multiply(X_24,X_25)),inverse(X_25)))) != inverse(X_25)
| multiply(X_25,multiply(inverse(multiply(X_24,X_25)),inverse(X_25))) != inverse(multiply(X_24,X_25))
| multiply(X_24,inverse(multiply(X_24,X_25))) = inverse(X_25) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_24,multiply(X_25,multiply(inverse(multiply(X_24,X_25)),inverse(X_25)))),inverse(X_25)) ),[0,1],$fot(inverse(multiply(X_24,X_25)))]]) ).
cnf(refute_0_200,plain,
( multiply(X_24,multiply(X_25,multiply(inverse(multiply(X_24,X_25)),inverse(X_25)))) != inverse(X_25)
| multiply(X_24,inverse(multiply(X_24,X_25))) = inverse(X_25) ),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(inverse(multiply(X_24,X_25)),inverse(X_25))),inverse(multiply(X_24,X_25))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
multiply(X_24,inverse(multiply(X_24,X_25))) = inverse(X_25),
inference(resolve,[$cnf( $equal(multiply(X_24,multiply(X_25,multiply(inverse(multiply(X_24,X_25)),inverse(X_25)))),inverse(X_25)) )],[refute_0_124,refute_0_200]) ).
cnf(refute_0_202,plain,
multiply(X_29,inverse(multiply(X_29,multiply(X_4,inverse(X_4))))) = inverse(multiply(X_4,inverse(X_4))),
inference(subst,[],[refute_0_201:[bind(X_24,$fot(X_29)),bind(X_25,$fot(multiply(X_4,inverse(X_4))))]]) ).
cnf(refute_0_203,plain,
multiply(multiply(X_19,inverse(X_4)),X_4) = multiply(X_4,multiply(X_19,inverse(X_4))),
inference(subst,[],[refute_0_80:[bind(X_9,$fot(multiply(X_19,inverse(X_4))))]]) ).
cnf(refute_0_204,plain,
multiply(X_4,multiply(X_19,inverse(X_4))) = X_19,
inference(subst,[],[refute_0_197:[bind(B,$fot(X_19)),bind(X_2,$fot(X_4))]]) ).
cnf(refute_0_205,plain,
( multiply(X_4,multiply(X_19,inverse(X_4))) != X_19
| multiply(multiply(X_19,inverse(X_4)),X_4) != multiply(X_4,multiply(X_19,inverse(X_4)))
| multiply(multiply(X_19,inverse(X_4)),X_4) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_19,inverse(X_4)),X_4),multiply(X_4,multiply(X_19,inverse(X_4)))) ),[1],$fot(X_19)]]) ).
cnf(refute_0_206,plain,
( multiply(multiply(X_19,inverse(X_4)),X_4) != multiply(X_4,multiply(X_19,inverse(X_4)))
| multiply(multiply(X_19,inverse(X_4)),X_4) = X_19 ),
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(X_19,inverse(X_4))),X_19) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
multiply(multiply(X_19,inverse(X_4)),X_4) = X_19,
inference(resolve,[$cnf( $equal(multiply(multiply(X_19,inverse(X_4)),X_4),multiply(X_4,multiply(X_19,inverse(X_4)))) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
multiply(X_2,multiply(A,B)) = multiply(multiply(A,B),X_2),
inference(subst,[],[refute_0_80:[bind(X_4,$fot(multiply(A,B))),bind(X_9,$fot(X_2))]]) ).
cnf(refute_0_209,plain,
( multiply(A,multiply(X_2,B)) != multiply(X_2,multiply(A,B))
| multiply(X_2,multiply(A,B)) != multiply(multiply(A,B),X_2)
| multiply(A,multiply(X_2,B)) = multiply(multiply(A,B),X_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,multiply(X_2,B)),multiply(multiply(A,B),X_2)) ),[0],$fot(multiply(X_2,multiply(A,B)))]]) ).
cnf(refute_0_210,plain,
( multiply(A,multiply(X_2,B)) != multiply(X_2,multiply(A,B))
| multiply(A,multiply(X_2,B)) = multiply(multiply(A,B),X_2) ),
inference(resolve,[$cnf( $equal(multiply(X_2,multiply(A,B)),multiply(multiply(A,B),X_2)) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
multiply(A,multiply(X_2,B)) = multiply(multiply(A,B),X_2),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_2,B)),multiply(X_2,multiply(A,B))) )],[refute_0_28,refute_0_210]) ).
cnf(refute_0_212,plain,
multiply(multiply(A,B),X_2) = multiply(A,multiply(B,X_2)),
inference(subst,[],[refute_0_58:[bind(C,$fot(B)),bind(X_13,$fot(A)),bind(X_14,$fot(X_2))]]) ).
cnf(refute_0_213,plain,
( multiply(A,multiply(X_2,B)) != multiply(multiply(A,B),X_2)
| multiply(multiply(A,B),X_2) != multiply(A,multiply(B,X_2))
| multiply(A,multiply(X_2,B)) = multiply(A,multiply(B,X_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,multiply(X_2,B)),multiply(A,multiply(B,X_2))) ),[0],$fot(multiply(multiply(A,B),X_2))]]) ).
cnf(refute_0_214,plain,
( multiply(A,multiply(X_2,B)) != multiply(multiply(A,B),X_2)
| multiply(A,multiply(X_2,B)) = multiply(A,multiply(B,X_2)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),X_2),multiply(A,multiply(B,X_2))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(A,multiply(X_2,B)) = multiply(A,multiply(B,X_2)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_2,B)),multiply(multiply(A,B),X_2)) )],[refute_0_211,refute_0_214]) ).
cnf(refute_0_216,plain,
( multiply(A,multiply(X_2,B)) != multiply(A,multiply(B,X_2))
| multiply(A,multiply(B,X_2)) = multiply(A,multiply(X_2,B)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(A,multiply(X_2,B)))),bind(Y,$fot(multiply(A,multiply(B,X_2))))]]) ).
cnf(refute_0_217,plain,
multiply(A,multiply(B,X_2)) = multiply(A,multiply(X_2,B)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_2,B)),multiply(A,multiply(B,X_2))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
multiply(X_19,multiply(inverse(X_4),X_4)) = multiply(X_19,multiply(X_4,inverse(X_4))),
inference(subst,[],[refute_0_217:[bind(A,$fot(X_19)),bind(B,$fot(inverse(X_4))),bind(X_2,$fot(X_4))]]) ).
cnf(refute_0_219,plain,
multiply(multiply(X_19,inverse(X_4)),X_4) = multiply(X_19,multiply(inverse(X_4),X_4)),
inference(subst,[],[refute_0_58:[bind(C,$fot(inverse(X_4))),bind(X_13,$fot(X_19)),bind(X_14,$fot(X_4))]]) ).
cnf(refute_0_220,plain,
( multiply(X_19,multiply(inverse(X_4),X_4)) != multiply(X_19,multiply(X_4,inverse(X_4)))
| multiply(multiply(X_19,inverse(X_4)),X_4) != multiply(X_19,multiply(inverse(X_4),X_4))
| multiply(multiply(X_19,inverse(X_4)),X_4) = multiply(X_19,multiply(X_4,inverse(X_4))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(X_19,inverse(X_4)),X_4))),bind(Y,$fot(multiply(X_19,multiply(inverse(X_4),X_4)))),bind(Z,$fot(multiply(X_19,multiply(X_4,inverse(X_4)))))]]) ).
cnf(refute_0_221,plain,
( multiply(X_19,multiply(inverse(X_4),X_4)) != multiply(X_19,multiply(X_4,inverse(X_4)))
| multiply(multiply(X_19,inverse(X_4)),X_4) = multiply(X_19,multiply(X_4,inverse(X_4))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_19,inverse(X_4)),X_4),multiply(X_19,multiply(inverse(X_4),X_4))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
multiply(multiply(X_19,inverse(X_4)),X_4) = multiply(X_19,multiply(X_4,inverse(X_4))),
inference(resolve,[$cnf( $equal(multiply(X_19,multiply(inverse(X_4),X_4)),multiply(X_19,multiply(X_4,inverse(X_4)))) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
( multiply(multiply(X_19,inverse(X_4)),X_4) != X_19
| multiply(multiply(X_19,inverse(X_4)),X_4) != multiply(X_19,multiply(X_4,inverse(X_4)))
| multiply(X_19,multiply(X_4,inverse(X_4))) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_19,inverse(X_4)),X_4),X_19) ),[0],$fot(multiply(X_19,multiply(X_4,inverse(X_4))))]]) ).
cnf(refute_0_224,plain,
( multiply(multiply(X_19,inverse(X_4)),X_4) != X_19
| multiply(X_19,multiply(X_4,inverse(X_4))) = X_19 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_19,inverse(X_4)),X_4),multiply(X_19,multiply(X_4,inverse(X_4)))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
multiply(X_19,multiply(X_4,inverse(X_4))) = X_19,
inference(resolve,[$cnf( $equal(multiply(multiply(X_19,inverse(X_4)),X_4),X_19) )],[refute_0_207,refute_0_224]) ).
cnf(refute_0_226,plain,
multiply(X_29,multiply(X_4,inverse(X_4))) = X_29,
inference(subst,[],[refute_0_225:[bind(X_19,$fot(X_29))]]) ).
cnf(refute_0_227,plain,
( multiply(X_29,multiply(X_4,inverse(X_4))) != X_29
| multiply(X_29,inverse(multiply(X_29,multiply(X_4,inverse(X_4))))) != inverse(multiply(X_4,inverse(X_4)))
| multiply(X_29,inverse(X_29)) = inverse(multiply(X_4,inverse(X_4))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_29,inverse(multiply(X_29,multiply(X_4,inverse(X_4))))),inverse(multiply(X_4,inverse(X_4)))) ),[0,1,0],$fot(X_29)]]) ).
cnf(refute_0_228,plain,
( multiply(X_29,inverse(multiply(X_29,multiply(X_4,inverse(X_4))))) != inverse(multiply(X_4,inverse(X_4)))
| multiply(X_29,inverse(X_29)) = inverse(multiply(X_4,inverse(X_4))) ),
inference(resolve,[$cnf( $equal(multiply(X_29,multiply(X_4,inverse(X_4))),X_29) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
multiply(X_29,inverse(X_29)) = inverse(multiply(X_4,inverse(X_4))),
inference(resolve,[$cnf( $equal(multiply(X_29,inverse(multiply(X_29,multiply(X_4,inverse(X_4))))),inverse(multiply(X_4,inverse(X_4)))) )],[refute_0_202,refute_0_228]) ).
cnf(refute_0_230,plain,
multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))) = inverse(multiply(X_27,inverse(X_27))),
inference(subst,[],[refute_0_225:[bind(X_19,$fot(inverse(multiply(X_27,inverse(X_27)))))]]) ).
cnf(refute_0_231,plain,
multiply(X_12,multiply(inverse(X_12),multiply(inverse(multiply(X_12,inverse(X_12))),X_26))) = multiply(inverse(multiply(X_12,inverse(X_12))),X_26),
inference(subst,[],[refute_0_185:[bind(X_4,$fot(multiply(inverse(multiply(X_12,inverse(X_12))),X_26)))]]) ).
cnf(refute_0_232,plain,
multiply(X_12,multiply(inverse(X_12),multiply(inverse(multiply(X_12,inverse(X_12))),X_26))) = X_26,
inference(subst,[],[refute_0_123:[bind(A,$fot(X_12)),bind(B,$fot(inverse(X_12))),bind(C,$fot(X_26))]]) ).
cnf(refute_0_233,plain,
( multiply(X_12,multiply(inverse(X_12),multiply(inverse(multiply(X_12,inverse(X_12))),X_26))) != X_26
| multiply(X_12,multiply(inverse(X_12),multiply(inverse(multiply(X_12,inverse(X_12))),X_26))) != multiply(inverse(multiply(X_12,inverse(X_12))),X_26)
| X_26 = multiply(inverse(multiply(X_12,inverse(X_12))),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_12,multiply(inverse(X_12),multiply(inverse(multiply(X_12,inverse(X_12))),X_26))),multiply(inverse(multiply(X_12,inverse(X_12))),X_26)) ),[0],$fot(X_26)]]) ).
cnf(refute_0_234,plain,
( multiply(X_12,multiply(inverse(X_12),multiply(inverse(multiply(X_12,inverse(X_12))),X_26))) != multiply(inverse(multiply(X_12,inverse(X_12))),X_26)
| X_26 = multiply(inverse(multiply(X_12,inverse(X_12))),X_26) ),
inference(resolve,[$cnf( $equal(multiply(X_12,multiply(inverse(X_12),multiply(inverse(multiply(X_12,inverse(X_12))),X_26))),X_26) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
X_26 = multiply(inverse(multiply(X_12,inverse(X_12))),X_26),
inference(resolve,[$cnf( $equal(multiply(X_12,multiply(inverse(X_12),multiply(inverse(multiply(X_12,inverse(X_12))),X_26))),multiply(inverse(multiply(X_12,inverse(X_12))),X_26)) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
multiply(X_4,inverse(X_4)) = multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))),
inference(subst,[],[refute_0_235:[bind(X_12,$fot(X_27)),bind(X_26,$fot(multiply(X_4,inverse(X_4))))]]) ).
cnf(refute_0_237,plain,
( multiply(X_4,inverse(X_4)) != multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4)))
| multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))) = multiply(X_4,inverse(X_4)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(X_4,inverse(X_4)))),bind(Y,$fot(multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4)))))]]) ).
cnf(refute_0_238,plain,
multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))) = multiply(X_4,inverse(X_4)),
inference(resolve,[$cnf( $equal(multiply(X_4,inverse(X_4)),multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4)))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
( multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))) != multiply(X_4,inverse(X_4))
| multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))) != inverse(multiply(X_27,inverse(X_27)))
| multiply(X_4,inverse(X_4)) = inverse(multiply(X_27,inverse(X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))),inverse(multiply(X_27,inverse(X_27)))) ),[0],$fot(multiply(X_4,inverse(X_4)))]]) ).
cnf(refute_0_240,plain,
( multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))) != inverse(multiply(X_27,inverse(X_27)))
| multiply(X_4,inverse(X_4)) = inverse(multiply(X_27,inverse(X_27))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))),multiply(X_4,inverse(X_4))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
multiply(X_4,inverse(X_4)) = inverse(multiply(X_27,inverse(X_27))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_27,inverse(X_27))),multiply(X_4,inverse(X_4))),inverse(multiply(X_27,inverse(X_27)))) )],[refute_0_230,refute_0_240]) ).
cnf(refute_0_242,plain,
( multiply(X_4,inverse(X_4)) != inverse(multiply(X_27,inverse(X_27)))
| inverse(multiply(X_27,inverse(X_27))) = multiply(X_4,inverse(X_4)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(X_4,inverse(X_4)))),bind(Y,$fot(inverse(multiply(X_27,inverse(X_27)))))]]) ).
cnf(refute_0_243,plain,
inverse(multiply(X_27,inverse(X_27))) = multiply(X_4,inverse(X_4)),
inference(resolve,[$cnf( $equal(multiply(X_4,inverse(X_4)),inverse(multiply(X_27,inverse(X_27)))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
inverse(multiply(X_4,inverse(X_4))) = multiply(X_4,inverse(X_4)),
inference(subst,[],[refute_0_243:[bind(X_27,$fot(X_4))]]) ).
cnf(refute_0_245,plain,
( multiply(X_29,inverse(X_29)) != inverse(multiply(X_4,inverse(X_4)))
| inverse(multiply(X_4,inverse(X_4))) != multiply(X_4,inverse(X_4))
| multiply(X_29,inverse(X_29)) = multiply(X_4,inverse(X_4)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_29,inverse(X_29)),multiply(X_4,inverse(X_4))) ),[0],$fot(inverse(multiply(X_4,inverse(X_4))))]]) ).
cnf(refute_0_246,plain,
( multiply(X_29,inverse(X_29)) != inverse(multiply(X_4,inverse(X_4)))
| multiply(X_29,inverse(X_29)) = multiply(X_4,inverse(X_4)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_4,inverse(X_4))),multiply(X_4,inverse(X_4))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(X_29,inverse(X_29)) = multiply(X_4,inverse(X_4)),
inference(resolve,[$cnf( $equal(multiply(X_29,inverse(X_29)),inverse(multiply(X_4,inverse(X_4)))) )],[refute_0_229,refute_0_246]) ).
cnf(refute_0_248,plain,
multiply(a1,inverse(a1)) = multiply(X_32,inverse(X_32)),
inference(subst,[],[refute_0_247:[bind(X_29,$fot(a1)),bind(X_4,$fot(X_32))]]) ).
cnf(refute_0_249,plain,
( multiply(X_32,inverse(X_32)) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) != multiply(X_32,inverse(X_32))
| multiply(a1,inverse(a1)) = multiply(b1,inverse(b1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(X_32,inverse(X_32))) ),[1],$fot(multiply(b1,inverse(b1)))]]) ).
cnf(refute_0_250,plain,
( multiply(X_32,inverse(X_32)) != multiply(b1,inverse(b1))
| multiply(a1,inverse(a1)) = multiply(b1,inverse(b1)) ),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(X_32,inverse(X_32))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
multiply(X_32,inverse(X_32)) != multiply(b1,inverse(b1)),
inference(resolve,[$cnf( $equal(multiply(a1,inverse(a1)),multiply(b1,inverse(b1))) )],[refute_0_250,refute_0_90]) ).
cnf(refute_0_252,plain,
( multiply(X_29,inverse(X_29)) != multiply(X_4,inverse(X_4))
| multiply(X_4,inverse(X_4)) = multiply(X_29,inverse(X_29)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(X_29,inverse(X_29)))),bind(Y,$fot(multiply(X_4,inverse(X_4))))]]) ).
cnf(refute_0_253,plain,
multiply(X_4,inverse(X_4)) = multiply(X_29,inverse(X_29)),
inference(resolve,[$cnf( $equal(multiply(X_29,inverse(X_29)),multiply(X_4,inverse(X_4))) )],[refute_0_247,refute_0_252]) ).
cnf(refute_0_254,plain,
multiply(X_32,inverse(X_32)) = multiply(b1,inverse(b1)),
inference(subst,[],[refute_0_253:[bind(X_29,$fot(b1)),bind(X_4,$fot(X_32))]]) ).
cnf(refute_0_255,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(X_32,inverse(X_32)),multiply(b1,inverse(b1))) )],[refute_0_254,refute_0_251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP517-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 21:37:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.52
%------------------------------------------------------------------------------